Available Projects
Welcome to the Project Catalog for National Science Foundation (NSF) Mathematical Sciences Graduate Internship (MSGI) Program. Students submitting an application to the NSF MSGI program are required to select at least one, but no more than three projects.
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Project Title  Citizenship Required  Reference Code  Posted Date  Posted Datetime  Hosting Site  Internship Location  Disciplines  Description 

No  NISTDOGAN1  12/8/2022  1670475600000  National Institute of Standards and Technology (NIST)  Gaithersburg, MD  Applied Mathematics, Geometry, Probability and Statistics 
Project Description:The goal of this project is to develop tools for image and data analysis, by leveraging scientific computing and machine learning algorithms. Various research opportunities exist in the following topics: Disciplines: Applied Mathematics, Geometry, and Probability and Statistics Hosting Site:National Institute of Standards and Technology (NIST) Internship location: Gaithersburg, MD Mentor:
Internship Coordinator:


No  LLNLCHOI1  12/8/2022  1670475600000  Lawrence Livermore National Laboratory (LLNL)  Livermore, CA  Analysis, Applied Mathematics, Mathematics (General), Operations Research, Probability and Statistics 
Project Description:We are developing efficient physicsinformed neural network reduced order models (NNROMs) to accelerate complicated, largescale physical simulations. Currently, our physicsinformed NNROM can reduce the dimensionality of an advectiondominated 2D Burgers simulation to a latent space of 5 with a relative error with respect to the corresponding full order model of less than 1% and accelerate the full order model simulation by a factor of 10, which cannot be achieved by any machinelearning black box approach. We plan to extend the ROM to largescale problems, such as advectiondominated hydrodynamics, transport problems, turbulence, and Rayleigh–Taylor instability simulations. We expect our NNROM will achieve a higher speedup when it is applied to largerscale problems. A student participating in our research project will first learn what our NNROM can do for the 2D Burgers simulation and then extend it to a new physics problem by training an autoencoder neural network and implementing NNROM on more complex problems, such as shockmoving hydrodynamics, porecollapse dynamics, particle transport, plasma physics, and earthquake inverse problems. Depending on the results, we will write a journal paper together. The experience of implementing NNROM will let the student to apply it to other problems, including those that may be part of the student’s Masters or PhD thesis. Disciplines: Analysis, Applied Mathematics, Mathematics (General), Operations Research, and Probability and Statistics Hosting Site:Lawrence Livermore National Laboratory (LLNL) Internship location: Livermore, CA Mentor:
Internship Coordinator:


No  LANLDesantis1  12/8/2022  1670475600000  Los Alamos National Laboratory (LANL)  Los Alamos, NM  Analysis, Applied Mathematics, Logic or Foundations of Mathematics, Mathematics (General), Probability and Statistics 
Project Description:The focus of this project is the application and development of trustworthy machine learning (ML) systems to study the Atlantic Meridional Overturning Circulation (AMOC), an important component of Earth's ocean circulation. The AMOC is responsible for the transport of water across the Atlantic through differences in temperature and salt content, and is responsible for the climate we experience today. Climate models suggest that AMOC will weaken over the 21st century, altering the Earth's climate system. Disciplines: Analysis, Applied Mathematics, Logic or Foundations of Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  ANLMadireddy1  12/8/2022  1670475600000  Argonne National Laboratory (ANL)  Lemont, IL  Applied Mathematics, Probability and Statistics 
Project Description:Probabilistic Machine Learning is a natural choice for modeling scientific data owing to their systematic approach to reason about the prediction uncertainty and encourage model robustness. Historically, the adoption of probabilistic modeling approaches has been limited by the scalability of the inference approaches. Recent advances in ensemble learning, sparse Bayesian deep learning with modern probabilistic programming languages and their informationtheoretic connections has enabled probabilistic inference on largescale models. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLZhang1  12/8/2022  1670475600000  Argonne National Laboratory (ANL)  Lemont, IL  Applied Mathematics 
Project Description:Adaptive time stepping is a key technique for improving the computational efficiency of numerical solutions of differential equations. Traditional methods determine the next step size based on a local error estimate at the current time step and do not account for longterm optimality over the entire simulation. In this project, we will develop a novel method that exploits the structures of the problem and formulates the task as a reinforcement learning problem. We will explore the application of various policy architectures with different generality and inductive bias. We will also investigate strategies to scale the method to largescale complex dynamical systems. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL Mentor:
Internship Coordinator:


No  LLNLGuenther1  12/8/2022  1670475600000  Lawrence Livermore National Laboratory (LLNL)  Livermore, CA  Applied Mathematics 
Project Description:To enable practically useful quantum computing, this project aims to improve the error rate of logical gates on superconducting quantum devices by augmenting the quantum dynamical model with a datadriven approach to identify and incorporate latent dynamics. Quantum dynamics are often modeled by Schrödinger’s and Liouvillevon Neumann’s equations, that evolve the quantum state and density matrix according to a Hamiltonian model. The Universal Differential Equations approach augments this model by a neural network that is trained from device data to account for unknown dynamics, such as drift in system parameters, control line losses, cross talk, and environmental interactions. The trained augmented model will provide a more accurate simulation of the quantum dynamics in superconducting quantum devices, that will then be used within our optimal control software stack to design control strategies that achieve higher fidelity of quantum gates on noisy quantum hardware. The trained neural network will further be analyzed using symbolic regression to provide a mathematical description and understanding of the latent quantum dynamics. Disciplines: Applied Mathematics Hosting Site:Lawrence Livermore National Laboratory (LLNL) Internship location: Livermore, CA Mentors:
Internship Coordinator:


Yes  NETLWright1  12/8/2022  1670475600000  National Energy Technology Laboratory (NETL)  Applied Mathematics, Mathematics (General), Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:This summer project provides opportunities for summer interns to collaborate on data analysis from distributed optical fiber sensors and other sensors using multivariate analysis or AI/ML techniques to enable multiparameter sensing or identify structural features of systems under test. For example, large datasets can be obtained from realtime distributed optical fiber acoustic sensors, advanced data analytics will accelerate data processing and identify or classify different features (e.g. defects, corrosion, leaks) of the pipe or tube under test. This technology is applicable for structural health monitoring of energy infrastructure such as natural gas pipelines, wellbores, or nuclear reactors. Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:National Energy Technology Laboratory (NETL) Mentors:
Internship Coordinator:


Yes  NETLWeber1  12/8/2022  1670475600000  National Energy Technology Laboratory (NETL)  Applied Mathematics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Particle Tracking Velocimetry (PTV) is a common measurement technique used to interrogate particle flow in granular and multiphase (primarily gassolid) flows. PTV is conceptually very simple: individual particles are identified in a given frame and then linked (tracked) from frame to frame to measure their displacement and, hence, velocity. However, in practice, both steps can be quite challenging and computationally expensive. Recently, the capability to use a neural network approach (specifically YOLOv7) for particle detection has been implemented NETL’s open source PTV code Tracker. Preliminary evidence suggests that YOLO detection may be at least as accurate as simpleblob detection of individual particles in dense particleladen flows with a significant computational savings. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:National Energy Technology Laboratory (NETL) Mentor:
Internship Coordinator:


No  ORNLPasini1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN 
Project Description:Deep learning models are gaining wide interest within the scientific computing community due to their role in detecting and explaining underlying correlations between the different physical quantities that characterize a complex system. In particular, graph convolutional neural networks (GCNNs) have been showing great potential to describe the behavior of materials at microscopic scale by accurately capturing and describing interatomic interactions.
The predictive performance of GCNNs is very sensitive to the choice of the architecture for multiple hyperparameters such as the number of neurons per layers, the number of convolutional layers, the number of fully connected layers, the radius cutoff, the activation functions at each hidden layer, the learning rate and the batch size to iteratively train the model. All these hyperparameters strongly impact the predictions made by a GCNN model and GCNNs with different hyperparameter setups may produce vastly different predictions for the same input data. In particular, some choice of hyperparameters may lead to a poor predictive performance due to numerical artifacts such as overfitting or underfitting. Therefore, identifying an appropriate setting of hyperparameters is essential to ensure the model’s accuracy and generalizability. Identifying a hyperparameter configuration that would make GCNN both accurate and robust requires performing an exhaustive search over a high dimensional space, which, in general, is computationally expensive. High performance computing can be leveraged to alleviate the computational burden of hyperparameter optimization (HPO) by concurrently exploring several hyperparameter configurations with distributed computing resources. In this work, we will develop and implement scalable HPO algorithms for GCNNs. We will use the RayTune library for hyperparameter tuning and we will integrate the RayTune functionalities into an existing implementation of GCNNs. The performance of the HPO procedure will be assessed in terms of: (1) scalability attained by distributing the hyperparameter search over hundreds of compute nodes on supercomputers at the Oak Ridge Leadership Computing Facility (OLCF) and (2) validation accuracy of the trained GCNN model on abinitio density functional theory (DFT) data generated by material scientists at Oak Ridge National Laboratory (ORNL) that describe the functional behavior of solid solution alloys at atomic scale. The expected outcome is a scalable HPO framework integrated with the existing implementation of the GCNN model that attains linear scaling up to 100 compute nodes on the OLCF supercomputer Summit, with an improved accuracy by a factor of 10x with respect to existing GCNN models trained on the DFT data. Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


No  ORNLTRAN1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Analysis, Applied Mathematics 
Project Description:The goal of this project is to develop and analyze an optimization framework for minimizing multimodal loss functions with a large number of local optima. Since the local gradient points to the direction of the steepest slope in an infinitesimal neighborhood, an optimizer guided by the local gradient is often trapped in a local minimum. To address this issue, we develop a nonlocal gradient using Gaussian smoothing technique to skip small local minima by capturing major structures of the loss’s landscape in blackbox optimization. In this project, the student will gain experience on highdimensional optimization, learn how to derive, analyze and test different adaptive techniques to accelerate our optimization algorithm with nonlocal gradient. They will be encouraged to apply the method to a diverse set of scientific and machine learning problems that necessitate optimization of noisy and complicated functions. Disciplines: Analysis, and Applied Mathematics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentors:
Internship Coordinator:


No  ORNLMoriano1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Analysis, Applied Mathematics, Mathematics (General), Operations Research, Probability and Statistics 
Project Description:Many complex systems are usually represented by networks (e.g., communication networks, power grids, social networks, etc.). Among the most commonly studied properties of networks, the community structure is key to understand their structure and function because communities represent important functional modules in networked systems. Thus, there is an increasing interest in understanding the limits of the robustness of the community structure. This is because maintaining the functionality of networked systems is heavily dependent on preserving their community representation. Given ORNL's expertise on modeling and simulation of complex systems using leadership computing facilities, this project will take advance of modern data science, machine learning, and network science techniques, or any technique of interest to the participant that could help on better understand the limits of the robustness of the community structure of complex interconnected systems. This project will allow the participant to actively drive an exciting facet of an ongoing research project at ORNL, and have their contributions directly integrated into the Computer Science and Mathematics Division research priorities. A successful student has prior experience with data science techniques, machine learning, and network science, but is not expected to have deep experience with programming. Notably, prior projects at ORNL by interns in this team have led to papers published at major computer science/applied mathematics conferences. Based on the findings here, we will also seek to publish a paper in a major data science venue with the participant as the lead author. Disciplines: Analysis, Applied Mathematics, Mathematics (General), Operations Research, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


Yes  LANLMONROE1*  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM  Algebra or Number Theory, Applied Mathematics, Mathematics (General) 
U.S. Citizenship is a requirement for this internship Project Description:Inexact computing is any kind of computing where one does not get the exact numerical result. This can include approximate and probabilistic computation. This will be applicable to a wide range of postMoore’s era architectures, because of reliability issues, potential power savings, increased resilience to faults and architectural changes. Some combination of general processors, general inexact processors and specialized inexact processors will have to be developed, as well as efficient ways to use them. LANL has an ongoing exploration of inexact computing techniques, with projects in a range of areas of inexact computing. We are exploring reduced precision, machine learning approaches, advanced error detection and correction methods and other techniques, and applying these to problems in computational mathematics, basic mathematics and computer science. The specific project we address with an NSFMSGI intern will depend on intern interests and background. Our current projects include:
>We encourage publication of results. LANL has a wide range of compute systems, and students will have access to cuttingedge devices of interest. If onsite activity is possible at the time of the internship, the intern will sit in the Ultrascale Systems Research Center, which supports a wide range of research in computer science. We are happy to discuss the project in more detail upon request. For further information, please contact: Dr. Laura Monroe (lmonroe@lanl.gov). Disciplines: Algebra or Number Theory, Applied Mathematics, and Mathematics (General) Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  ORNLPasini2  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:Scientific computing has recently shed light on the effectiveness of artificial neural network (ANN) models as surrogates for complex multiscale physicsbased models in order to accelerate expensive scientific calculations without compromising their accuracy.However, to this day ANN outputs are still challenging to interpret and explain in terms that are immediately mappable back to the application domain. This lack of interpretability and explainability limits the deployment of ANN models in several research applications where extracting meaningful causeeffect relationships is essential. Towards building an explainable and interpretable ANN model, one important task to complete is monitoring with sections of the ANN architecture are activated or deactivated when a new specific set of inputoutput features is processed during the learning phase. This project aims to build an interpretable ANN model for simple learning tasks such as image recognition. Through a series of experiments in which a small ANN is taught to distinguish simple geometric shapes, we will gain an understanding of the discernment procedure learned by the network as a first step towards a deeper understanding of why these structures perform well as classifiers. The participant will learn about artificial neural networks, become familiar with software packages for training these networks, and explore the fundamental structure of ANNs with the goal of elucidating how they perform their tasks. Learning objectives:
Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentors:


No  ORNLTRAN2  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Computational Mathematics 
Project Description:We will conduct fundamental research on AI and Scientific Machine Learning (SciML) for extracting interpretable information from scientific data, inferring physical laws, and steering experiments toward scientific discovery. US Department of Energy's (DOE) scientific user facilities generate a deluge of dynamic experimental data at a rapid velocity on a daily basis. This project will focus on developing novel SciML methods that can be practically used to analyze massive scientific data. Our research objectives include: (1) develop reliable and efficient feature extraction methods for both highfrequency highresolution dynamic data and highdimensional functional data collected at DOE's user facilities; (2) develop mathematical foundations for neural networkbased dynamics discovery models and stochastic backpropagation algorithms for training the neural network models; (3) develop goaloriented data assimilation methods for dynamic experimental design, i.e., optimally designing and steering a series of experiments to achieve a desired scientific goal. The outcome of this project will not only to demonstrate how the proposed SciML algorithms and mathematical analysis can help address current, urgent needs for advanced data analytics at DOE's user facilities, but also to show the critical role of the proposed research in establishing selfdriving user facilities in the near future. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentors:


No  ORNLMoriano2  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Probability and Statistics 
Project Description:The promise of ubiquitous connectivity brought by emerging technologies (i.e., 5G/6G) will enable interconnected systems (e.g., Internet of things (IoT), smart cities, science facilities, among others) to work faster and more efficiently. However, ubiquitous connectivity comes at the expense of augmenting the attack surface and the risk of suffering from advanced cyber attacks. Detection and adaptation to such threats requires collecting, filtering, and analyzing event data of heterogeneous scale, speed, and modality. The design and deployment of trustworthy methods and algorithms that can accommodate volume, velocity, and variety is key for near realtime detection, continuous adaptation, and quick attack recovery is challenging and requires innovation. Thus, to address the emerging challenges of next generation of cyber threats, the goal of this project is to design and implement a suite of algorithms that allow near realtime detection of adaptive cyber attacks in interconnected systems.Given ORNL's expertise in acquisition and processing of data for enterprise and cyber physical domains using leadership computing facilities along with leading researchers in applied mathematics, computer science, statistics, and cybersecurity, this project will take advance of modern data science, machine learning, or any technique of interest to the participant (including but not limited to multivariate time series analysis, clustering, graph mining, etc.) that could help to design and implement algorithms that will enable quick detection, adaptation, and recovery from sophisticated and evolving cyberattacks targeting modern interconnected systems. Learning objectives for the applicant include: (1) Develop a basic understanding of novel cyberattacks affecting modern interconnected systems; (2) Design and development of datadriven models for detecting advanced cyberattacks; (3) Validate the efficacy of developed algorithms using empirical data and compare its performance against stateoftheart classical approaches. This project will allow the participant to actively drive an exciting facet of an ongoing research project at ORNL, and have their contributions directly integrated into the Computer Science and Mathematics Division research priorities. A successful participant has prior experience with data science techniques and machine learning but is not expected to have deep experience with programming. Notably, prior projects at ORNL by NSF MSGI interns in this team led to papers published at major applied mathematics/data science venues. Based on the findings here, we will also seek to publish a paper in a major applied mathematics/data science venue with the participant as the lead author. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


No  ANLZhang2  12/12/2022  1670821200000  Argonne National Laboratory (ANL)  Lemont, IL or Virtual  Applied Mathematics, Computational Mathematics 
Project Description:Identifying hidden dynamics is one of the oldest problems in science. Recently, new methods that combine conventional time integrators and deep learning have emerged to address complex continuous dynamical systems and use observed data efficiently. This project aims to study consistency and convergence properties in timeintegrator based neuralnetworks such as neural ODEs. Based on the insights gained from the study, we will explore how to better embed neural networks into time integrators and how to reduce the discretization errors in the numerical approximation to the continuous models.The prospective student will obtain handson experience in deep learning, analysis of time integrators, and dynamical system modeling. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL or Virtual Mentor:


No  FNALKurkcuoglu2  12/12/2022  1670821200000  Fermi National Accelerator Laboratory (FNAL)  Batavia, IL or Virtual  Algebra or Number Theory, Applied Mathematics, Computational Mathematics 
Project Description:An alternative to the wellknown qubitbased quantum computing platform is the bosonic quantum computation. However, the error correction for the bosonic quantum computation is a relatively new area of study. Bosonic error models and error stabilizer codes are dramatically different than their qubitbased counterparts. We will theoretically explore the bosonic stabilizer codes and their computational complexity for decoding the quantum stabilizer code. For decoding the bosonic stabilizer codes, machine learning algorithms will also be considered. Time permitting, actual implementation of the stabilizer codes in bosonic quantum computation and their performance might be considered. For this position, prior knowledge about quantum computation and stabilizer codes are not needed, however an exposure could be helpful. The candidate should be a grad student in math, electronical engineering, computer science or a related field.Strong background in linear algebra and programming is preferred, although the candidate is free to choose a programming language to work on. This project will be conducted in a team setting under the primary direction of researchers at Fermilab. The entire project may be done remotely, with frequent video meetings and the use of other communication tools (e.g., Slack, email). Disciplines: Algebra or Number Theory, Applied Mathematics, and Computational Mathematics Hosting Site:Fermi National Accelerator Laboratory (FNAL) Internship location: Batavia, IL or Virtual Mentors:


Yes  LANLMONROE2  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM or Virtual  Algebra or Number Theory, Combinatorics, Geometry 
U.S. Citizenship is a requirement for this internship Project Description:This project is a search for graph topologies that are suited to the new generation of emerging routers coming from industry. This is true crossdisciplinary work between mathematics and computer science, like that that took place in the 40s and 50s. We are addressing the degreediameter problem of graph theory and applying our results to postexascale computer networks, in collaboration with a major vendor.We have already used this approach to create PolarFly, a new family of diameter2 topologies. This topology supports radixes suited to the new highradix routers, aymptotically approaches the maximum number of nodes for the radix and diameter, exploits mathematical symmetries for modularity, and outperforms other networks in terms of scalability, cost and performance. This has resulted in a paper presented in a toptier conference, another submitted to a toptier conference, and a patent application. Diameter 2 is suited to smaller systems, but not exascale. In this work, we hope to introduce further mathematical advances to develop new diameter3 topologies, which would position such networks to address exascale and postexascale systems. We want to survey the wide area of graph theory to find graphs well suited to postexascale networks. We hope that advances will result in further publications, and more importantly, we hope to influence a mathematical approach to network design over the next decade or more. Background: Photonic technology has improved greatly over the last few years. Recent advances in copackaged optics make it possible to drive multiple terabytes per second out of a single socket. In addition, the photonic ecosystem is advancing rapidly, making copackaged optics an excellent candidate for upcoming generations of postexascale systems. The primary advantage of this technology is performance – speedoflight latency for short and longreach communication, combined with an exponential growth of communication bandwidth. An important aspect of integrated optics is the level of connectivity: it is now possible to drive 3264 optical connections out of a single highradix device. This level of connectivity is a real advancement, but current network designs do not fully exploit this opportunity. Without advances in system design, these systems will not reach their potential. Such advances are especially needed in network topology and system design, which are still open areas of research. In particular, this calls upon successful approaches to the degreediameter problem, a classical but very open problem in graph theory. We propose to use mathematical graph theory and projective geometry to design very large and compact interconnection networks that are optimally tailored to this emerging technology. Disciplines: Algebra or Number Theory, Combinatorics, and Geometry Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM or Virtual Mentor:


Yes  NETLMUSSER1  12/12/2022  1670821200000  National Energy Technology Laboratory (NETL)  Applied Mathematics, Computational Mathematics 
U.S. Citizenship is a requirement for this internship Project Description:Fast and accurate multiphase computational fluid dynamics (CFD) models are needed to support the scale up and commercialization of innovative carbon capture and directair capture devices. This project aims to generate highfidelity datadriven models to improve the accuracy of lowerfidelity models. Specifically, the recently developed exascalecapable CFDDEM (discrete element method) code MFIXExa is being used to create a particleladen flow database spanning a range of solids concentration and Archimedes number. MFIXExa’s Particle in Cell (PIC) is the lowerfidelity model targeted in this work. Unlike CFDDEM which models individual particles interacting through collisions, PIC models statistical representations of a collection of particles called parcels that interact through a solids stress model. The goal of this project is to use the CFDDEM data to construct a machine learningbased solids stress model that improves PIC predictions. Though beyond the scope work, the MLenhanced PIC model may be considered for inclusion in the MFIXExa, providing credible datadriven prediction at a significantly reduced computational cost. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:National Energy Technology Laboratory (NETL) Mentors:
Internship Coordinator:


No  ORNLPasini3  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:Description: This project aims at exploring and implementing new mathematical solutions to improve the predictive performance of message passing operations in graph layers used by GNN models in material science applications.Graph neural networks (GNNs) naturally interpret the atomic structure of materials as graphs, where atoms are interpreted as graph nodes and interatomic bonds are interpreted as graph edges. The accuracy of the GNN model strongly depends on the mathematical operations performed in transferring information across adjacent nodes in the graph representation of the atomic structure, also called message passing operations. Student Requirements: The student is required to have preliminary fundamental knowledge about deep learning concepts and familiarity with PyTorch. Competence using PyTorchGeometric is desirable, but not required. Student Responsibilities: The student is expected to implement and test new message passing algorithms and test the performance of such algorithms opensource material science datasets. The student will collabrate with ORNL staff to validate the impact of the work performed to solve relevant scientific problems address but the material science community at ORNL. Learning objectives:
Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentors:
Internship Coordinator:


No  ORNLLim1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN 
Project Description:Neural dynamics models such as spiking neural networks display flexible computational capacities in mammalian brains. Extracting computations from spiking neural networks requires identifying useful abstractions of the combinatorically explosive number of possible activity patterns. We would like to describe the causality patterns in neural dynamics using graphical models, for decomposing neuronal activities and measuring their similarities.Neural activity is shaped by network connectivity. By combining activity with connectivity in a single mathematical structure, we extract computational "threads" the emerge from synaptic plasticity in simulated spiking networks. These threads are extended and overlap in time. We introduce a method to identify recurrences of causallysimilar threads. In this project, we would like to perform functional analysis (also known as graph kernels) on graphrepresented decomposed neural dynamics, from which we can compare similarities between the causality patterns in neuron activities in a computationally efficient manner. Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


Yes  USACEMAYO1  01/5/2023  1672894800000  U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC)  Hanover, NH  Applied Mathematics, Biometrics and Biostatistics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:The goal of this funded basic research project is to test the following hypothesis. If deep learning (DL) models can be trained to associate surface data (e.g., LIDAR forest canopy data) with specific undersurface/understory structural parameters (e.g., stem density, positions), then: (H1) their hidden networks encode these correlations; and (H2) tracking how these networks process information will identify specific surface features (input data subsets) that are uniquely predictive of undersurface parameters. There are a number of opportunities for graduate students to participate in this project, from helping to develop neural network models derived from imperfect datasets, to applying the principles and metrics of information theory (e.g., mutual information, transfer entropy) to help us formulate a more concrete understanding of how information flows throughs the hidden layers of neural network models. Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC) Internship location: Hanover, NH Mentors:
Internship Coordinator:


No  NISTZwolak1  12/12/2022  1670821200000  National Institute of Standards and Technology (NIST)  Gaithersburg, MD or Virtual  Probability and Statistics 
Project Description:Given the current importance and widespread application of machine learning (ML), there has been a growing need for explainable ML to support applications that require human users to understand why a model provides the output it does. Since correlation is not the same as causal relations, a solid model understanding and the transparency of predictions are often necessary when it comes to making decisions, especially in medicine or finance. Models such as decision trees, linear regression, or classification rules – socalled glassbox models – have the benefit that the models themselves are relatively easy for humans to interpret. However, these models tend to underperform stateoftheart models, such as deep neural networks or random forests – the socalled blackbox models. Moreover, glassbox models are not always easily adaptable to image data. At the same time, the more complex relationship between inputs and outputs in the blackbox models makes them difficult to interpret, limiting their application in areas where humanuser understanding of the model output is strictly necessary. While there have been numerous efforts on combining black and glassbox methods to aid explainable ML in computer vision, the problem of blackbox model interpretability remains largely unresolved. Disciplines: Probability and Statistics Hosting Site:National Institute of Standards and Technology (NIST) Internship location: Gaithersburg, MD or Virtual Mentors:


No  LANLBhattarai1  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM or Virtual  Applied Mathematics, Probability and Statistics 
Project Description:Deep Neural Networks (DNNs) have demonstrated breakthrough performance in solving various complex problems across several fields. The vulnerability of supervised DNNs to small (unperceivable to humans) input perturbations, known as adversarial attacks, prevent their use in critical decisionmaking and security scenarios, e.g., where human life could be lost. It is equally important and a largely unexplored topic to examine the robustness of extracted latent features in unsupervised learning applications, which are vital for blind source separation, anomaly detection, dimension reduction, etc. This project's scope is to: 1) Evaluate the adversarial robustness of unsupervised frameworks and 2) Explore the representation ability of these unsupervised models and Generative Adversarial Networks (GAN)like architectures for constructing defense tools against adversarial attacks.The student will develop a novel GANlike architecture called UNSUPGAN to harden the DNN models against previously unseen adversarial attacks. UNSUPGAN will determine whether a previously unseen adversarial attack is applied to the data. UNSUPGAN will open a new direction for adversarial noise defense, which the existing defense models are vulnerable against. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM or Virtual Mentors:
Internship Coordinator:


No  LBNLLiu1  12/12/2022  1670821200000  Lawrence Berkeley National Laboratory (LBNL)  Berkeley, CA  Applied Mathematics, Computational Mathematics 
Project Description:Butterfly decompositions are numerical linear algebra tools wellsuited to represent many highly oscillatory transforms and integrals encountered in e.g., solving wave equations, signal processing and Fourier transforms. Although they can be used to efficiently compress the operators in low dimensions, their application to high dimensional problems, e.g., 6D transforms and 3D wave equations, yields large prefactors or nonoptimal asymptotic complexities. The project aims at investigating the tensor form, instead of the matrix form, of butterfly decompositions to address these highdimensional challenges. The student will get familiarity with butterfly algorithms, tensor computation with both matlab and HPC implementations. With the guidance of a mentor, the student will conduct preliminary complexity analysis and numerical experiments to validate the benefits of tensorized butterfly representations.Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Lawrence Berkeley National Laboratory (LBNL) Internship location: Berkeley, CA Mentor:


Yes  USACEBarker1  12/12/2022  1670821200000  U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL)  Fairbanks, AK  Analysis, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:For watersheds and soil systems in the arctic, there is an intense seasonality. Seasonal transitions significantly impact watershed geochemistry and impact the soil thermal regime. In the spring, there is a large increase in water flow as a result of snowpack melting. During summer, the thawing of the active layer extends and the majority of surface water flow is derived from rainfall and the little bit of baseflow that may exist. In the late fall, pore waters are pushed deeper in the soil column and the surface of the soil is frozen, but the active layer is at its’ deepest yearly extent. This time of the year is often not studied because access gets tricky in the winter and everything is assumed to be frozen, but in reality, reactions do still continue to occur and as you move into winter there is a portion of the active layer that remains thawed while the surface is frozen. As deepening of the active layer into previously frozen material is expected with climate change there remains a limited understanding of subsurface geochemistry and elemental behavior during this shoulder season. We have robust datasets that include thousands of thaw depth measurements tied to soil chemistry and soil temperature data where specific correlations, relationships, and key variables need to be determined and may help to elucidate the complicated soil thermal regime in the arctic.The intern will assist with statistical and multivariate analysis, including but not limited to principal component analysis, linear combination fitting, and variance analyses. The intern will join a wellrounded group of scientists in various disciplines like geochemistry, engineering, geophysics, and sensor development, join office meetings, present results, and may assist with field work in Alaska, if interested. The intern should have experience with algorithm development, MATLAB, multivariate statistical analysis, as well as an interest in geochemistry, geology, and/or chemistry. Disciplines: Analysis, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL) Internship location: Fairbanks, AK Mentors:
Internship Coordinator:


No  NRELEgan1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Applied Mathematics, Computational Mathematics 
Project Description:Wake interactions, when the momentum deficit and coherent turbulence downstream of one turbine impact the operation of another, are the greatest single source of power losses in a wind plant. While large eddy simulations can accurately model wake interaction, highfidelity modeling is too expensive for practical engineering applications. Specifically, enabling realtime control for wind plant power production and producing the next generation of wind plant design tools will require fast evaluation of wind turbine wake dynamics under large ranges of potential operating conditions.This issue motivates the construction of reliable reduced order models that capture the dynamics and physics of the high fidelity models at a much lower computational cost. As part of this project the student will apply novel AI architectures and sophisticated sampling techniques to the development of modular, adaptable reduced order models of windturbine wake interactions. This opportunity will set the stage for future integration with experimental wind turbine data from NREL site projects, and more general dynamic control scheme optimization. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:
Internship Coordinator:


No  LANLPetersen1  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM or Virtual  Applied Mathematics, Computational Mathematics 
Project Description:Climate research at the U.S. Department of Energy (DOE) includes the development of ocean, seaice, atmosphere, landvegetation and landice models. The ability to run highresolution global simulations efficiently on the world’s largest computers is a priority for the DOE. The proposed project is to assist in the development of a new ocean model component for the Energy Exascale Earth System Model (E3SM), which will be designed to run at scale on new exascale computers, and take full advantage of graphical processing units (GPU)accelerated hardware. Applications of E3SM include the simulation of 20thcentury and future climate scenarios, as well as special configurations where model resolution is enhanced in regions of particular interest, like coastal areas, the Arctic, or below Antarctic ice shelves (Petersen et al. 2019).Global highresolution modeling remains very computationally expensive. The primary feature of E3SM is the ability to use variableresolution unstructured meshes to focus high spatial resolution where it is needed. Spherical Centroidal Voronoi Tesselations (SCVTs) are used to cover the sphere based on an arbitrary density of generator points that can be specified to focus spatial resolution where needed. In order to solve the primitive equations on the sphere for the ocean model, appropriate discrete forms of these equations must be defined on SCVT meshes. It is also desirable for these discrete forms to preserve properties of the continuous equations, a quality known as mimetic discretization. For SCVT meshes, members of our team have developed discretizations that conserve energy and potential vorticity (Ringler et al. 2010). These were developed in the Model for Prediction Across ScalesOcean (MPASOcean), which was designed for CPUbased highperformance computers using MPI and OpenMP, and can scale to over 50,000 processors (Ringler et al. 2013, Petersen et al, 2015). Nextgeneration supercomputer architectures for reaching exaflop computations utilize graphical processing units (GPUs) as accelerators, each of which are designed to operate on many thousands of threads of execution. We are creating a new ocean model, named Omega, to be able to run on these new architectures. This includes exploring a number of new approaches to take advantage of this extreme parallelism, including new programming models and new algorithms. During the summer research internship, the student would participate in the design, code development, and verification of numerical methods for the new ocean model. This includes performance measurement and optimization for GPU hardware on DOE exascale computers. The student will learn skills in realworld applications of computational fluid dynamics and high performance computing. Applied Mathematics topics include solving partial differential equations for reference solutions; documenting the stability and accuracy of spatial operators and timestepping methods; and verifying these in the newlydesigned code. A specific application is the design of a new momentum diffusion operator on SCVTs that is consistent with the analytic form near the gridscale. This is important to dissipate energy at small scales, and is challenging for unstructured meshes. Petersen, M. R. et al. (2019). https://doi.org/10.1029/2018MS001373 Petersen, M.R., et al. (2015) http://dx.doi.org/10.1016/j.ocemod.2014.12.004. Ringler, T.,et al (2013) https://doi.org/10.1016/j.ocemod.2013.04.010 Ringler et al. (2010) doi:10.1016/j.jcp.2009.12.007 Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM or Virtual Mentor:


No  ORNLBurkovska1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN or Virtual  Analysis, Applied Mathematics, Computational Mathematics 
Project Description:This project aims to investigate efficient approximation schemes for nonlocal phasefield models based on nonlocal AllenCahn or CahnHilliard type equations. Phasefield models play an important role in many applications, such as, e.g., solidification dynamics in additive manufacturing. It has been already demonstrated that nonlocal variants of those models can provide a flexible framework that can better describe physical processes that admit discontinuities, sharp interfaces and lack of regularity in a solution. In this project the intern student will develop appropriate approximation schemes (e.g., based on discontinuous Galerkin finite elements, FFT or machine learning kernel evaluation techniques), and conduct the corresponding analysis and implementation.Disciplines: Analysis, Applied Mathematics, and Computational Mathematics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN or Virtual Mentor:


Yes  USACECegan1  12/12/2022  1670821200000  U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC)  Analysis, Computational Mathematics, Probability and Statistics, Topology 
U.S. Citizenship is a requirement for this internship Project Description:The cooccurrence of two or more major disturbances is defined as a compounding threat. Because these disturbances can interact with one another, a compounding threat poses potentially more serious challenges than if the individual disturbances occurred in isolation. Examples include situations such as hurricaneforce winds causing power outages, while storm surge flooding damages hospital backup generators, which in turn affects full ICUs coping with a pandemic surge that includes patients on electricallypowered ventilators. Decision makers involved in emergency response and recovery need decision support that addresses the impacts of compounding threats during planning and preparation, impact assessment, coordination, and intervention. In this project, we will leverage the latest research in modeling resilience in transportation networks and develop new mathematically and statistically rigorous algorithms for dataintensive scientific machine learning applications to assess network resiliency in the face of multiple disturbances.Disciplines: Analysis, Computational Mathematics, Probability and Statistics, and Topology Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC) Mentor:


No  ORNLLaiu1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Computational Mathematics 
Project Description:This project aims to provide a learning scheme for building stable and structurepreserving dynamical surrogate models that benefit both simulations and data interpretation. With the advances in machine learning and artificial intelligence, datadriven surrogate models have become an important tool for design and simulation in many scientific areas, in which the underlying physical systems are either unknown or computationally expensive. Most existing approaches focus on learning accurate surrogate models from data, while stability of the learned surrogate is often ignored. Without stability, the error of surrogate models can grow exponentially over time, especially in unseen system states. This project will focus on the development and analysis of a universal learning scheme that can guarantee the stability of learned surrogate models of different forms, including classical basisexpansionbased surrogate models and blackbox neural networks with various architectures.Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentors:


Yes  NISTGrey1  12/12/2022  1670821200000  National Institute of Standards and Technology (NIST)  Boulder, CO  Applied Mathematics, Geometry, Probability and Statistics, Topology 
U.S. Citizenship is a requirement for this internship Project Description:We'll be assisting with perspectives and interpretations applying differential geometry and competitive linear and nonlinear modelbased dimension reductions to explore applications ranging from computer vision to materials science and next generation communications technology. Example applications include: statistics of material microstructures, general image classification, and highdimensional bicriteria optimization for next generation wireless spectrum sharing. The position requires a candidate curious to explore some or all of the following topics in applied mathematics: (i) novel lowdimensional visualization and approximation methods, (ii) abstractions of computational differential geometry over matrix manifolds, (iii) linear and nonlinear modelparameter dimension reduction, and (iv) infinite dimensional extensions of spaces of discrete shapes. Disciplines: Applied Mathematics, Geometry, Probability and Statistics, and Topology Hosting Site:National Institute of Standards and Technology (NIST) Internship location: Boulder, CO Mentor:
Internship Coordinator:


No  ANLLarson1  12/12/2022  1670821200000  Argonne National Laboratory (ANL)  Lemont, IL or Virtual  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:Optimizing stochastic objective functions can be considerably more difficult than solving deterministic optimization problems. This is due to the fact that repeated calls to the objective with a fixed set of input variables produces outputs that vary. This project seeks to develop, analyze, and implement numerical methods for optimizing objectives that are stochastic in nature and that are relatively expensive to evaluate. Application problems include stochastic oracles that appear in quantum across the quantum information sciences. We are especially interested in using modelbased methods to identify highquality local optima for such problems. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL or Virtual Mentor:


Yes  USACEReichenbach1  12/12/2022  1670821200000  U.S. Army Corps of Engineers, Geospatial Research Laboratory  Alexandria, VA  Applied Mathematics 
U.S. Citizenship is a requirement for this internship Project Description:The intern will investigate methods to identify roads in highresolution remote sensing imagery, using appropriate machine learning methods such as neural networks and randomforest classifiers. This opportunity will help members of the Enhanced Terrain Processing team to better understand the challenges and feasibility of using machine learning models to extract roads from imagery. Most geographic data sources identify roads as vectors, but pixellevel classifiers require raster data, so successfully converting road vectors to raster data is a nontrivial problem. For this project, the intern will have the opportunity to investigate stateoftheart methods for dataconversion and machine learning. Additionally, with guidance from a mentor, they will generate appropriate training data, train their fitted models, and compare accuracy metrics on a test dataset. Time permitting, the intern may also investigate the effect of including multispectral bands on model accuracy. A successful intern should have an interest in geospatial applications of machine learning; knowledge of GIS software (QGIS, ArcGIS) and Python programming is helpful, but not required.Disciplines: Applied Mathematics Hosting Site:U.S. Army Corps of Engineers, Geospatial Research Laboratory Internship location: Alexandria, VA Mentors:
Internship Coordinator:


No  LANLCasleton1  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM or Virtual  Applied Mathematics, Probability and Statistics 
Project Description:State of the art machine learning approaches, including deep learning models designed for domains such as natural language processing and computer vision, are often evaluated with a metric on a benchmark data set, i.e., a test set of data that the ML models did not have access to during training and validation stages. The use of a standardized benchmark data set allows practitioners to assess how well their ML model performs on unseen data compared to other ML models, yielding a ranking of competing alternatives. However, rarely does such a comparison take into account variability or uncertainty in the performance metric being used to assess each ML model. Constructing an error bar for the evaluation metric, such as a confidence interval, allows one to determine whether a particular ML model significantly outperforms a competing ML model or whether better performance could be attributed to sampling variability, for example.The goal of this project will be to investigate sound methodology for computing uncertainties for ML evaluation metrics starting with familiar choices such as mean squared error for the prediction of continuous outcomes and classification accuracy for the prediction of discrete outcomes. Salient challenges are that test data are not always sampled in a way that is representative of all data the ML model could see in practice, test sample sizes are not always large, and mean error is not always used for an evaluation metric. To address these challenges, the student will investigate resampling methods, such as the bootstrap, for estimating the variance of test error. A major student contribution of the project will be to produce best practices for generating uncertainty estimates of ML evaluation metrics used to compare distinct models. For specificity, the student will develop these best practices for quantifying uncertainties in evaluation metrics with ML tasks such as image and scene classification. We will use public satellite and aerial imagery benchmarks with known performance baselines. The benchmarks will consist of datasets of overhead imagery representing various scene classes (e.g., thermal power stations, harbors, residential areas, etc.), with variation in image spatial resolution, viewpoint, illumination, occlusion, and background. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM or Virtual Mentor:


No  ORNLArchibald1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN or Virtual  Analysis, Applied Mathematics, Probability and Statistics 
Project Description:This project will use recent advancements in mathematics to develop unique streaming compression methods for computational and experimental data at the US Department of Energy (DOE). We will exploit the fact that scientific data follow some underlying physical principle (e.g., experimental data) or some known, possibly complex model (e.g., computational simulation data). Such underlying properties allow for compression methods with unique designs capable of orders of magnitude reductions with prescribed accuracy in goaloriented lossy and lossless compression. The key challenges that face data compression at DOE include: (1) the incorporation of known scientific information into compression; (2) the massive volume of data produced requiring methods that act on streaming data near the point of generation; (3) the uncertainty quantification for data with noise, error, or missing pieces; and (4) the ability to effectively use new computing architecture, both centralized and at the edge. With guidance from a mentor, the student will help design compression methods to provide scientific users with a range of options to balance computational cost and compression rate and accuracy. If users can spend more computational cost in either compression or decompression, then greater accuracy and compression are possible.Disciplines: Analysis, Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN or Virtual Mentor:


No  NRELSharma1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:Wind farm flow modeling is one of the primary challenges in wind farm design due to the complex unsteady nature of interactions between turbine and wakes from other turbines and neighboring wind farms as well as the atmosphere. A wind farm wake prediction model should be sufficiently accurate and computationally cheaperto be employed for tasks like wind farm layout optimization and wind farm controls. This project will focus on combining different fidelities of wind farm simulation data using machine learning. The student will collaborate with NREL staff to strategically generate simulation datasets and use them for the development and application of cuttingedge multifidelity machine learning techniques for dataenhanced modeling of wind farm flow. Skills required include proficiency in machine learning techniques (Deep learning, reinforcement learning, Gaussian techniques, etc.), and related software packages. Previous experience in assisting with multifidelity data sets would be beneficial. Additionally, proficiency in Python is needed to be able to successfully navigate this project. Familiarity with wind farm physics, although a plus, is not required. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO Mentors:
Internship Coordinator:


No  LANLNegre1  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM  Applied Mathematics, Combinatorics, Computational Mathematics, Geometry 
Project Description:Crystal shape prediction methods are essential for understanding material properties. Attempts to predict crystal shapes date back to the mid19th century, when crystal shapes were predicted from pure geometric arguments[1,2]. The incorporation of surface energies increased the accuracy of such predictions. However, computing power is still a limiting factor for atomistic simulations[3]. The awakening of practical quantum computing using Quantum Annealers (QA) led scientists to "rethink" alternative ways of solving optimization problems. Many optimization problems were revisited using a quadratic binary optimization (QUBO) formulation to fit the architecture of annealers[4]. In this project we will build an Ising model for crystal growth and reformulate the optimization problem as QUBO. The calculations will be carried out in both classical and quantum annealers. We will use Monte Carlo (MC) simulations as a benchmark for comparison.The student will develop many different skills such as complex geometry calculations involved in crystal structure research, optimization, Monte Carlo (MC) simulation, HPC techniques, and quantum computing. The student will also learn to develop a scientific code using best software practices, including version control method and regression testing. We will use this code to predict the optimal shapes of crystals structures. Some previous experience with HPC, python and Fortran programming is recommended, as well as a fair geometry and linear algebra math background. 1 Docherty, R., Clydesdale, G., Roberts, K. J. & Bennema, P. Application of BravaisFriedelDonnayHarker, attachment energy and Ising models to predicting and understanding the morphology of molecular crystals. J. Phys. D. Appl. Phys. 24, 89–99 (1991) 2 Tran, Richard, Zihan Xu, Balachandran Radhakrishnan, Donald Winston, Wenhao Sun, Kristin A. Persson, and Shyue Ping Ong. 2016. “Surface Energies of Elemental Crystals.” Scientific Data 3 (September): 160080. 3 ZepedaRuiz, Luis A., and George H. Gilmer. 2015. “10  Monte Carlo Simulations of Crystal Growth.” In Handbook of Crystal Growth (Second Edition), edited by Tatau Nishinaga, 445–75. Boston: Elsevier. 4Terry, Jason P., Prosper D. Akrobotu, Christian F. A. Negre, and Susan M. Mniszewski. 2020. “Quantum Isomer Search.” PloS One 15 (1): e0226787. Disciplines: Applied Mathematics, Combinatorics, Computational Mathematics, and Geometry Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM Mentors:


No  LANLSkurikhin1  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM or Virtual  Applied Mathematics, Probability and Statistics 
Project Description:Labeled data are expensive and timeconsuming to obtain in many realworld domains, while unlabeled data is abundant. However, knowledge of structure, e.g., number of clusters, from unlabeled data sets is difficult to know a priori. Bayesian nonparametric (BNP) modeling, e.g., the Dirichlet Process Mixture (DPM) model, offers a powerful approach to infer an appropriate number of latent patterns, i.e., clusters, directly from unlabeled data, and as more data are acquired, the model can grow and incorporate new patterns. One of main issues hindering broader acceptance of BNP learning is computational tractability. Recently developed (in 2022) is a deepclustering split/merge framework, DeepDPM, which opens the door for an effective and computationally efficient approach to learn the number of clusters directly from unlabeled data. The student will focus on the adaptation of DeepDPM to remote sensing data, in particular to solve the task of unsupervised image/scene clustering in large aerial and/or satellite image datasets. It will involve development of appropriate feature extraction, examining contrastive learning techniques and evaluation of DeepDPM based on various metrics. The project will explore public aerial and satellite imagery benchmark datasets regularly used by the machine learning and remote sensing communities. The benchmarks provide ground truth for evaluating DeepDPM, with class annotations and have baselines available to compare DeepDPM against. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM or Virtual Mentors:


Yes  USACEStrelzoff1  12/12/2022  1670821200000  U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC)  Analysis, Computational Mathematics 
U.S. Citizenship is a requirement for this internship Project Description:The Defense Advanced Research Projects Agency (DARPA) has identified a need to anticipateand mitigate potential supply chain shocks, that may affect the acquisition and procurement of required assets. These shocks result from complex combinations of physical locations of required assets, transportations grids and capabilities, real time cyber command, control and defense and necessary financial support for contractual arrangement of supply chain orchestration. DARPA’s proposed RSDN program will support the development of novel technologies and their incorporation into a DARPA Supply Chain Analysis workbench. The overall goal of the Resilient SupplyandDemand Network (RSDN) program effort is to develop methodology for supplyanddemand network resilience analytics across complex interconnected networks, approaches for stress testing and identification of cascading failure pathways. The US Army Engineer Research and Development Center (ERDC) is acting in support of these objectives as Government Evaluator; ERDC will: (i) host the tools developed by contractors and ensuring their interoperability, (ii) operate the tools with data that may not be publicly available or sanitize the data so it can be used by contractors, (iii). Use metrics provided by DARPA and develop additional metrics to assess programlevel effectiveness and achievement of DARPA goals during the performance period and at the conclusion of various program milestones. This project will allow the participant to actively engage not only with ERDC scientist, but also with an ongoing research collaboration with DARPA on a high profile Department of Defense supply chain problem. A successful student has prior experience with data science techniques and machine learning; Cloudbased experience would be also be useful. Multiple publications are planned based on the findings here, including the opportunity for the participant to publish as the lead author. Disciplines: Analysis, and Computational Mathematics Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC) Mentors:
Internship Coordinator:


No  LANLSalvesen1  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM  Applied Mathematics 
Project Description:A black hole is often surrounded by a swirling reservoir of gas, called an accretion disk, whose geometry can be thin (like a pancake) or thick (like a donut). Some observations suggest that thin disks are strongly magnetized, but conventional theory suggests that only thick disks can accumulate a substantial magnetic field. The goal of this project is to revisit whether magnetic field can accumulate in a thin disk, by scrutinizing the assumptions built into the classic model.A vertical magnetic field threading the disk evolves in time according to the induction equation, which describes the competition between the field’s inward advection and outward diffusion. Under several assumptions, the classic model derives one equation for two unknowns, and adopts a questionable closure relation. Our preliminary work identified a more physical closure relation, which allows thin disks to efficiently advect magnetic field. If robust, this would be a transformative result that resolves inconsistencies between observations and theory of black hole accretion disks. The main goal of this project is to achieve our conjectured closure relation (or something like it) through a more formal and selfconsistent mathematical analysis. This will require scrutinizing the classic semianalytic model, which suffers from inconsistencies and whose description in the literature lacks sufficient clarity to be easily reproducible. The learning objectives include: reproducing the work from a classic paper, which may require reaching out to its author directly; assessing the physical justifications for various simplifying assumptions; developing proficiency in vector calculus; numerically solving an integrodifferential equation; experimenting with different choices of boundary conditions; and collaborating with an astronomer (yours truly) who has limited formal mathematical training. Disciplines: Applied Mathematics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  LBNLGuerrero1  12/12/2022  1670821200000  Lawrence Berkeley National Laboratory (LBNL)  Berkeley, CA or Virtual  Algebra or Number Theory, Applied Mathematics 
Project Description:Race logic is a peculiar timebased computing paradigm where information is encoded in the timing of events, i.e., the positive edge of digital signals in CMOS, or the appearance of a singleflux quanta pulse in superconductors. Computation is performed by manipulating delays between racing events. Note that an event arrives at time = t with respect to a temporal origin at time = 0. In the absence of an event, the temporal value is infinity.Some examples of accelerating dynamic programming algorithms and graph problems have been demonstrated using the racelogic paradigm. One of the early examples of this is the NeedlemanWunsch DNA alignment algorithm's efficient adaptation to race logic. However, there is no methodology to take a graph problem or dynamic programming algorithm and generate racelogic hardware. The purpose of this internship is to use the theoretical basis of tropical algebra, race logic, and GraphBLAS (Graph Basic Linear Algebra Subprograms) to produce a universal methodology to map any graph problem to a racelogicbased accelerator. Disciplines: Algebra or Number Theory, and Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory (LBNL) Internship location: Berkeley, CA or Virtual Mentors:
Internship Coordinator:


No  NRELMueller1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Applied Mathematics, Computational Mathematics 
Project Description:Optimization problems with computationally expensive black box objective functions arise in many application areas relevant to the National Renewable Energy Lab (NREL), including autonomous synthesis, biofuel development, and grid optimization. Often, objective functions are available at different levels of fidelity with lower fidelity models computing faster and being less accurate than higher fidelity models. These lower fidelity models, while computationally nontrivial, can aid the optimization of the highfidelity simulations.
Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentors:
Internship Coordinator:


No  LANLSweeney1  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM  Applied Mathematics, Computational Mathematics 
Project Description:The Computational Earth Science (EES16) group at Los Alamos National Laboratory (LANL) is looking for a highly motivated student with a strong background in computational and applied mathematics to join us as we develop and implement interface tracking algorithms for subsurface flow and transport codes. Mixing of multifluid mixtures in fractured subsurface rocks is prevalent in a variety of important applications of concern to LANL. To quantitatively understand mixing in these fracture networks, we must understand the interfacial dynamics and how fluidfluid interfaces develop, stretch, and deform as they are advected through the domain. To that end, we can quantify the degree or efficiency of chaotic mixing by calculation of Lyapunov exponents for different flow fields and fracture networks, which would be of critical importance for problems such as hydrogen storage, CO2 sequestration, and spent fuel waste disposal. Our efforts will be focused on implementing existing algorithms, such as volume of fluid and level set methods, but will be complicated by the unstructured and fractional dimension nature of our meshes. Consequently, several fundamental contributions will result from the successful completion of this project that will be of interest to both the computational mathematics and earth science communities. The student will collaborate directly with LANL scientists and there will be opportunities to interact and work with other students and group members. With guidance from a mentor, the student will also be encouraged to participate in the LANL student symposium and prepare their duties for publication.No prior knowledge of subsurface flow and transport is required. A successful applicant should have some background in code development, computational physics, or fluid dynamics. Programming experience in Python and any of C, C++, or Fortran is required. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  NRELDong1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Analysis, Applied Mathematics, Computational Mathematics, Topology 
Project Description:This project aims to improve existing power system stability analysis methods by leveraging stateoftheart mathematical tools in dynamical system, machine learning, and other areas. Conventional power systems are dominated by synchronous generators (SGs), and their stability analysis has been well handled by classical and modern control theories. However, the stability analysis of modern power systems is challenged by the newly integrated inverterbased resources (IBRs) with different dynamical behaviors. For example, unlike SGs with secondlevel dynamics, the IBRs introduce wideband dynamics ranging from milliseconds to seconds to minutes. Also, the IBR models are typically not available or shared in blackbox forms to protect vendor’s intellectual property (IP), and this hinders the modelbased stability analysis. Moreover, since IBRs have various heterogenous controller designs, we should evaluate the interoperability of SGs and different IBRs.In this project, the intern would collabrate closely with NREL researchers, combine the mathematical theories and realworld power system problems, and push the boundaries of modern power system stability analysis. Specifically, we could propose new methods to consider multitimescale dynamics in modern power systems, develop advanced system identification methods or measurementbased tools to address the blackbox IBR model challenge, and/or offer new methods to analyze the interaction between different dynamical components. Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Topology Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentors:
Internship Coordinator:


No  NRELMartin1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Applied Mathematics, Computational Mathematics 
Project Description:Fluids with complex equations of state (EoSs) are critical to decarbonizing both the energy system and manufacturing. NREL’s High Performance Algorithms and Complex Fluids (HPACF) Group is particularly interested in supercritical carbon dioxide and its use in highefficiency energy systems that enable carbon separation, utilization, and storage (CCUS). NREL is currently implementing these equations of state in a broad range of computational fluid dynamics (CFD) solvers, ranging from commercial codes to the highfidelity opensource Pele combustion solver being developed as an application for exascale computing. Previous NREL work has shown that both the computational time required, and the physical results, are extremely sensitive to which of multiple possible equations of state are selected for calculating fluid properties. (Rasmussen, et al, J. of Supercritical Fluids, 171 105141, 2021)This project will build on previous work to study the impact of EoS choice on the stability, solution time, and physical accuracy of the solutions obtained from CFD solvers for realistic energy systems simulations. The student will build fundamental physical understanding of the behavior of complex fluids, tying the equation of state used to determine the density to other key properties such as internal energy. Research will be tied to actual energy system applications. This is a relatively open field with significant opportunities for future work and publication. The intern can expect to build skills in the following areas: 1) Highperformance computing. 2) Numerical analysis including computational fluid dynamics. 3) Energy systems modeling. Interns in HPACF generally present at the Rocky Mountain Fluids Symposium, held every August in Boulder, and are encouraged to present elsewhere. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:
Internship Coordinator:


Yes  NRELGlaws1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Applied Mathematics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Perovskite solar cells have rapidly reached high power conversion efficiencies, but their stability and degradation still must be addressed to reach commercialization. Despite substantial multimodal data obtained through robust imaging and screening processes, we lack the analysis tools to understand the stability of perovskite solar cells across a statistically significant range of device constructions and defect types. This project will explore the use of machine learning (ML) and other statistical modeling tools to facilitate rapid multimodal analysis of perovskite solar cell electrical and image data.Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:
Internship Coordinator:


No  LANLSkurikhin2  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM or Virtual  Probability and Statistics 
Project Description:Recently introduced foundation models (FMs) open new opportunities for generalization of deep models across different applied domains. FMs are largescale deep learning neural network models (e.g., transformers) that are trained on very large unlabeled datasets and are expected to be tuned to a wide range of downstream tasks with relatively little additional taskspecific training. They have already made a huge impact in natural language processing and have also been applied to electrooptical (EO, e.g., RGBcolor) image data interpretation. However, most FMs are currently restricted to two or three modalities such as text, images, video, and/or depth. The development of multispectral FMs that operate on images with several to hundreds of spectral bands is both challenging and crucial for many problem domains. This project will focus on the testing and evaluation of recently developed transformer model(s) for the analysis of multispectral and hyperspectral imagery (MSI/HSI) for downstream tasks such as landuse/landcover classification which are essential for the characterization of objects and activities of interest. The project will use public MSI/HSI benchmark datasets used by machine learning and MSI/HSI communities. In addition to evaluation of existing transformer models on MSI/HSI data, the project will extend and evaluate selfsupervised tasks proposed for RGB images (such as SimCLR or MoCo) to MSI/HSI data.Disciplines: Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM or Virtual Mentors:


No  NRELMaack1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Applied Mathematics, Computational Mathematics, Geometry 
Project Description:Traditionally, the power systems models have relied on a linearized version of power flow physics in optimization problems resulting in a convex optimization problem. However, increasing usage of renewable generation (e.g. wind and solar power) requires higher fidelity power flow models. The full fidelity steadystate power flow equations (called AC power flow) are nonlinear and nonconvex. While the resulting optimization problem is difficult to solve and poses a significant computational bottle neck. However, it can be shown that the power flow equations form a smooth manifold (cleverly called the power flow manifold). After restricting to this manifold, the remaining optimization problem is relatively straightforward. By solving the optimization directly on the power flow manifold, we hope to remove the computational bottle neck created by high fidelity power flow equations.This project will involve developing prototype algorithms and software (preferably in Julia) to test out constrained manifold optimization techniques (which, to date, has been relatively unexplored). The student can expect build skills in basic steadystate power systems modeling, computational math (including highperformance computing and, if desired, GPU programming), basic smooth manifold theory and constrained and unconstrained optimization. Disciplines: Applied Mathematics, Computational Mathematics, and Geometry Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:
Internship Coordinator:


No  SNLTencer1  12/12/2022  1670821200000  Sandia National Laboratories (SNL)  Albuquerque, NM or Virtual  Applied Mathematics, Computational Mathematics 
Project Description:Simulating parameterized systems of transient partial differential equations is ubiquitous in science and engineering, playing an important role in fields such as engineering, ecology, and epidemiology. It is often the case that solving such systems is a computationally intensive process. For manyquery analyses such as uncertainty quantification and optimization, lowercost approximate models are need to make the analysis tractable.Projectionbased reducedorder models (pROMs) are surrogate models constructed via a combination of a priori training data and a projection process applied to governing equations. pROMs comprise a class of approximation techniques that, at their core, operate by replacing a highdimensional system with a lowdimensional system. pROMs operate in an online—offline paradigm similar to other machine learning techniques. In the offline stage, a computationally intensive process is undertaken to identify a lowdimensional trial subspace on which the system state can be well approximated. Typically, this process involves solving the original system, i.e., the fullorder model (FOM), over time for select parameter instances. In the online phase, pROMs then compute approximations to the governing equations that reside on this lowdimensional trial subspace. The results of this process is a fast approximate model that adheres to the governing equations. One challenge in constructing pROMs (and other surrogate models) is the efficient generation and processing of training data in the offline stage. For transient simulations, a large number of time instances present possible choices for snapshot selection. Unfortunately, utilizing all available data is both computationally impractical and potentially undesirable. In some cases, utilizing additional training data has been observed to degrade the performance of the resulting pROM in prediction scenarios. This project will rely on the opensource Pythonbased suite of Pressio demo applications (https://pressio.github.io/pressiodemoapps/) to explore potential sampling strategies (borrowing from information sciences e.g., maximizing local spatial variability across the parametrictemporal domain) to optimize the generalizability of pROMs. Knowledge of projectionbased modeling is not required, but knowledge of physics and statistics are highly desirable. The intern will explore sampling methodologies applied to a variety of physical applications, ranging from heat conduction to compressible flow. If successful, this opportunity would be appropriate for peerreviewed publication and would be incorporated into existing ROM workflows in use across Sandia National Laboratories. The internship will involve close collaboration with leading domain researchers and opportunities to network with other groups within the national laboratories. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Sandia National Laboratories (SNL) Internship location: Albuquerque, NM or Virtual Mentors:


No  ORNLFattebert1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN or Virtual  Computational Mathematics 
Project Description:Solving eigenvalue problems is at the core of electronic structure calculations in chemistry and materials sciences. As computer architectures change, specifically with Graphics Processing Units (GPU) accelerators, new algorithms that better exploit fine grain parallelism can help take advantage of these powerful computer resources. One aspect to take into account is also the potential speedup on can obtain using mixed/low precision floating point operations, in particular using tensor cores on NVIDIA GPUs.
Disciplines: Computational Mathematics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN or Virtual Mentor:


Yes  USACEMarchant1  12/12/2022  1670821200000  U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC)  Applied Mathematics 
U.S. Citizenship is a requirement for this internship Project Description:Airborne lidar sensors capture highresolution 3D pointcloud imagery of terrain and complex scenes. This technology enables terrain mapping, inspection of civilian infrastructure, battlefield analysis, and military operations planning. Lidar pointcloud imagery is captured as laser scans of terrain, buildings, and vegetation, which are represented by datasets of threedimensional coordinates. Image segmentation of point clouds involves subdividing the image into neighborhoods with locally similar characteristics. This processing step enables image filtering, compression, and feature classification of the point cloud.The participant will investigate methods for image segmentation of 3D pointcloud lidar imagery of terrain. The participant will gain knowledge about 3D imagery collection and applications and will apply this knowledge to the investigation of mathematical techniques for segmentation and classification of 3D point clouds. The participant will collaborate within a 3D imagery team that works to apply these techniques towards defense applications such as intelligence gathering and operations planning. Disciplines: Applied Mathematics Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC) Mentor:
Internship Coordinator:


Yes  USDAVuolo1  12/12/2022  1670821200000  USDA Animal and Plant Health Inspection Service (APHIS)  Analysis, Applied Mathematics, Computational Mathematics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:The National Animal Health Monitoring System (NAHMS) is a United States Department of Agriculture (USDA) program that performs nationallevel surveys of U.S. livestock and poultry management and health. Please check out our data products at https://www.aphis.usda.gov/nahms.Recently, NAHMS has moved away from static PDF reports to interactive Tableau dashboards for publishing study results, and we've been increasingly automating our data wrangling and data analysis processes using SAS, a SAScallable software package called SUDAAN, and other statistical software. The intern would assist with several short miniprojects themed around data automation and will regularly use SAS and SUDAAN throughout these miniprojects. The miniprojects the intern will assist with are (from most important to least important  time allowing for the later projects): (1) A printout of 95% confidence intervals is generated for every estimate in every table in a very long internal report to determine statistically significant differences among estimates. The goal for this project is to automatically identify the statistically significant differences in this report to save time having to manually read through the report. (2) As part of an upcoming Federal requirement, metadata files need to be created for NAHMS' historical datasets, which date back to the 1990s. The won't take long for each NAHMS study and will give the intern the opportunity to look through lots of past NAHMS studies and become familiar with the statistical sampling and survey designs for each study. (3) With NAHMS moving to Tableau dashboards for our data products, NAHMS has internally created advanced SAS macros to create CSV files of our data that can then be imported by Tableau. The intern would incorporate these SAS macros into existing SAS code from older NAHMS reports, especially in preparation for the upcoming NAHMS Sheep 2024 study which will feature a trends over time report of several NAHMS Sheep studies dating back to 1996. (4) The intern would create a short info sheet(s) via an analysis of recently collected data from either the NAHMS Swine 2021, NAHMS Feedlot 2021, or NAHMS Bison 2022 studies. These info sheets are targeted at a more casual or lay audience than a standard NAHMS report and are important data products for the general public. (5) Protecting the confidentiality of survey participants is a critical component of NAHMS studies. While NAHMS reports our data in aggregate, mathematical techniques exist that can crack individual respondent data from aggregate estimates in certain scenarios. To protect against this, NAHMS employs several number suppression rules to mute data output that could be tied back to an individual respondent. The number suppression process is currently semiautomated, and the intern would fully automate this process. A NAHMS mathematical statistician will mentor the intern throughout their time with us. The statistician will provide a detailed description and background as to how the intern’s projects fits into the broader NAHMS study process, review associated statistical methodology, and be readily available to answer any questions or provide assistance with SAS coding, statistics, etc. to the intern. Experience in SAS is preferred, but having some experience in other coding languages (e.g. R, Python) and a willingness to learn SAS would suffice. We are a dynamic and friendly team composed of veterinary epidemiologists and statisticians who very much enjoy working with new students and teaching new skills. We regularly have students and recent graduates working with us. Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:USDA Animal and Plant Health Inspection Service (APHIS) Mentor:


Yes  NRELWalker1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Analysis, Applied Mathematics, Foundations, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Timeseries simulation is the mainstay of energy analysis for buildings and renewable eneryg systems such as solar and wind projects. Existing computer programs employ the "steadystate" assumption that all values are constant over the duration of timestep, often one hour. This steady state assumption does a good job of estimating total energy (kWh) production but a very poor job estimating phenomenon of interest to grid integration such as inverter clipping and sellback of excess energy to a utility. NREL has developed a distribution function based on the maximum value, the minimum value and the total energy (area under the curve) for each timestep. Deployment of this distriubtion in the HOMER software has improved accuracy of these estimates by orders of magnitude, but only for one technology (solar PV). The mathematics of how to combine distribution functions for other technologies (PV+wind+battery) in combination has not been figured out yet, and combining a distribution function for solar PV with anohter distribution function for load has been worked out only on power point slides (not programed or demonstrated). So the "invention" of this internship will be to figure out how to mathematically superimpose 2 or more distribution functions to calcuate phenomenon of interest for each timestep of a timeseries simulation.Disciplines: Analysis, Applied Mathematics, Foundations, and Probability and Statistics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:


No  USDAAmatya1  12/12/2022  1670821200000  USDA Forest Service, Southern Research Station  Analysis, Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:With rapid development in computing and their ability to process big data combined with artificial intelligence theory, extreme learning machine (ELM) and adaptive neurofuzzy inference system (ANFIS) models are gaining attention in large applications. For this study, our focus is limited to computing evapotranspiration (ET, the loss of water to the atmosphere) using highresolution weather data. ET is a critical climate variable that uniquely links the water cycle (evaporation), energy cycle (latent heat flux), and carbon cycle (transpirationphotosynthesis tradeoff), each of which is described by complex processbased mathematical equations and their physical parameters. ET for an ecosystem is a complex and nonlinear process that is difficult to measure accurately and estimate/predict. This complexity can be solved by applying the machine learning techniques with different sets of hydrometeorological input variables. We hypothesize that machine learning models, including artificial neural network (ANN), support vector machine (SVM), and random forest (RF) with different optimization techniques, can predict ecosystem ET better than that by myriad of empirical models available in literature. This study will investigate the performance of different machine learning and deep learning models to predict daily ET using available meteorological and ecohydrological data. The candidate will be introduced to background of datadriven empirical statistical models and their parameters. With their background in Mathematics and Statistics, they will apply a suite of machine learning and deep learning models with optimization techniques to simulate ET values using weather data recorded at the USDA Forest Service Experimental Forest sites in coastal South Carolina, as well as Coweeta Hydrology Laboratory in upland North Carolina, both being used for longterm silvicultural research involving hydrology, ecology, soils, and vegetation. The candidate will be mentored by two hydroinformaticians and will be provided with an opportunity to make the project live and publishable and develop networking opportunities by presenting at the annual Santee Experimental Forest Research Forum and others near the end of the completion of the project. The students will also learn about field experimental studies, hydrologic processes including ET represented by mathematical equations and their prediction uncertainties, realtime monitoring technology, and managing and analyzing the Big Data sets using statistics at the host SEF study site.Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:USDA Forest Service, Southern Research Station Mentors:


Yes  NETLZhang1  12/12/2022  1670821200000  National Energy Technology Laboratory (NETL)  Algebra or Number Theory, Applied Mathematics, Computational Mathematics 
U.S. Citizenship is a requirement for this internship Project Description:Study the relationship between artificial neural network (ANN) structure and the structure of training data type. The structure of training data includes the dimension of input, and how the target parameter of the training data set correlates to the input parameters. The ANN structure can be of many options. This includes the number of hidden layers, the number of neurons in each layer, and the choice of the transfer function to each layer output. The question is if there is an optimized neural network structure for a given input type that leads to the best performance, while the best performance mainly refers to the highest prediction accuracy. The analytic approach is expected to explain the relationship from mathematics derivations. A good understanding of the ANN algorithm[Hagan, Neural Network Design, 2nd edition, eBook] will be needed. A training and validation data set with a sound physics basis will be provided for validation. Existing software is available that allows adjustment of the neural network structure, choice of input size and type, and evaluation for each of the above combinations.Disciplines: Algebra or Number Theory, Applied Mathematics, and Computational Mathematics Hosting Site:National Energy Technology Laboratory (NETL) Mentor:


No  FNALShyamsundar1  12/12/2022  1670821200000  Fermi National Accelerator Laboratory (FNAL)  Batavia, IL or Virtual  Applied Mathematics, Combinatorics, Computational Mathematics, Probability and Statistics 
Project Description:With guidance from a mentor, this project involves designing quantuminspired classical optimization algorithms. Quantum computing is a rapidly emerging domain. Many quantum algorithms offer demonstrable improvements over their classical counterparts for computationally complex problems. Quantum Approximate Optimization Algorithm (QAOA) is a popular quantum algorithm used to solve a class of computationally difficult optimization problems called Quadratic Unconstrained Binary Optimization (QUBO).In this project we will develop a novel class of QAOAinspired classical algorithms to tackle QUBO problems. These methods will search through the probability space of allowed solutions to find highquality solutions efficiently, by morphing the original discrete optimization problem into a continuous optimization problem (over the parameters of highly parameterized probability distributions). Consequently, our methods will be able to leverage the stateoftheart techniques and technologies for continuous optimization from the field of machine learning. Students will be involved in a combination of theoretical and practical work, the latter performed using modern machine learning tools. Students are encouraged to work onsite at Fermilab. However, if desired, the entire project may be performed remotely, with periodic virtual meetings. Students will work in collaboration with researchers at the Fermi National Accelerator Laboratory (Fermilab). Fermilab is a premier national laboratory overseen by the U.S. Department of Energy, with a primary focus in the fields of particle physics and quantum information science. It is the home of several ongoing highprofile experiments and collaborations, including LBNF/DUNE, Muon g2, SQMS, and LPC. Fermilab's Tevatron was a landmark particle accelerator, where the top quark was discovered in 1995. Disciplines: Applied Mathematics, Combinatorics, Computational Mathematics, and Probability and Statistics Hosting Site:Fermi National Accelerator Laboratory (FNAL) Internship location: Batavia, IL or Virtual Mentors:
Internship Coordinator:


No  ORNLEndeve1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Analysis, Applied Mathematics, Computational Mathematics 
Project Description:The goal of this project is to design and analyze structurepreserving numerical methods for modeling particle transport in relativistic astrophysical systems. We consider a model derived from taking angular moments of the relativistic Boltzmann equation, applicable to photon and neutrino transport. Structurepreserving methods aim to capture key properties of continuum models at the discrete level (such as conservation, symmetries, asymptotic limits, and maximum principles), and often improve robustness and accuracy in longterm simulations. For the moment model, we are want to maintain bounds consistent with a nonnegative particle distribution as well as conservation properties, and we will design and analyze a method based on discontinuous Galerkin phasespace discretization. With guidance from a mentor, the student will analyze and implement numerical methods, be introduced to numerical relativity and computational astrophysics, and have the opportunity to interact with postdocs and lab staff. Disciplines: Analysis, Applied Mathematics, and Computational Mathematics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


No  LBNLNigmetov1  12/12/2022  1670821200000  Lawrence Berkeley National Laboratory (LBNL)  Berkeley, CA or Virtual  Applied Mathematics, Computational Mathematics, Topology 
Project Description:The goal of the project is to implement an algorithm to perform topological optimization on functions with certain conservation constraints. The main ingredient will be the algorithm proposed in prepint arXiv:2203.16748, but there are details that require thinking through.Experiments will model the following problem. We are given some scalar function f that comes from experiments. E.g., f is the density of matter in a domain that contains a complex molecule. This function is noisy and we need to modify it so that it better reflects the true structure of the molecule. If we know how the 'mean shape' of this class of molecules looks like, we can add a topological constraint that will drive the modification process in this direction (we want the 'shape' of f to resemble the mean shape). This is the algorithm from the preprint. However, in this case it will be beneficial to add one more ingredient and work with socalled distancetomeasure (DTM) function, not with f directly. The intern will learn basic notions of Topological Data Analysis: persistent homology, persistence diagrams (the topological descriptor that is a formalization of what is meant by 'shape' of function), the notion of DTM and the algorithms necessary to perform the computations. Expected background: programming experience with C++ will be a strong advantage, since the project is going to be experimental, and most libraries are in this language. Familiarity with Python will also be helpful. elementary algebraic topology notions will helpful (simplicial homology). Disciplines: Applied Mathematics, Computational Mathematics, and Topology Hosting Site:Lawrence Berkeley National Laboratory (LBNL) Internship location: Berkeley, CA or Virtual Mentor:
Internship Coordinator:


No  FNALPerdue1  12/12/2022  1670821200000  Fermi National Accelerator Laboratory (FNAL)  Batavia, IL or Virtual  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:This project involves utilizing machine learning techniques for quantum optimal control. Our goal is to efficiently calibrate high fidelity quantum operations for quantum computing tasks. Quantum computing is carried out on superconducting transmon qubits by utilizing microwave pulses and we will utilize machine learning algorithms as interpolators to generate pulses for parameterized quantum operations. There are two particular challenges we face – estimating the fidelity of the quantum operation we intended to execute based on qubit measurements and updating the model in the face of noise and drifting qubit parameters. We will study what measurements can efficiently approximate the infidelity of SU(2) and SU(4) pulse realization on quantum hardware and the related error bounds. We will explore the advantages and constraints of online learning by leveraging related studies on gate fidelity estimation.Physics knowledge and quantum computing are not required for this project. Students should be comfortable with mathematical optimization problems and machine learning, and have some experience (or a willingness to learn) programming in Python or Julia. Students will collaborate with researchers at the Fermi National Accelerator Laboratory (Fermilab). The student is encouraged to participate onsite at Fermilab, but the program duties may be conducted remotely if the student has a strong preference to avoid travel. Fermilab is a premier national laboratory overseen by the U.S. Department of Energy, with a primary focus in the fields of particle physics and quantum information science. It is the home of several ongoing highprofile experiments and collaborations, including LBNF/DUNE, Muon g2, SQMS, and LPC. Fermilab's Tevatron was a landmark particle accelerator, where the top quark was discovered in 1995. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Fermi National Accelerator Laboratory (FNAL) Internship location: Batavia, IL or Virtual Mentors:


No  ANLJin1  12/12/2022  1670821200000  Argonne National Laboratory (ANL)  Lemont, IL or Virtual  Applied Mathematics, Combinatorics, Geometry, Topology 
Project Description:Attributed graphs, having side information from nodes and edges, are widely used in many fields within the DOE applications, such as neuroscience, biological discovery, power grid, and distributed computing facilities. Learning the similarities of graphs, also known as graph matching, is one of the fundamental problems in machine learning tasks with structured data. Even though the graphmatching problem has been studied in the last decades, the research on learning the similarities between attributed graphs still remains open. Moreover, methods inspired by optimal transport, such as GromovHausdorff and (Fused) GromovWasserstein distances, have shown promising results to compare not only on structures but also in attributed graphs.
Disciplines: Applied Mathematics, Combinatorics, Geometry, and Topology Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL or Virtual Mentor:
Internship Coordinator:


No  LANLSchwenk1  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM  Applied Mathematics, Probability and Statistics 
Project Description:Climatechange and large variations in land use have significantly increased the number of rare events such as largescale forest fires, major flooding, and longterm droughts in complex earth systems in recent decades. However, due to complex nonlinear interactions of the earth system giving rise to these events, prediction from deterministic models (i.e. firstprinciples) becomes highly uncertain. On the other hand, due to the lack of sufficiently large observational datasets of these extreme events, machine learning approaches can not solely solve the problem either. Therefore, a paradigm shift that considers the system’s deterministic nonlinearity within a datadriven context is warranted. Recent advances in nonlinear mathematical modeling combined with machine learning have demonstrated an ability to identify rare dynamical changes in large earth systems from noisy data (Malik 2020).The prediction of streamflow based on meteorological forcings represents an inherently nonlinear system that has been modeled as a stochastic process (e.g. ARIMA) or with datadriven approaches (eg. neuralhydrology). However, both methods struggle to capture flood flow in rare events. Recent advances in chaos theory and other nonlinear mathematical concepts have been introduced for dynamical streamflow modeling with variable success (e.g, Sivakumar, 2003). However, wide adoption of these methods for streamflow modeling in a rapidly changing climate have been slow due to uneven spatial sampling, noisy data, inherent large uncertainties in climate models, and lack of interdisciplinary research in complex systems. Recent development of a flexible framework for mapping, modeling, and monitoring the Earth’s river networks (VotE) by our group has allowed us to utilize an unprecedented scale of highquality historical streamflow measurements and river network features along with numerically simulated and observed meteorologies to develop a global generalizable model for streamflow and flood prediction. We aim to use VotE to investigate new, hybrid models that combine dynamical systems theory and machine learning that capture streamflow extremes. The selected student would collaborate closely with a team with expertise in hydrology and are not expected to understand the details of streamflow modeling. The student will ideally have some experience in applying dynamical systems theory to model and predict time series. This project will provide you with the opportunity to learn about streamflow and flooding while exploring and/or creating new techniques for interpreting models. Our VotE platform will allow you to spend more time on model building and exploration and less time on data manipulation. We prefer to use Python; take a look at the neuralhydrology Python package for a sense of the data driven models that are currently being implemented. This project ultimately hopes to provide global flooding projections under various projected climate scenarios, but we are also intent on providing a deeper understanding of the models that generate these projections. With guidance from a mentor, your participation would contribute to cuttingedge, impactful science to help anticipate and guide floodrelated management and mitigation. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


Yes  USACEBecker1  12/12/2022  1670821200000  U.S. Army Corps of Engineers, Geospatial Research Laboratory  Alexandria, VA or Virtual  Analysis, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:This research seeks is to understand how material surface metrics can be used to assess spectropolarimetric separability measured by Stokes Vectors in laboratory and aerial imagery. The research explores how aerial field spectropolarimetric measurements of manmade materials relate to laboratory measurements. The NSF intern, alongside the mentors, will explore this relationship through analysis of multiband data, from overhead imagery and collected in the laboratory, of various materials’ spectropolarimetric signatures in the visibleinfrared region of the electromagnetic spectrum. The objective is to discover the most effective mapping of subsets of these attributed signature bands to the spectral radiant energy interaction with object materials. Distinguishable signatures among materials will better inform future research in image science and object recognition.Disciplines: Analysis, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Geospatial Research Laboratory Internship location: Alexandria, VA or Virtual Mentor:


Yes  USACEPILKIEWICZ1  12/12/2022  1670821200000  U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC)  Computational Mathematics, Probability and Statistics, Topology 
U.S. Citizenship is a requirement for this internship Project Description:In many complex dynamical systems, only a limited number of the phase space variables can be directly observed. For example, in a colloid, the positions and velocities of the large colloid particles can often be tracked with time, but those of the much smaller and more numerous solvent molecules typically cannot. The usual prescription is to treat the unknown parameter space stochastically as a noisy background, constrained by the requirement that the ensemble of colloid particle configurations produced by this noise be indistinguishable from that observed over time in experiments. The problem with this approach is that it washes away any real correlations between timeseparated configurations of the system that could be leveraged to make predictions about the motion of individual colloid particles over time.Complex, highdimensional mechanical systems like colloids typically exhibit chaos, meaning that a set of similar initial configurations will evolve over time into disparate end states that appear uniformly selected from the configurational possibility space; but, analogous to a pseudorandom cryptographic engine, this seeming randomness is in actuality the consequence of a deterministic algorithm (in this case the dynamics). The unobservable state variables that control the output of this algorithm (the ones usually approximated as noise) are the analog of the cryptographic key. The objective of this project is to leverage this analogy between chaotic dynamical systems and cryptography and use the formalisms of cryptanalysis to identify hidden correlations between timeseparated configurations that can be used to distinguish the dynamics from true random behavior. Our primary interest is in using this approach to better predict the movements of animal groups, where the tracks of the organisms can be observed, but not the cognitive or metabolic processes driving their motion. Interns will have the opportunity to assist with real data generated from motiontracking experiments and use a combination of statistical and computational tools to search for functions of the measurable configurational variables that exhibit longlasting temporal correlations capable of being leveraged for dynamical predictions. Disciplines: Computational Mathematics, Probability and Statistics, and Topology Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC) Mentors:


No  ORNLBridges1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN or Virtual  Analysis, Applied Mathematics, Probability and Statistics 
Project Description:As collection and storage of data on entities and individuals becomes more frequent, rigorous methods for ensuring privacy while permitting data analytics are needed, esp. for DOE research domains that require sensitive data. Differential privacy (DP) is a field of mathematics and computer science that permits presenting necessary information from a private database to an untrusted outsider with formal (mathematical) privacy guarantees on the records in the private database. A quintessential example is an analyst (untrusted outsider) performing statistics on US Census datathis is necessary but such analytics should not admit specific knowledge of any individual represented in the data. DP is the worldwide accepted way to permit both basic statistics, and ideally advanced machine learning (ML) on private data.While there is abundant need spanning many science domains to make open source (make public) ML algorithms that are fit on private data, differentially private ML is constrained in its efficacy. Implementing DP entails leveraging randomness, that affects accuracy of the analytics to ensure privacy of records in the data. Current methods for differentially private ML entail and the accuracyprivacy tradeoff that is often untenable for use. This project requires a math mind with some Python programming experience to work on a fundamentally different approach to optimization with privacy guarantees (in particular, fitting ML to private data with DP guarantees). The project involves probability theory, information theory, basics of machine learning, and deep learning. The goal is to exhibit experiments on many datasets to fleshout and test the new method against the current state of the art. Further, upon successful research results, research to deploy this approach to privacy on large healthcare datasets will ensue. Disciplines: Analysis, Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN or Virtual Mentors:
Internship Coordinator:


No  NRELCui1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:The massive integration of distributed energy resources (DERs) in electric distribution systems provides great flexibility that can be harnessed to assist the bulk power system operation through effective flexibility characterization and coordination. The student will have opportunity to explore this exciting possibility through advanced modeling and algorithmic development in power systems. Specifically, the student will get exposure to the development of modeling and control methods that integrate DERs to bulk power system and explore novel computational methods to address practical concerns such as uncertainty and scalability.Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentors:
Internship Coordinator:


Yes  USACEBaines1  12/12/2022  1670821200000  U.S. Army Corps of Engineers, Geospatial Research Laboratory  Alexandria, VA  Applied Mathematics, Computational Mathematics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Remote sensing technologies such as Light Detection and Ranging (LiDAR), TimeofFlight (TOF) cameras and stereoscopic imagery can produce 3D pointclouds of imaged targets. When these technologies are used in the geospatial setting, large swaths of land are imaged, with several distinct objects such as trees, buildings, roads, power lines, etc. An automatic and robust method to label points from such pointclouds as belonging to different objects is highly desirable for several applications. To this end we wish to investigate methods of machine learning for pointcloud segmentation. These pointclouds, however, are unstructured and are not easily processed by conventional methods for regularly sampled data. The size, density and quality of the pointclouds also present a difficult challenge, as proposed methods must be computationally feasible. Nonetheless, abundant data – both labeled and unlabeled  is available for developing datadriven processing methods. We are seeking interns with programming experience (Python preferred) and some familiarity with machine learning. Intern will be tasked with exploring methods of segmentation using machine learning, through both literature review and experimentation. The Geospatial Research Laboratory is part of the United States Army Engineer Research and Development Center and is located in Alexandria, VA approximately 20 miles from Washington D.C. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Geospatial Research Laboratory Internship location: Alexandria, VA Mentors:
Internship Coordinator:


No  NISTLu1  12/12/2022  1670821200000  National Institute of Standards and Technology (NIST)  Gaithersburg, MD or Virtual  Probability and Statistics 
Project Description:In collaboration with NIST scientists in some standard developments, certain manufactured thin multilayered materials needed to be measured based on some purely 3dimage analysis programs (in MATLAB). This project is an effort to validate the imagebased measurement uncertainty analysis, and to compare the used program with existing or potential alternative image analysis methodology to be developed in the 2023 summer. The student is expected to be familiar with either MATLAB or R and will likely use R to protype any new methodology to do the comparison image analysis. The student, if not already having experience in at least one of the areas, should gain substantial experiences with time series analysis, nonparametric regression, or statistical image analysis as well as programming and working with big data sets.Disciplines: Probability and Statistics Hosting Site:National Institute of Standards and Technology (NIST) Internship location: Gaithersburg, MD or Virtual Mentor:
Internship Coordinator:


No  NRELHodge1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Applied Mathematics 
Project Description:With the increasing amounts of renewable energy being added into the power system there has been an increased focus on the inverters that interface wind and solar photovoltaic generation with the grid. Power system stability has traditionally been dominated by the synchronous generators, driven predominantly by thermal power generation, but is changing dramatically with the introduction of more renewable inverterbased generation. This change means that many of the fundamental assumptions around simulating power system dynamics may no longer hold valid.This project will examine new methods to solve the largescale systems of stiff ODEs that constitute power system dynamic simulations. Traditional methods have focused on static geographic deaggregation where portions of the system were represented in less detail than the focus areas. To better represent the changing power system we will focus on dynamic methods of deaggregation that allow for enhanced resolution in the changing areas of importance, as the topology of the system changes. Disciplines: Applied Mathematics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:
Internship Coordinator:


No  NRELReynolds1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:Essential to operating the next generation of power grids is the ability to skillfully forecast power generation from renewable energy resources. Furthermore, as penetrations of renewable energy resources continue to increase, generation forecasts become necessary tools not only for operations, but for longerterm planning of infrastructure, e.g., transmission lines and storage, as well. Using existing NREL tools for modeling wind power generation, our group has developed approaches for operating and planning power grids and placing emergency infrastructure during extreme events using multistage stochastic programming techniques. To compliment these capabilities we plan to develop, refine, and evaluate probabilistic forecasting methods used for building input scenario sets into stochastic programs. This project will involve using existing NREL wind power data sets and infrastructure models, machine learning tools, and probabilistic forecasting techniques to building uncertainty sets describing wind power generation at geographically distributed wind farms for multiple timescales. With guidance from a mentor, the intern can expect to build skills in: Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO Mentors:
Internship Coordinator:


No  LBNLJambunathan1  12/12/2022  1670821200000  Lawrence Berkeley National Laboratory (LBNL)  Berkeley, CA  Applied Mathematics, Computational Mathematics 
Project Description:Pulsars are rapidly rotating neutron stars emitting a wide spectrum of electromagnetic radiation. The highenergy emission is understood to be driven by reconnecting magnetic fields accelerating particles. However, the structure, plasma composition, sites for plasma production, and particle acceleration are still not quite well understood. Firstprinciple simulations using the particleincell method are required to obtain a clear perspective of particle acceleration in these highenergy environments. We use WarpX, an electromagnetic PIC code for our simulations of relativistic plasma in the pulsar magnetosphere, and also perform separate zoomedin simulations of relativistic magnetic reconnection to understand the fundamental processes involved in particle acceleration.We propose to extend this opportunity by incorporating radiative cooling and quantum electrodynamic pairproduction processes to selfconsistently model plasma production in pulsar magnetospheres. This research project requires coupling quantum electrodynamic processes with classical electrodynamics using the particleincell method. We will also use the meshrefinement technique to improve computational efficiency, which may require new development for multiple levels of refinement. This opportunity will enable efficient modeling of threedimensional relativistic magnetic reconnection and uncover the kinetic mechanisms driving largescale electromagnetic radiation. This project will involve close collaboration an interdisciplinary team of astrophysicists, applied mathematicians, and computational scientists in the Center for Computational Sciences and Engineering (CCSE) as well as with plasma physicists in the Accelerator Technology and Applied Physics (ATAP) group at Lawrence Berkeley National Laboratory. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Lawrence Berkeley National Laboratory (LBNL) Internship location: Berkeley, CA Mentor:
Internship Coordinator:


Yes  NRELTillman1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Applied Mathematics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:This summer project provides opportunities for summer interns to collaborate on multivariate data calibration techniques using spectroscopy data relevant to bioenergy feedstocks and biofuel process intermediates. Available datasets will include nearinfrared (NIR) reflectance spectra of dedicated bioenergy feedstock samples grown at different locations and collected using different spectrometers and NIR transflectance spectra of liquid bioenergy process intermediate streams. The goal of the project is to investigate the utility of nonlinear, Bayesian, or AI/ML techniques as alternatives to traditional linear modeling algorithms for the development of robust calibration models.Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentors:
Internship Coordinator:


No  ANLMallick1  12/12/2022  1670821200000  Argonne National Laboratory (ANL)  Lemont, IL  Analysis, Applied Mathematics 
Project Description:Spatiotemporal graph neural networks (GNNs) are widely used in many different applications, including frequency prediction on the power grid, traffic forecasting, and weather forecasting. However, as data sets grow larger and models become more complex, there is a pressing need to accelerate spatiotemporal GNNs for effective training and inference. To that end, we will investigate the graph sampling and sparsification strategies for spatiotemporal GNNs. In the sampling process, the features are aggregated by choosing a specific number of neighbors for each node or a specific number of nodes per layer. The features from numerous neighbors are aggregated as the depth of the GNNs grows. However, using neighborhood aggregation, sometimes taskirrelevant information is intermingled into nodes, resulting in poor generalization performance for the learned models. Therefore, in this project, we will concentrate on creating sparsification algorithms for spatiotemporal Graph Neural Networks, where the sparsification will be built as a learnable module. Sparsification and sampling on the sparse graph will aid in the removal of taskirrelevant edges as well as the reduction of subsequent computation and memory access.Disciplines: Analysis, and Applied Mathematics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL Mentors:


No  LANLHlavacek1  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM or Virtual  Applied Mathematics, Mathematical Biology, Probability and Statistics 
Project Description:In this project, the trainee will reanalyze data generated in massively parallel experiments aimed at defining quantitative sequencefunction relationships. Data from these experiments, which characterize gene expression level, are noisy and readouts are binned into a finite number of categories. The trainee will apply multinomial logistic regression to obtain estimates of parameters in biophysical models for transcription factor (TF) binding to DNA regulatory sequences and TFdependent promoter activity. The trainee will determine if parameter estimates obtained via this approach are consistent with estimates obtained using other methods.Learning Objectives: The student will learn about biophysical modeling of transcriptional processes and statistical inference. Fields: Gene Regulation, Biophysical Modeling, Statistical Inference Disciplines: Applied Mathematics, Mathematical Biology, and Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM or Virtual Mentor:


No  ORNLSeleson1  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN or Virtual  Applied Mathematics, Computational Mathematics 
Project Description:Recent advances in scientific machine learning (SciML) have enabled datadriven learning of operators describing the dynamics of complex systems. Most of the project's focus is on systems involving differential operators and smooth solutions, but there are many physical phenomena that are more accurately described by integral operators. Peridynamics is a nonlocal reformulation of classical continuum mechanics that is well suited for fracture and damage modeling, and the peridynamic governing equations involve integral operators and allow nonsmooth solutions. This project will focus on using methods from SciML (e.g., physicsinformed neural networks) to learn peridynamic operators from data.Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN or Virtual Mentor:


Yes  LANLLei1  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM  Applied Mathematics, Computational Mathematics 
U.S. Citizenship is a requirement for this internship Project Description:Numerical modeling of nonlinear processes plays a key role in understanding nearfield dynamics of underground explosions and the monitoring of farfield seismic data for nuclear treaty enforcement. The objective of this project is to conduct nearsource physics modeling for selected experiments conducted under U.S. Department of Energy, National Nuclear Security Administration’s Source Physics Experiments (SPEs). The goal is to gain more insight in the generation of shear waves in explosions.In this project, the simulations will be conducted using LANL’s Hybrid Optimization Software Suite (HOSS). HOSS, a 2016 R&D 100 Finalist, is a hybrid multiphysics software package integrating computational fluid dynamics (CFD) with stateoftheart combined finitediscrete element methodologies (FDEM). HOSS has been widely used to predict predict shock wave propagation, large material deformation and failure under extreme conditions (e.g. underground explosion). Alongside a mentor, the successful applicant will have an excellent opportunity to perform research on modeling of underground explosions under the supervision of LANL’s scientists; he/she will have the chance to enhance their knowledge on a wide range of fields from material modeling, numerical methods, and computational physics as well as high performance computing. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM Mentor:


No  ANLSun1  12/12/2022  1670821200000  Argonne National Laboratory (ANL)  Lemont, IL or Virtual  Applied Mathematics, Probability and Statistics 
Project Description:Complex systems in many scientific and engineering applications are modeled by partial differential equations (PDEs), e.g., nuclear reactors, traffic systems, and accelerators. Controlling these systems typically requires the iterative application of the forward solvers, prohibiting fast and efficient development of the control schemes. In this project, we will leverage the recent advances in reinforcement learning, such as Proximal Policy Optimization (PPO), and differentiable physics, such as PhiFlow (https://github.com/tumpbs/PhiFlow), to develop mathematically rigorous algorithms for effective and efficient control of PDEs.Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL or Virtual Mentor:


No  LBNLLi1  12/12/2022  1670821200000  Lawrence Berkeley National Laboratory (LBNL)  Berkeley, CA or Virtual  Computational Mathematics, Probability and Statistics 
Project Description:Randomized algorithms on networks often involve sampling nodes, edges, or subnetworks. These sampling techniques are used as subroutines (1) for the solution of fundamental problems on networks, such as connected components, the assignment problem, breadthfirst search on longdiameter graphs, or global minimum cut, and (2) for graph learning problems trained with variants of minibatch stochastic gradient. These problems are widely used in DOE applications, e.g., the use of assignment problem in optimal transport (transforming probability distributions) for cosmology, the use of connected components in genomics problems. Sketching and sparsification, which are other randomization techniques used for networks, can be used to find approximate solutions for higherlevel problems where the network problem is a subroutine. The applications for DOE include domaindecomposition solvers, iterative solvers, preconditioning for sparse systems using approximate factorization. Sampling and sketching can also be used as a coarsening technique in multilevel graph partitioning. Unfortunately, the impressive advances in the theory of randomized algorithms for networks has not been translated into practical demonstrations. Our project aims to bridge this gap between theory and practice, hence it will produce highquality software running on modern HPC hardware with demonstrations on application codes.Disciplines: Computational Mathematics, and Probability and Statistics Hosting Site:Lawrence Berkeley National Laboratory (LBNL) Internship location: Berkeley, CA or Virtual Mentor:


No  PNNLHoward1  12/12/2022  1670821200000  Pacific Northwest National Laboratory (PNNL)  Richland, WA or Virtual  Applied Mathematics 
Project Description:This project is focused on modeling the behavior of chaotic dynamical systems using physicsinformed neural networks. We will consider a novel continual learning framework for physicsinformed neural networks that will allow for modeling systems such as the Lorenz system. This opportunity will allow for fast computations of the dynamics of complex systems of equations, without the need for computationally expensive codes.Disciplines: Applied Mathematics Hosting Site:Pacific Northwest National Laboratory (PNNL) Internship location: Richland, WA or Virtual Mentors:
Internship Coordinator:


Yes  NISTZwolak2  12/12/2022  1670821200000  National Institute of Standards and Technology (NIST)  Gaithersburg, MD or Virtual  Applied Mathematics, Computational Mathematics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:While the recent advances in readout optimization are encouraging, it is not clear to what extent the optimized measurement readout determined using a particular set of gates on a given quantum dot device will hold when another set of gates is used (due to fabrication imperfections that result in a disordered potential landscape). Similarly, given the high cost of establishing the optimized readout ab initio, an active readout optimization strategy that automatically, in realtime detects and corrects for unexpected changes in the readout sensitivity (due to, e.g., drift) is highly desirable.Tuning quantum dot devices in the presence of noise is a crucial first step in realizing largescale faulttolerant quantum computation. A major impediment in this endeavor is that the current experiments tend to be optimized using manual labor and rely heavily on heuristics and experience. Using the Elzerman spin readout as a test bed, we will begin our study by investigating the robustness of the optimization protocol against various types of noise typical of quantum dot experiments. To this end, we will expand the opensource simulation of the Elzerman readout available via the Quantum Technology Toolbox to incorporate both realworld noise and, later on, the effect of the circuit used in the measurements. This will allow us to conduct a controlled study of the effusiveness and robustness of the optimization. Using tools from artificial intelligence and machine learning (e.g., natural language processing techniques and active learning), our aim is to first make the readout more robust against noise and then to develop a selfoptimizing readout protocol that will incorporate dynamic, realtime recalibration against drift. The resulting protocol will be validated using both, simulation and experimental data corrupted by noise. The overarching goal is to use the selfoptimizing readout and the extended simulation incorporating hardware effect on measurement to investigate the correlation between measurement stability and the circuit design. Here, our goal is to understand how much improvement to the readout fidelity can be achieved with a carefully designed readout circuit. To complement the analysis of the highdimensional continuous parameter space defining the circuit board we will employ the explainable boosting machines. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:National Institute of Standards and Technology (NIST) Internship location: Gaithersburg, MD or Virtual Mentor:


No  LANLBhattarai2  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM or Virtual  Analysis, Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:Matrix diagonalization is obtaining the set of eigenvalues and eigenvectors. Typical research areas requiring diagonalization include computational fluid dynamics, quantum chemistry, dimensionality reduction, and Vibrations Analysis in material design, to name a few. Common algorithms for diagonalizing matrices (e.g., Jacobi and QR) require many iterations that translate into high computational costs. This project aims to develop a faster matrix diagonalization framework that will reduce the number of iterations needed for convergence and, subsequently, minimize the overall computational cost. Deep reinforcement learning(RL) has recently found solutions to problems considered intractable/unsolvable. The examples are alpha fold for solving protein folding, alpha go zero to beat the human expert in the game go, and alpha tensor for faster multiplication of two matrices.With guidance from a mentor, the student is expected to extend the capabilities of this alphazero framework in estimating the fastest path for diagonalizing the matrix. This diagonalization process can be structured as a game where the RL agent is only informed about the diagonalization rules. Then from a series of selftraining, the agent should ultimately find the least number of steps for diagonalizing the matrix. This project also seeks the potential integration of the stateoftheart decision transformer's offline learning and the alpha zero's online learning capabilities for faster overall model training and superior test performances. Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM or Virtual Mentors:
Internship Coordinator:


No  ORNLBurkovska2  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN or Virtual  Applied Mathematics, Computational Mathematics 
Project Description:Nonlocal models with inequality constraints arise in various applications, such as, option pricing in mathematical finance, phasefield modeling in solidification or optimization tasks. A special structure of the model and nonlocal kernel may allow for the characterization of the solution in terms of a special representation formula. The aim of this project is to exploit this to design more efficient solution algorithms. With guidance from a mentor, the intern student will investigate such a representation analytically and augment it with different machine learning tools: either model order reduction, kernelbased techniques, or artificial neural networks. The student will also learn how this can be incorporated into the kernel learning tasks in scientific applications.Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN or Virtual Mentor:


No  ORNLLaiu2  12/12/2022  1670821200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:Federated learning builds global predictive models on a central server from data distributed on multiple local devices without sharing local data. Standard federated learning algorithms train models on each local devices and require communications of the model parameters between the central server and local devices. For learning complicated models with many parameters, the communication cost often becomes significant. This project aims to investigate both randomized and deterministic approaches for reducing the communication cost in federated learning algorithms. The student will learn about basic federated learning algorithms, dimensional reduction techniques, numerical analysis, and writing/presentation skills.Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


No  NRELMueller2  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Applied Mathematics, Computational Mathematics 
Project Description:Computationally expensive black box simulations and resourceintensive experiments are used in many application areas relevant to the National Renewable Energy Lab (NREL), including autonomous synthesis, biofuel development, and grid stability. When scaling up experiments and simulations such that they function in the real world, uncertainties naturally arise due to larger spatial and temporal scales that often lead to new physics.In this project, your research will focus on developing novel sampling strategies that exploit multiple fidelity information from experiments and simulations in order to efficiently and effectively quantify and reduce uncertainties. Alongside a mentor, you will devise methods that identify when uncertainties arise (e.g., due to extrapolation) and you will optimally leverage different compute resources (e.g., HPC, cloud, edge) to minimize the computational effort required for uncertainty quantification. You will collaborate closely with our application experts and deploy your developments on real world highimpact problems. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentors:
Internship Coordinator:


No  SNLBlonigan1  12/12/2022  1670821200000  Sandia National Laboratories (SNL)  Albuquerque, NM or Virtual  Applied Mathematics, Computational Mathematics 
Project Description:Simulating parameterized systems of transient partial differential equations is ubiquitous in science and engineering, playing an important role in fields such as engineering, ecology, and epidemiology. It is often the case that solving such systems is a computationally intensive process. For manyquery analyses such as uncertainty quantification and optimization, lowercost approximate models are need to make the analysis tractable. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Sandia National Laboratories (SNL) Internship location: Albuquerque, NM or Virtual Mentors:
Internship Coordinator:


Yes  USACEBaines2  12/12/2022  1670821200000  U.S. Army Corps of Engineers, Geospatial Research Laboratory  Alexandria, VA  Analysis, Applied Mathematics, Computational Mathematics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Point set registration is concerned with the estimation of transformations between source and target point sets which minimize their distance in a suitable sense. We propose research into novel methods of point set registration which utilize a broader class of transformations and l1 type distance functions which have the potential to improve registration. Point set registration is frequently used in the processing of geospatial data, as well as improving the signaltonoise ratio in Geigermode light detection and ranging (LiDAR). Registration algorithms typically aim to estimate an Affine mapping via least squares or divergence type distance functions to accomplish this, which often gives satisfactory results. However, in cases when point sets are subject to spatially varying distortion and noise  e.g. atmospheric distortion in very high altitude and satellite imagery  Affine mapping is suboptimal for registration.We are seeking interns with programming experience, and some familiarity working with big data is a plus. Alongside a mentor, the intern will be tasked with exploring novel methods of registration, including the design and analysis of distance functions over different candidate spaces. The Geospatial Research Laboratory is part of the United States Army Engineer Research and Development Center and is located in Alexandria, VA approximately 20 miles from Washington D.C. Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Geospatial Research Laboratory Internship location: Alexandria, VA Mentors:
Internship Coordinator:


No  ANLMallick2  12/12/2022  1670821200000  Argonne National Laboratory (ANL)  Lemont, IL  Analysis, Applied Mathematics 
Project Description:Convolutional Neural Networks (CNNs) offer an efficient architecture in machine learning problems where the coordinates of the underlying data representation have a regular or Euclidian structure. The ability of CNNs to learn local stationary structures and compose them to form multiscale hierarchical patterns has led to breakthroughs in image, video, and sound recognition tasks. Nevertheless, in several scientific domains, one cannot apply standard CNNs: material structure data, gene data from biological regulatory networks, traffic data from road networks are important examples of data lying on irregular or nonEuclidean domains. The irregular or nonEuclidean domains can be represented by graphs, which are universal representations of heterogeneous pairwise relationships. Representation of the data informs of directed/ undirected graph and apply convolution/ pooling is not straightforward as the convolution and pooling operators are only defined for regular grids.In this project, we will focus on neural networks that operate on graphs. We will develop domainspecific convolution and pooling operations that extract patterns from data defined on graph. We will evaluate the efficacy of the developed methods on data from transportation and supercomputers interconnect networks. Disciplines: Analysis, and Applied Mathematics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL Mentors:


No  LANLBhattarai3  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM or Virtual  Applied Mathematics, Probability and Statistics 
Project Description:Matrix and tensor factorization (TF) tools have demonstrated superior performance in the Natural processing Language domain, majorly in unsupervised tasks such as topic extraction, topic evolution, and authors ranking. Although the TFs come with the added advantage of explainability and interpretability, their performance is significantly impacted by the NLP preprocessing stages in constructing TFIDF matrices. Specifically, the NLP analysis on corpus corresponding to specific domains such as chemistry, material science, and others that involved mathematical expressions, symbols, abbreviations, and equations are eliminated with standard NLP preprocessing pipelines. To address such an issue, this project aims to augment the standard pipeline with an AIbased framework that can selectively extract the domainspecific keywords/ expressions and augment this data to the standard preprocessed data. Named Entity recognition is one of the current stateoftheart solutions for extracting such domainspecific keywords. To achieve this objective, the students will develop BERTlike Transformer based models for creating domainspecific NER under self/semisupervised settings.Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM or Virtual Mentors:
Internship Coordinator:


No  LANLBhattarai4  12/12/2022  1670821200000  Los Alamos National Laboratory (LANL)  Los Alamos, NM or Virtual  Computational Mathematics, Mathematical Biology, Probability and Statistics 
Project Description:Active transcription is initiated and assisted by transcription factors (TF) binding to DNA, a process influenced by various epigenomic mechanisms. Local biophysical properties of DNA, such as local thermodynamic stability, shape, and flexibility, are essential for TFDNA binding. Stateoftheart tools such as Deep Bind and Deep Sea utilize only the sequence information for predicting the TF binding sites. In this project, we aim to utilize the biophysical properties of the DNA along with the Sequence information to enhance the predictability of the TF binding sites. The student for this project will assist on the development of a multimodel deep learning framework that can efficiently fuse the information from sequences and biophysical characteristics for efficiently modeling the TF binding specificity.Disciplines: Computational Mathematics, Mathematical Biology, and Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM or Virtual Mentors:
Internship Coordinator:


No  NRELCole1  12/12/2022  1670821200000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Analysis 
Project Description:NREL’s Capacity Expansion and Energy Markets group has been using the Regional Energy Deployment System (ReEDS) model to perform extensive analysis of the U.S. electricity sector (see https://www.nrel.gov/analysis/reeds/publications.html). Recent enhancements to the model have increased the spatial and temporal resolution to the extent that the nationalscale version of the model can no longer be solved without turning off model features or aggregating regions or time periods. This project will assist with the ReEDS modeling team and with staff at GAMS to explore ways to solve larger versions of the model. These can include reformulating constraints, applying alternative solver techniques, parameter scaling, or model reduction. The duties completed in this project will be applied to analysis examining the decarbonization of the electricity sector. With guidance from mentor, the intern will gain significant exposure to the electricity system and electricity markets, and will assist with one of NREL’s flagship models for electricity sector analysis. Disciplines: Analysis Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentors:
Internship Coordinator:


No  ORNLTombs1  12/13/2022  1670907600000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:As collection and storage of data on entities and individuals becomes more frequent, rigorous methods for ensuring privacy while permitting data analytics are needed, esp. for DOE research domains that require sensitive data. Differential privacy (DP) is a field of mathematics and computer science that permits presenting necessary information from a private database to an untrusted outsider with formal (mathematical) privacy guarantees on the records in the private database. A quintessential example is an analyst (untrusted outsider) performing statistics on US Census datathis is necessary but such analytics should not admit specific knowledge of any individual represented in the data. DP is the worldwide accepted way to permit both basic statistics, and ideally advanced machine learning (ML) on private data.While there is abundant need spanning many science domains to make open source (make public) ML algorithms that are fit on private data, differentially private ML is constrained in its efficacy. Implementing DP entails leveraging randomness, that affects accuracy of the analytics to ensure privacy of records in the data. Current methods for differentially private ML entail and the accuracyprivacy tradeoff that is often untenable for use. This project requires a math mind with some Python programming experience to work on a fundamentally different approach to optimization with privacy guarantees (in particular, fitting ML to private data with DP guarantees). The project involves probability theory, information theory, basics of machine learning, and deep learning. The goal is to exhibit experiments on many datasets to fleshout and test the new method against the current state of the art. Further, upon successful research results, research to deploy this approach to privacy on large healthcare datasets will ensue. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentors:


No  ORNLOstrouchov1  12/13/2022  1670907600000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Probability and Statistics 
Project Description:The recent success of AI models stems in part from their ability to combine feature construction with model fitting for prediction. However, the constructed features remain hidden in complex neural models, hindering relationship discovery and requiring substantial additional computing for even limited understanding and explainability. We will explore alternative approaches to building predictive models by automating graphical construction of model features through categorical analysis of variance and polynomial models, where explainability is builtin and the computational difficulty is cast as a combinatorial model selection problem.Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


Yes  USACEBarbato1  12/13/2022  1670907600000  U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL)  Hanover, NH  Analysis, Mathematical Biology, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Soil is an incredibly complex media that has a dynamic interplay of abiotic and biotic factors whose interactions are not yet fully understood. We seek an intern to help our lab relate these groups of factors through the development and use of mathematical and numerical models as well as algorithms. Specific tasks include developing models to describe and predict the soil microbe’s response to abiotic factors such as temperature and moisture, model and predict soil microbiome activity (respiration) over time and with spatial components, and model and predict fluxes in enzymatic activity over time and with influence of abiotic variables. The intern will be part of a small but cooperative group and collaborate closely with many individuals, participate in lab meetings, showcase results, and be highly engaged. The intern may also be part of a paper currently in development and be asked to contribute to methods sections and writeups describing the models and algorithms developed.The intern should have experience with algorithm development, coding, script development, MATLAB (or something similar), multivariate statistical analysis, and stochastic modeling as well as an interest in microbiology or biology. Disciplines: Analysis, Mathematical Biology, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL) Internship location: Hanover, NH Mentors:
Internship Coordinator:


Yes  USACEBarbato2  12/13/2022  1670907600000  U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL)  Hanover, NH  Analysis, Mathematical Biology, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Permafrost soils contain complex communities of coldadapted microbes that mediate soil processes such as carbon and nitrogen cycling. Climatechange induced permafrost thaw is expected to raise microbial respiration rates, releasing into the atmosphere some of the 1,500 gigatons of carbon stored in permafrost. However, the expected rate and extent of carbon release is unknown and likely to vary between locations, depending on factors such as soil nutrient profiles and microbial community composition. Our ability to make predictions is limited by, among other things, our understanding of the ecological drivers that structure microbial communities as permafrost thaws, and how such restructuring will affect soil processes.The intern will apply ecological theory and mathematical modeling to investigate dynamics and emergent properties of the permafrost microbiome through climatechange induced thaw, collaborating closely with members of the Soil Micro research group. Results will be communicated through participation in lab meetings, and in written reports. Results will help inform broader efforts to generate predictive models relating to cold regions environments. The intern will have opportunities for mentorship and collaboration with a diverse research team that includes soils scientists, microbial ecologists, molecular biologists, and mathematical modelers. The intern should have experience with algorithm development, coding, script development, multivariate statistical analysis, and stochastic modeling as well as an interest in microbiology or biology. The intern should have an interest in applying mathematical techniques to studying ecological systems. Experience with relevant modeling approaches such as LotkaVolterra, consumerresource, or traitbased models (and their extensions) would be very helpful but not essential. Experience with software tools such as Mathematica, MATLAB may also be helpful. Disciplines: Analysis, Mathematical Biology, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL) Internship location: Hanover, NH Mentors:
Internship Coordinator:


Yes  USACEBragdon1  12/13/2022  1670907600000  U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL)  Hanover, NH or Virtual  Analysis, Applied Mathematics 
U.S. Citizenship is a requirement for this internship Project Description:The ability to detect and classify buried targets using thermal IR imagery is impacted by the environmental and meteorological conditions at the time of imaging. The modernizing environmental signature physics for target detection project seeks to leverage the environmental conditions to increase the probability of detection while minimizing false alarms. The intern will support this project by developing a physicsbased model to improve the detection and classification algorithms by incorporating the environmental conditions. The activity will require familiarity with fitting sensor data to physicsbased models using physicsinformed machine learning. The project involves assessing the soil and meteorological conditions that hamper improvised buried object detection yielding inconsistent probability of detections and high false alarm rates. The intern will join a growing cooperative group and will assist many group members, participate in laboratory meetings, and showcase results.The intern should have experience with algorithm development, machine learning, physicsinformed neural networks, and Python (e.g., pytorch, pandas, tensorflow, etc). The intern should have an interest in physics applications of mathematics. Disciplines: Analysis, and Applied Mathematics Hosting Site:U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL) Internship location: Hanover, NH or Virtual Mentors:
Internship Coordinator:


No  ORNLNutaro2  01/6/2023  1672981200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Probability and Statistics 
Project Description:The focus of this research will be to establish a theoretical basis for observed errors in the numerical simulation of radio waves propagated on a lattice with spacings in excess of the wave length. There is substantial empirical evidence that wave propagation calculations can be usefully performed on lattices with a lattice spacing much in excess of the wave length if the object of interest is power delivered to a point. In radio networks, power delivered to the antennae is of prime importance, with direction of arrival and multipath signals following closely after. Each of these quantities can be extracted from calculations performed using transmission line matrix techniques, and they exhibit errors that follow an empirically known relationship between lattice spacing and wave length. It remains to establish a theoretical basis for this relationship, and the investigation of this basis will be the focus of research for this project. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


Yes  USACEJones1  12/13/2022  1670907600000  U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL)  Hanover, NH or Virtual  Applied Mathematics, Computational Mathematics 
U.S. Citizenship is a requirement for this internship Project Description:Melanin is a blackbrown pigmented macromolecule found ubiquitously in nature and forms particularly thick layers in some species of fungi. Melanin also has unique electrical properties that may be leverageable for applications in bioelectronics. However, the interactions of electricity and cellular melanin are still poorly understood particularly in regard to the movement of current through melanin. In this research we are investigating the current propagation dynamics of melanized fungal tissue through the transmission of signal waveforms. Previous research has demonstrated that sinusoidal signals can propagate through melanized fungal tissue at a low frequency however a full characterization of the transmittable signal remains elusive. This is largely in part due to a lack of a comprehensive model of the electrical properties of the fungal tissue that could be transformed into an equivalent circuit model. Additionally, it has been proposed that finiteelement methods (FEM) may be utilized to aid in the modelling of electrical behavior and could be utilized to explain signal transmission in tissues. In this project the goal is to construct equivalent circuit models and FEM models to allow for indepth characterization of the signal transmission properties of melanized fungal tissue.The intern will be tasked with developing and validating a FEM model to aid in the characterization of signal transmission phenomena in melanized fungal tissue. The intern will assist with running signal transmission tests to gather data to aid in the construction of a FEM of the melanized fungal tissue. The intern will join a growing cooperative group and will assist many group members, participate in lab meetings, and showcase results. The intern should have experience with finiteelement methods, coding, script development, MATLAB or comparable software, modelling, electrical engineering, signal processing, as well as an interest in microbiology or biology. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL) Internship location: Hanover, NH or Virtual Mentors:
Internship Coordinator:


No  LLNLChoi2  12/16/2022  1671166800000  Lawrence Livermore National Laboratory (LLNL)  Livermore, CA  Analysis, Applied Mathematics, Mathematics (General), Operations Research, Probability and Statistics 
Project Description:We are developing efficient latentspace dynamics identification (LaSDI) algorithms to accurately accelerate parametric and complex physical systems. The reduced space dynamics after compression are often much simpler than the corresponding full space dynamics. Therefore, various models can be fit to identify the hidden dynamics in the reduced space, which in turn can be used to predict system response to new input parameter. We have successfully applied the latentspace learning algorithm, so called LaSDI, to accurately accelerate various benchmark problems, such as advection equation, Burgers’ equation, and heat conduction problems. A student participating in our research project will first learn our existing tool box, LaSDI and gLaSDI. Then he or she will further improve LaSDI by exploiting other latent space model and extend it to more complex problems, such as shockmoving hydrodynamics, porecollapse dynamics, particle transport, plasma physics, and earthquake inverse problems. Depending on the results, we will write a journal paper together. Our LaSDI is applicationagnostic, so by the end of summer, the student will be able to apply the improved LaSDI method to a broad range of physical simulations, including those that may be part of the student’s Masters or PhD thesis. Disciplines: Analysis, Applied Mathematics, Mathematics (General), Operations Research, and Probability and Statistics Hosting Site:Lawrence Livermore National Laboratory (LLNL) Internship location: Livermore, CA Mentor:
Internship Coordinator:


No  LBNLSrivastava1  12/19/2022  1671426000000  Lawrence Berkeley National Laboratory (LBNL)  Berkeley, CA  Applied Mathematics 
Project Description:Stateoftheart fluid separation technologies, such as in gas purification, water desalination and chemical processing, involve flows of fluid mixtures across nanoporous graphene and graphene oxide membranes. The fluid dynamics at the nanoscale is predominantly governed by thermal fluctuations and Knudsen effusion, where the classical NavierStokes equations are not valid, and one has to rely on a molecular description of the fluid dynamics. Our group has developed numerical methods for simulating continuum fluctuating hydrodynamics (FHD) for fluids at the nanoscale by incorporating stochastic fluxes that correctly account for intrinsic thermal fluctuations. Furthermore, we also have expertise in using Discrete Simulation Monte Carlo (DSMC) methods for a highfidelity, but computationally expensive, molecular representation of the nanoscale fluid. We propose implementing an adaptive mesh and algorithm refinement (AMAR) hybrid numerical method to simulate gas permeation across nanoporous membranes. In this method, the nanoscale fluid dynamics will have a highfidelity DSMC representation in the region near the membranes, whereas a continuum FHD will be implemented far from the membrane for enhanced computational performance. In this project, we will work together to develop and implement numerical methods to couple DSMC and continuum FHD representation of nanoscale fluid dynamics using AMAR. This project will involve collaboration with a team of applied mathematicians and computational physicists in the Center for Computational Sciences and Engineering at Lawrence Berkeley National Laboratory. Disciplines: Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory (LBNL) Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LBNLSrivastava2  12/19/2022  1671426000000  Lawrence Berkeley National Laboratory (LBNL)  Berkeley, CA  Applied Mathematics 
Project Description:A defining feature of many complex fluids is the presence of a yield stress: for an insufficiently stressed material, they behave like an elastic solid, but once the yield stress is exceeded, they flow like a fluid. This broad class of fluids encompasses various materials of industrial and natural importance such as granular fluids, polymeric fluids, gels and suspensions. Unlike Newtonian fluids, the constitutive behavior of these fluids is highly complex, and they display intriguing phenomena such shear thickening, shear thinning, jamming, shear banding and normal stress differences. Disciplines: Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory (LBNL) Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LBNLMorozov1  12/19/2022  1671426000000  Lawrence Berkeley National Laboratory (LBNL)  Berkeley, CA  Applied Mathematics, Geometry, Mathematics (General), Topology 
Project Description:A research topic that has emerged in the last few years is using features derived from topological data analysis as input to machine learning algorithms. Such methods have been shown to yield significant improvements both on the benchmark and stateoftheart scientific problems. Simultaneously they have revealed topological insights by identifying structures that correlate with a particular learning task. Recently a new approach to the multiparameter analysis has emerged in TDA. Generalizing combinatorial properties of persistence diagrams, it allows to analyze multiparameter measurements in a way that is both stable to the perturbations of the input and amenable to integration into the machine learning algorithms. The goal of this project is to investigate using the new multiparameter topological descriptors as inputs to machine learning algorithms. In particular, we want to understand which of the existing methods extend into the new setting and how the machine learning with a multiparameter descriptor compares to learning from multiple singleparameter descriptors. Disciplines: Applied Mathematics, Geometry, Mathematics (General), and Topology Hosting Site:Lawrence Berkeley National Laboratory (LBNL) Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  ornlkumar1  12/19/2022  1671426000000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Computational Mathematics, Mathematics (General), Probability and Statistics 
Project Description:Conventional analysis of neutron reflectivity data involves multilayer model building and optimization of parameters relevant to multiple layers such as thicknesses, roughness’s, and number of layers. At present, most of published data are obtained with specular reflectivity, from which the structural information perpendicular to the sample surface is obtained along the Qz component of the wave vector transfer. The conventional analysis of neutron reflectivity works for simple systems and is very time consuming, sometimes even prone to several errors in the case of complex systems involving multicomponent systems. To keep up with the flux of data and details of experimental systems, one needs a different approach to the data analysis, that includes computational workflow capable of generating theoretical models in quantitative agreement with the data. Neutron reflectivity is a depth sensitive technique which provides details of the structure in the thin films. Direct comparisons with the neutron reflectivity experiments and furthermore, ability to capture details of the reflectivity profiles using theoretical models are no ordinary feats. The aim of present study is to develop machine learning based tools to fit experimentally measured neutron reflectivity curves for thin films containing charged copolymers. These tools will be developed by building on our previous projects related to development of machine learning tools for extracting parameters from scattering length density curves, and physicsbased model building for interpreting neutron reflectivity curves. Hyperparameter optimization required to interpret experimental results will be done using neural networks, which will be trained for the systems studied by us in the past. To the best of our knowledge such an approach to the model building for multicomponent softmatter and hybrid system is unprecedented and will lead to development of tools for interpreting timedependent neutron reflectivity measurements. This opportunity will contribute to development of the next generation data handling modus operandi that will empower the user to establish the logical connections between the structures observed in the neutron experiments and the physical interactions existing among the material components. Disciplines: Applied Mathematics, Computational Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentors:


No  llnlmittal1  12/19/2022  1671426000000  Lawrence Livermore National Laboratory (LLNL)  Livermore, CA  Applied Mathematics 
Project Description:Highorder meshes are crucial for an accurate discretization of geometry and solutionfeatures in the domain of interest when solving a PDE. The goal of the ETHOS project at the Center of Applied Scientific Computing in Lawrence Livermore National Lab is to advance the theoretical understanding and practical utility of arbitrarily highorder unstructured meshes. Some notable advancements made under this project include a novel framework for highorder mesh optimization using the TargetMatrix Optimization Paradigm (TMOP), simulationdriven radaptivity for Lagrangian Hydrodynamics, and boundary and interface alignment of highorder meshes to levelset functions. Disciplines: Applied Mathematics Hosting Site:Lawrence Livermore National Laboratory (LLNL) Internship location: Livermore, CA Mentor:


No  nrelcavraro1  12/19/2022  1671426000000  National Renewable Energy Laboratory (NREL)  Golden, CO  Applied Mathematics, Computational Mathematics 
Project Description:In a networked cyberphysical system (NCPS), the cyber layer consists of intelligent agents, the physical layer consists of the system's physical infrastructure over which the agents interact. The actions taken by one agent affect possibly all the others. Given the number of modern infrastructures and engineering systems that can be modeled as NCPSs, e.g., power grids, traffic networks, and social networks, methods for NCPSs have a variety of practical applications.The project aims to design novel control and optimization strategies for optimizing NCPSs' performance while meeting important operational requirements and targeting power grids and/or railway system applications. The need for novel techniques for these systems is motivated by recent technological advances. On one hand, traditional control techniques for power systems do not account for the high variability resulting from the massive deployment of Distributed Energy Resources (DERs). On the other hand, the new technology of batterypowered (BP) railway vehicles is still not supported by proper control and optimization strategies. Both DERs and railway vehicles can be interpreted as smart agents interacting over a network, i.e., the power grid or the railway system. The student will use tools from distributed control, optimal control, reinforcement learning, and optimization. Further, the student will focus on (one or more) of the following goals: integrating DERs into bulk power systems; enhancing the efficiency of BP railway vehicles; regulating the interaction between power and railway systems. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO Mentor:


Yes  netllalam1  12/19/2022  1671426000000  National Energy Technology Laboratory (NETL)  Analysis 
U.S. Citizenship is a requirement for this internship Project Description:Fiber optic based acoustic sensing is a novel technology that can offer high sensitivity, wide frequency band measurement, robustness, remote monitoring, and immune to any electromagnetic interferences; making fiber optic acoustic sensor suitable for monitoring critical energy infrastructures, aviation, and seismology applications.This project aims to develop advanced data analytics algorithms to process the experimental data obtained from a recently developed fiber optic acoustic/vibration system. The student will collaborate with NETL staff to generate experimental data and use it for novel data processing algorithms development. The student will also explore how the fiber optic acoustic/vibration system works and need to be optimized its sensing performance, and sensor packaging. Handson experience in fiber optics and/or experimental sensor data processing would be preferred, but not essential. Disciplines: Analysis Hosting Site:National Energy Technology Laboratory (NETL) Mentor:
Internship Coordinator:


No  lbnlwu1  12/19/2022  1671426000000  Lawrence Berkeley National Laboratory (LBNL)  Berkeley, CA or Virtual  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:Accessing data residing on permanent storage systems generally takes much longer than the time to compute on the same data. Motivated by this observation, this proposal aims to bring a few mathematical tools to reduce the data access time. Much of the existing math research on data analysis focuses on data analysis algorithms, without considering how to get the data from their permanent storage to the computation memory system. Part of the reason is a lack of information from storage systems because the existing file system software treats user data as a opaque sequence of bytes. With the advent of the object store tech nology, the data storage systems are poised to provide considerably more semantic and structural inforation, which would enable more operations to be performed on such semantic information. In many applications, especially those involving sensor measurements and large simulations, the data objects are multidimensional arrays, such as time series (1D), images (2D), and simulation of weather conditions for the next few days (4D). This project brings together a number of mathematical tools to analyze common tasks on these arrays, including finding portions of an array satisfying some userspecified conditions (querying) and computing on the selected values (aggregation). To support efficient data accesses, compression and indexing are carefully examined. Initial tests show that the compression technique could reduce the storage required by over 100 times while still preserve important features of the data. The indexing technique takes advantage of the block nature of the storage systems, and only consider block level information. The initial demonstration shows that it is able to reduce the data access time. The authors further propose compressive sensing as a general framework to further extend the compression and indexing work. Based on the fact that compressive sensing is amenable to analysis, the authors provides a strong argument that compressive sensing would be able to provide a better theoretical understanding of the similarity based compression and provide strong alternatives to data sketching for largescale data analysis. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Lawrence Berkeley National Laboratory (LBNL) Internship location: Berkeley, CA or Virtual Mentor:
Internship Coordinator:


No  nrelguerra1  12/19/2022  1671426000000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Analysis, Applied Mathematics, Computational Mathematics 
Project Description:Despite recent progress on the technoeconomic modeling of energy storage, the modeling of energy storage—particularly for longduration and seasonal applications—in longterm and largescale energy planning and operation models remains a major challenge due to the temporal representations in power sector planning and operations models. Power capacity planning models are often based on time slices or representative days and balancing areas with a limited representation of the chronology of operational decisions. This approximation is made to improve computational tractability but is fundamentally incapable of accurately representing storage technologies due to their nonMarkovian nature. Production cost models are used to assess system operations by sequentially optimizing unit commitment and economic dispatch decisions on relatively short time horizons (typically 48 hours) to mimic typical market clearing processes. This too is fundamentally incapable of accurately representing many storage technologies due to the inability of the model to see the value of storing energy for usage outside any single 48 hour optimization window.The objective of the proposed project is to develop a scalable decomposition approach for the design and planning of longduration and seasonal energy storage in view of high and ultrahigh carbonfree and renewable power systems. The proposed approach will satisfy the following requirements to provide benefits throughout energy modeling ecosystems: (i) The approach will represent the spatial and temporal details required to capture the value of storage technologies that can operate over timescales ranging from several minutes to several months. (ii) The approach will be executable and accessible through standard cosimulation interfaces (e.g., Python, Julia, etc.) to ensure integration with other energy modeling tools, e.g., ReEDS, PLEXOS, SIIP, etc. (iii) The approach will be general enough to represent a variety of long duration storage technologies, including renewable fuels, thermal energy storage, CAES, PHS, hydrogen storage, and others. (iv) The approach will be used to evaluate the value of longduration and seasonal storage for transmission deferral and resiliency in view of extreme weather events, e.g., droughts, aboveaverage wildfires, and snow storms, and recurring climate patterns, e.g., El Niño and La Niño Southern Oscillation (ENSO). Disciplines: Analysis, Applied Mathematics, and Computational Mathematics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:
Internship Coordinator:


Yes  LANLKoglin1  12/19/2022  1671426000000  Los Alamos National Laboratory (LANL)  Los Alamos, NM  Analysis, Applied Mathematics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Adaptive machine learning (AML) methods are being developed to unwrap the phase of a series of interferometer images that capture the density evolution for a range of materials that have been rapidly heated with an intense relativistic electron beam. A physicsbased model of the density evolution is being built into the analysis using Python in the Mystic framework. You will be collaborating with several mentors to develop and apply increasingly complex physics models to the datasets. You will need to be familiar with machine learning and statistical analysis techniques and should have an interest in physics as well as mathematics. The toolset developed in this proposal will be deployed in an interactive analysis tool to provide rapid feedback during future experiments, and will be used to guide the development of the system and experimental approach to future measurements. Disciplines: Analysis, Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory (LANL) Internship location: Los Alamos, NM Mentors:


No  ANLMaulik1  12/21/2022  1671598800000  Argonne National Laboratory (ANL)  Lemont, IL  Applied Mathematics, Probability and Statistics 
Project Description:In this project, novel deep learning algorithms will be constructed to learn solutions to the FokkerPlanck equations for stochastic dynamical systems. The key challenges to overcome include the possibility of nonlocality, i.e., when such systems are driven by Levy noise; highdimensionality, and nonMarkovian characteristics. Potential datadriven solutions to such systems include the use of normalizing flows, generative adversarial networks, and neural stochastic differential equations. Some preliminary work in this area has been done by our team (across ANL, IITChicago, Johns Hopkins University) here: https://arxiv.org/pdf/2107.13735.pdf Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL Mentor:
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No  ANLMaulik2  12/23/2022  1671771600000  Argonne National Laboratory (ANL)  Lemont, IL  Applied Mathematics, Probability and Statistics 
Project Description:In this project, we will explore the development and application of algorithms that can learn the timeevolution of both dissipative and conservative dynamical systems. We will investigate the GENERIC formulation (https://doi.org/10.1016/j.jcp.2020.109950), which has demonstrated success in learning such behavior for canonical dynamical systems, for instance to predict the behavior of a double pendulum. In this project, we will build on this framework so that it may be deployed on highdimensional dynamical systems emerging from weather, climate, nuclear fusion applications by investigating couplings with dimensionality reduction techniques. We will also investigate techniques to make such systems more robust to noisy data for their application to realworld problems. Please reach out to Romit Maulik (rmaulik@anl.gov) for more details. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL Mentor:
Internship Coordinator:


No  FNALOzguler1  12/23/2022  1671771600000  Fermi National Accelerator Laboratory (FNAL)  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:This project aims to develop advanced quantum control techniques to increase the efficiency and practical usage of quantum computers. Increasing the performance of quantum processors through scalable quantum control is required to achieve breakthroughs in quantum information science. One can achieve comparable functionality using significantly less computation by approximating existing quantum control algorithms using machine learning (ML). Quantum control workflows that utilize artificial intelligence (AI) agents provide an opportunity to leverage existing highperformance computing capabilities to maximize the performance of quantum computers. The intern will develop ML frameworks to convert the gates constituting a quantum circuit to electromagnetic pulses that can be used to control quantum hardware with enhanced error thresholds. The intern will use AI agents that can perform autonomous learning control to synthesize highfidelity and noiserobust quantum logic gates, which are essential for realizing scalable quantum computing. The intern will perform simulations for pulse optimizations with many parameters and perform verifications and benchmarks with supercomputers & quantum computers. This project has two specific aims: 1) Explore and identify the ML models with deep learning capability, 2) Test the models in simulations (numerical experiments on synthetic data) and evaluate their performance with benchmarks on HPC. Time permitting, the interns can run the ML control framework on real quantum computers and analyze their realworld problemsolving efficacy. Students should be comfortable with mathematical optimization problems & machine learning and have some experience (or a willingness to learn) programming in Python or Julia. For the numerical work, we will share initial notebooks with students to begin the project. Supercomputer clusters will be available for this project, and their use is expected early on in the project. Previous knowledge of quantum hardware and quantum programming is not required. However, students interested and willing to understand the underlying subject are preferred. The students will collaborate with researchers at Fermi National Accelerator Laboratory (Fermilab) and Princeton University. The students will be able to network with researchers from universities, national labs, and industry and get multiple perspectives on postgraduate life. The student is encouraged to participate onsite at Fermilab, but the program duties may be conducted remotely if the student prefers to avoid travel. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Fermi National Accelerator Laboratory (FNAL) Mentors:
Internship Coordinator:


No  FNALOzguler2  12/23/2022  1671771600000  Fermi National Accelerator Laboratory (FNAL)  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:This project aims to develop machinelearningassisted models to create efficient and noiserobust quantum gates for quantum information processing. With the realization of highly coherent quantum devices, such as the quantum computer being developed at Fermilab, complicated interacting quantum systems storing many computational states can be successfully built. Offlineoptimized electromagnetic pulses are often used to control the device. The numerical simulations of these large quantum systems are conducted on highperformance computers (HPC). Numerical models of quantum processors are typically incomplete and thus unable to capture a quantum system’s dynamics sufficiently. Consequently, theoretical models can be inadequate for offline analysis due to a lack of information on the actual quantum system. Characterizing a quantum system sufficiently well is timeconsuming, resourceintensive, and cumbersome. Many proposed methods to close the gap between the theoretical model and the natural quantum system are thus impractical. Therefore, a simple and efficient approach to closing the gap between theoretical models and physical quantum systems is of high interest. This project has three specific aims: 1) Generate a quantum processor emulator using machine learningassisted Hamiltonians, 2) Evaluate optimal control tool performance, and 3) Identify system parameters and correlations using advanced computational tools. The intern will develop machinelearningassisted models by combining the “known” Hamiltonianbased model with a neural network to account for uncharacterized dynamics in the quantum system. Then, the generated models can be used to create gate pulse shapes offline. The student will compare the machinelearningassisted model with the “known” model and compare the predicted pulse parameters to fully optimized ones. Time permitting, the intern can analyze the quantum system models with advanced mathematical tools to extract underlying correlations in the dynamics. The students will collaborate with researchers at Fermi National Accelerator Laboratory (Fermilab) and Princeton University. The students will be able to network with researchers from universities, national labs, and industry and get multiple perspectives on postgraduate life. The student is encouraged to participate onsite at Fermilab, but the program duties may be conducted remotely if the student prefers to avoid travel. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Fermi National Accelerator Laboratory (FNAL) Mentors:
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No  NRELSharma2  01/5/2023  1672894800000  National Renewable Energy Laboratory (NREL)  Golden, CO  Applied Mathematics, Computational Mathematics 
Project Description:Modeling wind farm flow is essential to predicting the power output of a wind farm. The physics involved can be quite challenging, ranging from interaction between turbines and wakes, deep array effects, complexterrain impacts, and wakeatmosphere interaction. As the industry moves offshore, of particular importance is the capability to model wakeatmosphere interaction accounting for mesoscale weather phenomenon and understanding the associated impact on a wind farm's power output. This project will focus on exploring mesomicro (weatherfarm) coupling strategies for accurate modeling of coastal offshore wind farm flow physics targeting the Northern US Atlantic shoreline. The student will collaborate with NREL staff to strategically develop NREL's highfidelity wind farm simulation software to perform and analyze largeeddy simulations (LES) representative of the geographical regions of interest. Skills required include proficiency in turbulence modeling using LES. Proficiency in developing scientific software using C++ is required to be able to successfully navigate this project. Familiarity with wind farm physics, although a plus, is not required. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO Mentors:
Internship Coordinator:


No  ORNLMcCollum1  01/5/2023  1672894800000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Analysis, Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:Meeting today’s grand challenges of climate change and decarbonization (e.g., Paris Agreement targets of limiting global warming to 2 or 1.5 °C) necessitates a wholesale transformation of the global energy and land system. Countries, cities, companies, and organizations at all levels of society are now pushing toward the ambitious goal of net zero carbon emissions by midcentury. Yet, it is not yet clear how the energy transition will unfold in different contexts, as it depends on myriad uncertainties spanning several dimensions: technological, economic, sociocultural, institutional, and geophysical. The overarching aim of this project is to look at the energy transition from a multidimensional perspective, using advanced mathematical tools to shed new light on where the possible bottlenecks to the transition could be as well as which constellations of factors could allow decarbonization efforts to be accelerated. Novel data science approaches are now being employed to offer new perspectives on potential pathways toward deep decarbonization that deploy new technologies, policies, business models, and institutional arrangements. A good example is described in Alova et al. (2021, Nature Energy) and McCollum (2021, Nature Energy), wherein a machinelearning model is built to predict powergeneration project failure and success using a large dataset on historic and planned power plants for Africa combined with a host of projectspecific and countrylevel indicators. The NSFMSGI project would follow this exemplary approach but would apply a new methodology to a new problem and dataset in a different context. The student would have flexibility in designing the research focus and the chosen methods. Possibilities could include predicting the siting of electric vehicle charging infrastructure based on past experience and infrastructure buildout; estimating the likelihood of geoengineering deployment by various state and nonstate actors based on historical analogs; evaluating the potential of residential solar PV installations and home energy efficiency upgrades based on neighborhoodlevel sociodemographic and economic characteristics; informing the netzero plans of countries, cities, and companies based on a survey of existing plans by similarly positioned entities; and so on. These examples are presented for illustration only and are definitely not meant to be prescriptive or restrictive. Again, the student will have considerable flexibility in scoping a project that is of most interest, both in terms of substance and methodology. The focus could be the US or international. The student should already have experience with Machine Learning, Analysis, Applied Mathematics, Computational Mathematics, and/or Probability and Statistics. Having domain knowledge in the chosen research area (e.g., electric vehicles, geoengineering) is not required per se; however, there should be a keen interest in the topic, as this will make the work more productive and enjoyable. Some amount of time during the internship will likely be needed to assemble (or add to) a dataset with enough depth and breadth (size and dimensionality) that is conducive to deep analysis. This will depend on data availability in the research area converged upon by the student and their advisor. The student will collaborate with researchers at Oak Ridge National Laboratory as well as at other DOE national energy laboratories and universities, and possibly with colleagues in government and private industry. The student will have the opportunity to become integrated into existing communities within ORNL, such as DecisionScience@ORNL and the Climate Change Science Institute. Beyond ORNL, there are several research networks the student could be plugged into  in the US as well as internationally (Europe, Asia, etc.). The student is encouraged to participate onsite at ORNL, though a remote appointment could possibly be considered depending on the circumstances. Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


No  ANLRao1  01/5/2023  1672894800000  Argonne National Laboratory (ANL)  Lemont, IL or Virtual  Computational Mathematics, Probability and Statistics 
Project Description:This project investigates the spatiotemporal extents of intensity, duration, and frequency of climate extremes. Specifically, this project will explore the use of ML based algorithms to identify and characterize climatic extremes such as droughts.Disciplines: Computational Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL or Virtual Mentors:
Internship Coordinator:


No  ANLRao2  01/5/2023  1672894800000  Argonne National Laboratory (ANL)  Lemont, IL or Virtual  Computational Mathematics, Probability and Statistics 
Project Description:This project will explore efficient solutions methods for solving a Bayesian inverse problem (i.e. recovering model parameters from observations) in systems modeled by stochastic PDEs with highdimensional input data. The solution methods will rely on surrogate models of the PDE solver  a cheaptoevaluate function that maps a sample of the stochastic input to the dependent variable in the PDE. In order to efficiently construct a surrogate with limited data, we leverage several key building blocks from stateoftheart deep learning that encode desirable inductive biases into the model. Additionally, we will also explore sampling methods such as Normalizing flows to sample from the posterior.Disciplines: Computational Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory (ANL) Internship location: Lemont, IL or Virtual Mentors:
Internship Coordinator:


No  ORNLOu1  01/10/2023  1673326800000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Analysis, Applied Mathematics, Probability and Statistics 
Project Description:This project is aimed at creating systematic dynamic models for the vehicle system and market as well as transportation systems; and facilitating understanding of how to efficiently and effectively transition from the current petroleumbased transportation energy system to one that is more sustainable, intelligent and energydiverse. The project includes machine learning, data analytics in the transportation energy market and systems implemented through mathematical method such as discrete choice modeling and reinforcement learning algorithms. Mature coding capabilities with Python are required in this project. Learning objectives for the applicant include: (i) analyze the transportation impacts on energy and environment based on data analytics; (ii) acquire skills in modeling the advanced transportation system (the battery system in electric vehicle) for optimizing technology application; and (iii) gain experience in decisionmaking for stakeholders on vehicle market dynamics (majorly the U.S. and China’s markets), vehicle policies and transportation systems. The expectations of products that the intern will produce with the mentor are: (i) the expansion of BREVO (Battery Rundown under Electric Vehicle Operation) model with machine learning algorithm implemented; (ii) the construction of the truck choice modeling with considering the driver behavior analysis and discrete choice modeling integrated; (iii) ultimately, together with the mentor, the intern is expected to have a poster presentation or a paper manuscript on discussing the contributions on the model constructions. Disciplines: Analysis, Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLOu2  01/10/2023  1673326800000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Analysis, Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:The proposed project aims to improve the current multinomial logit methodbased vehicle dynamic projection model by integrating the machine learning algorithm so that the new version is able to deliver a systematic, comprehensive, and flexible sales dynamics model for evaluating benefits of technological advances and informing investments and policies for efficient and equitable electrification transitions. The current vehicle dynamic model  the Market Acceptance of Advanced Automotive Technologies (MA3T) model (https://teem.ornl.gov/ma3t.shtml) is used to simulate market demand for advanced vehicle technologies by representing relevant attributes of technologies and consumer behavior such as technological learning by doing, range anxiety, access to recharging points, daily driving patterns, and willingness to accept technological innovation. There are two parts of the study: ML calibration and ML Reduced form. ML calibration: This study expects to develop datadriven ML algorithms to simultaneously calibrate multiple parameters in MA3T based on historical data and empirical study findings. Currently in MA3T, only Alternative Specific Constants are calibrated online. Due to complexity of MA3T, many other parameters with high impact, high uncertainty and correlation are calibrated offline, including price coefficients, value of technology risk, value of range anxiety, value of range uncertainty, availability of charging or refueling infrastructure, statespecific constants and groupspecific constants. In this program, the intern will implement ML online simultaneous calibration of all these parameters to improve the coherence and accuracy of MA3T. ML reduced form: The current MA3T requires 58 minutes per scenario simulation, acceptable for most application contexts but not suitable if parameter and input stochastics, largebatch inputs and outputs and nontechnical users are considered. This study aims to develop “MLaided usage” algorithms to simulate sufficient MA3T scenario results and construct the reduced form of MA3T. This reduced form will be a set of quick input–output nonlinear functions. Multiple ML algorithms, such as decision tree, neural network, and Hidden Markov model, are expected to be compared (e.g., running time, projection accuracy compared with MA3T simulation results) for identifying the most suitable method. The student should already have experience with Machine Learning, Analysis, Applied Mathematics, Computational Mathematics, Probability and Statistics. It would be a plus if the student is interested and have basic knowledge in the vehicle market and economics. The student will closely collaborate with researchers at the Transportation Energy Evolution Modeling Program (https://teem.ornl.gov/) in the Oak Ridge National Laboratory during the onsite internship. Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  NRELSINGH1  01/10/2023  1673326800000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Analysis, Computational Mathematics, Probability and Statistics, Topology 
Project Description:A team of researchers from Cybersecurity Evaluation & Application (CEA) and Computational Science groups at the National Renewable Energy Laboratory (NREL) is proposing a novel anomaly detection and mitigation methodology against cyber threats by developing digital twin (DT) models of distributed energy resources (DERs) using deep learning algorithms. In this method, twin models of DERs are developed using the federated transfer learning (FTL) approach at the substation edge by utilizing quasirealtime grid measurements, geographical, weather, and other information. The proposed research and development (R&D) tasks include i) DTbased highfidelity model development for DERs using feedforward neural network (FNN)based model training/update and deep Q network (DQN)based hyperparameter tuning and optimization; ii) Deep Reinforcement Learning (DRL)based global model development for anomaly detection; iii) Federated transfer learning approach to provide rulesbased attack mitigations by integrating individual local models with a master global; iv) Data management and experimental evaluation in a cyberphysical testbed environment with multiple usecase scenarios. The FTL consists of two components: federated learning and transfer learning. During federated learning, the trained and updated models share their model parameters to the central aggregator, deployed at the control center, which performs federated averaging to create a global model that detects anomalies based on a global view of the grid and updated weights and parameters from local models. Once an anomaly is detected, the global model initiates an appropriate mitigation strategy through DRL actions by coordinating with local twin models through the transfer learning approach. The appropriate mitigation strategy is decided based on the nature, severity, and location of cyberattacks. Disciplines: Analysis, Computational Mathematics, Probability and Statistics, and Topology Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:
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No  NRELSINGH2  01/10/2023  1673326800000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Analysis, Applied Mathematics, Probability and Statistics, Topology 
Project Description:Cybersecurity situational awareness for hydropower can predict stealthy attacks at an early stage, minimize evolving cybersecurity risks, and assist grid operators to take intelligent decisions against cyber threats while enhancing hydropower plants’ resiliency. We envision achieving this innovation through the proposed research and corresponding tool development for the hydropowerintegrated distributed energy resources (DERs). We propose an artificial intelligence (AI)driven methodology coupled with model and signaturebased approaches to develop intrusion detection and mitigation system while considering the participation of hydropower with other DERs in the frequencyregulation market. Based on the industry guidance, this userfriendly tool will integrate a cloudbased data analytics platform to support grid monitoring, events visualization, and management of heterogenous datasets to enable plugandplay tool for demonstration and possible commercialization. The proposed tool will be tested and evaluated using the formulated technical and economical metrics and will be demonstrated in the hardwareintheloop (HIL) testbed environment to go towards the pilot phases with the utility partners Disciplines: Analysis, Applied Mathematics, Probability and Statistics, and Topology Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:
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No  LLNLVOGL1  01/10/2023  1673326800000  Lawrence Livermore National Laboratory (LLNL)  Livermore, CA  Applied Mathematics, Computational Mathematics 
Project Description:The damaging impacts of the Earth's changing climate are widespread and include sealevel rise, more damaging hurricanes, and more extreme droughts and torrential downpours. Accurate forecasting of the climate is essential for preparing both communities, and the critical infrastructure they depend on (e.g., power grid), for the new hazards faced in this century. To this end, the Energy Exascale Earth System Model (https://e3sm.org) Project continues to leverage advanced computational resources and methods to ensure planning groups have the necessary forecasts to ensure both national and global safety. This internship project is part of a multiinstitutional endeavor (https://paescalscidac5.github.io/) to leverage the expertise of both atmospheric physics scientists and computational mathematicians for improving the resolution of various scales in the atmosphere component of E3SM. The multidisciplinary team is systematically identifying critical processes to target with improved numerical techniques, and then developing those improved techniques to cater both to the specific physical process(es) and to the software requirements of E3SM. The team includes E3SM software developers to ensure that the improved numerical approaches, both in time integration and in spatial discretization, are quickly incorporated into the E3SM code to maximize the impact on production runs. The NSF MSGI intern will first and foremost work with LLNL research scientists developing and prototyping the new numerical techniques mentioned above. As such, strong numerical analysis skills in methods for partial differential equations are required. The intern will also interact with the multiinstitutional team to gain experience collaborating with domain/application scientists and grow their professional network. As such, an interest in atmosphere modeling/simulation is ideal but not required. Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Lawrence Livermore National Laboratory (LLNL) Internship location: Livermore, CA Mentor:


No  LBNLWILD1  01/10/2023  1673326800000  Lawrence Berkeley National Laboratory (LBNL)  Berkeley, CA or Virtual  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:This summer experience revolves around algorithm creation and analysis for design problems for which goals are only available through observations of complex systems. Such settings commonly arise in the fields of derivativefree (zerothorder) optimization. Our objectives include some combination of modeling specific problems, implementing novel algorithms, and analyzing (non)asymptotic performance. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:Lawrence Berkeley National Laboratory (LBNL) Internship location: Berkeley, CA or Virtual Mentor:


No  NRELWRIGHT1  01/10/2023  1673326800000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Analysis, Computational Mathematics, Probability and Statistics 
Project Description:To meet national targets of clean electricity by 2035 and a decarbonized economy by 2050, the electric power transmission system needs significant enhancements to accommodate the growth of renewable generation and electrified loads. producing portfolios of interregional transmission network expansion options based upon a set of planning scenarios requires improved model linkages and transmission expansion optimisation techniques to be applied at scale with the intention of national, state, industry and regional planning entities benefiting from better articulated processes/approaches and tools developed from an effort of this magnitude. Most transmission expansion exercises are interative in nature and based on a combination of transmission expansion planning expertise, heuristics and iterative techniques. The intention of this project is to better formulate the transmission expansion planning problem atscale, solving it and improving approaches further considering the range of uncertain input parameters that define the problem. In this, informed solutions to interregional transmission expansion needs are intended to be highlighted via moving from zonal capacity expansion modelling domains to increased spatial and temporal levels of detail in nodal modelling domains (production cost, powerflow, resource adequacy). Disciplines: Analysis, Computational Mathematics, and Probability and Statistics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:
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No  ORNLXUE1  01/10/2023  1673326800000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Computational Mathematics 
Project Description:The US Power grid itself is a complex mathematical system. Conventional grid math has been well established in the last decades, such as the power flow problem, swing equation, state estimate, and optimal power flow problems. However, the grid has been experiencing dramatic changes in the recent two decades with highly fluctuating renewable resources, more and more power electronics devices and other new technologies. All of these have resulted in new mathematical problems for grid modeling, analysis, and simulations. Harmonic statespace method has been identified as one of the potential approaches for the new power grid. Nevertheless, there are still computational challenges and unsolved problems to be tackled. This project will offer learning experience for future applied "mathematicians" to explore power grid modeling and stability analysis problems, and the cuttingedge R&D in power grid modeling and controls.Disciplines: Applied Mathematics, and Computational Mathematics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


No  NRELZAMZAM1  01/10/2023  1673326800000  National Renewable Energy Laboratory (NREL)  Golden, CO or Virtual  Applied Mathematics, Computational Mathematics, Probability and Statistics 
Project Description:The massive integration of electric vehicles (EV) charging infrastructure in distribution networks presents new challenges due their novel operational constraints. But their flexibility also presents an opportunity to enhance the resiliency of electric grids. In addition, EV charging networks can harness the flexible operation to optimize their profits. This position will require the candidate to have background on stochastic optimization techniques, game theory, and dynamical systems theory. The student will work with power systems control and optimization scientists to model the EV charging problem and to develop an algorithm to solve it using stochastic optimization techniques. The student will be expected to draft a research paper by the end of the internship. Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics Hosting Site:National Renewable Energy Laboratory (NREL) Internship location: Golden, CO or Virtual Mentor:
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Yes  USACEStyles1  01/11/2023  1673413200000  U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC)  Vicksburg, MS  Analysis, Applied Mathematics, Mathematics (General), Operations Research, Probability and Statistics, Topology 
U.S. Citizenship is a requirement for this internship Project Description:Student will utilize spectrogram images/digital data to identify patterns that indicate the passage of watercraft. An extensive suite of vessel wake data is available to develop robust training algorithms as well as sample data to verify and develop a vessel wake detection algorithm. Student should possess working knowledge of ML concepts and be able to work independently in MATLAB and/or Python environment. Experience with data analysis, including digital filtering, wavelet analysis and higher level ML tools/applications is highly desirable. Work will mostly be in an office setting but some possibility for field work during vessel wake collections for interested students. Disciplines: Analysis, Applied Mathematics, Mathematics (General), Operations Research, Probability and Statistics, and Topology Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC) Internship location: Vicksburg, MS Mentor:
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No  ANLHückelheim1  01/11/2023  1673413200000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:Our group has decades of experience on developing and using automatic differentiation, which is known as backpropagation or autodiff in the Machine Learning frameworks. We are developing alternatives to backpropagation that take a more flexible approach on how to compute gradients, inspired by techniques developed in the context of differential equations and related problems. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
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No  ANLHückelheim2  01/11/2023  1673413200000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:Our group has developed methods for mapping the evaluation of certain mathematical functions to modern processors, for example by exploiting the associativity of operators to allow dynamic scheduling and accumulation of results. This allows us to compute these functions faster and using less energy. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
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No  ANLBalaprakash1  01/11/2023  1673413200000  Argonne National Laboratory  Lemont, IL  Applied Mathematics, Probability and Statistics 
Project Description:The success of deep learning (DL) has spurred the interest of scientists in adopting deep neural networks (DNNs) on their datasets to build stateoftheart predictive models for accelerating scientific progress. Despite recent successes, however, designing DNNs for scientific and engineering applications remains a challenging task, requiring timeconsuming manual architecture engineering by DL experts. Moreover, most DNNs provide only deterministic predictions and cannot model uncertainties associated with the predictions. This shortcoming is a significant obstacle to adoption in many scientific applications for which model predictions are not trusted or used if they do not account for uncertainties. To that end, we have developed DeepHyper (https://deephyper.readthedocs.io/en/latest/), a software package that automates the endtoend process of applying DL to various scientific applications. In this project, we will focus on the design and development of optimization methods to automate the development of neural network ensembles and use them for uncertainty quantification. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentor:
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No  ANLBalaprakash2  01/11/2023  1673413200000  Argonne National Laboratory  Lemont, IL  Applied Mathematics, Probability and Statistics 
Project Description:Missioncritical dataintensive DOE applications such as climate/weather simulations increasingly draw on combinations of classic methodology for solving forward simulation and inverse problems with modern machine learning techniques for (i) calibrating forward models to match large volumes of diverse experimental/observational data, and (ii) automatically identifying the new data that would be most valuable to acquire. Both these goals depend on probabilistic inference, to quantify uncertainty over the states, parameters, structure, and predictions of complex forward models in the light of data. Probabilistic programming (PP) offers new avenues for automating the solution of probabilistic inference problems given source code for forward models. In this project, we will leverage recent breakthroughs in PP systems, such as Gen (https://www.gen.dev/) and PyProb (https://github.com/pyprob/pyprob), to develop new mathematically and statistically rigorous inversion algorithms for dataintensive scientific machine learning applications. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentor:
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No  ANLRAGHAVAN1  01/11/2023  1673413200000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:Dataset imbalance refers to the issue when certain classes are represented by significantly more number of data points relative to others. It is a prevalent issue in machine learning especially classification problems in many scientific applications. This issue materializes itself when the final performance of a model is biased towards the class with a larger number of sample points. One way to correct this bias is to equalize the imbalance and intelligent sampling strategies play a critical role in this procedure. However, due to a lack of efficient approaches, a common way to address the issue involves trial and error driven uniform oversampling of the underrepresented class or undersampling of the overrepresented class. In this project, we will formulate the problem of imbalance in a data batch as an optimization problem and derive conditions which must be satisfied for sampling a balanced data batch. We then integrate the condition into the neural network learning problem. We will develop a game theoretic approach to resolve the tradeoff between the performance of the neural network and the variance in the data. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
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No  ANLRAGHAVAN2  01/11/2023  1673413200000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:In many applications, relevant data is scarce and the large scale experiments required to generate relevant data is expensive. To correct this issue it is desirable to learn a transformation between an inexpensive simulation data distribution (source) and expensive experimental data distribution (target). A promising approach for such transformation is optimal transport. However, the computational cost of constructing an optimal transport map between source and target scales nonlinearly with sample size which can be cost prohibitive. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
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No  USFSSkowronski1  01/11/2023  1673413200000  USDA Forest Service, Northern Research Station  Morgantown, WV  Applied Mathematics, Probability and Statistics, Topology 
Project Description:Wildland fire is a natural process that has become problematic in society because of the expansion of human developments, increased fuel loads due to past fire suppression activities, climate change, and a myriad of other factors. Solutions for this problem require a more advanced understanding of the fundamental physical processes of these fires and how they propagate from the very small scale (fuel particles) to landscapes. Large efforts are currently underway to integrate highly instrumented field experiments, machine learning, artificial intelligence, and computational fluid dynamics models to advance our decision making in the future. The applicant, with the guidance of several mentors, will have the opportunity to design an experience that focuses on their analytical strengths to help us to disentangle and understand complex relationships of fire spread and behavior. The applicant will examine a set (n=30) of recent fire field experiments with data including multitemporal 3D laser scanning (LiDAR), infrared and color video, 3D wind fields, temperature profiles, and radiative fluxes. The primary objectives of the experience are: 1) Expand the applicant’s understanding of datasets of different spatial and temporal resolutions, 2) develop an approach to decompose and relate these data streams, and 3) to present the techniques and results in a way that is understandable to scientists from other disciplines and land managers. This internship will be based at the Forestry Sciences Laboratory in Morgantown, WV in collaboration with Scientists from the USDA Forest Service, Rochester Institute of Technology, West Virginia University, and other institutions. The applicant will have the opportunity to collect data (in a learning setting) with the same instruments used in the fire experiments to understand their intricacies and limitations. Depending on Covid restrictions, the applicant may have the opportunity to visit several field sites, interact with other scientists and fire managers, and observe a prescribed burn. Disciplines: Applied Mathematics, Probability and Statistics, and Topology Hosting Site:USDA Forest Service, Northern Research Station Internship location: Morgantown, WV Mentors:


No  ORNLDate1  01/11/2023  1673413200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Analysis, Applied Mathematics, Mathematics (General), Operations Research, Probability and Statistics 
Project Description:This project explores the efficacy of quantum computers for solving problems in the broad field of artificial intelligence (AI). The applicant will have the freedom to choose a specific problem in AI such as natural language, speech recognition, computer vision, machine learning, deep learning, NPcomplete problems etc. and use stateoftheart quantum computers to solve them. This project would provide a unique experience of running jobs on adiabatic quantum computers like DWave 2000Q, and universal quantum computers like IBM Q. Learning objectives for the applicant include: (1) Develop a basic understanding of adiabatic and universal quantum computers; (2) Design novel approaches to solve challenging AI problems leveraging quantum computers; and (3) Validate the approach on benchmark problems and compare its performance to stateoftheart classical approaches. Disciplines: Analysis, Applied Mathematics, Mathematics (General), Operations Research, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:


No  FNALKurkcuoglu1  01/11/2023  1673413200000  Fermi National Accelerator Laboratory (FNAL)  Batavia, IL  Applied Mathematics 
Project Description:We are interested in developing efficient computational methods for synthesizing specific qudit gates necessary for quantum simulations of highenergy and many body physics problems. A qudit is the Nlevel generalization of the wellknown 2level qubit. The specific qudit gates will be built from the fundamental qudit gates available on the hardware we are presently developing at Fermilab. The fundamental cavity QED gates that can be experimentally created are different from the more familiar qubit based hardware gates. Finding the optimal tuning parameters of these qudit gates is a computationally difficult task especially when the system consists of multiple qudits with large qudit size N. Therefore, we want to study new computational methods to efficiently compile qudit gates with large qudit size, and find new gates to synthesize in qudits. We are also interested in comparing these methods with the qubit based algorithms. The problems we work on require knowledge on working with large, sparse or dense matrices and numerical optimization methods. Students will develop expertise in using iterative methods, variational methods in python and Julia using computing clusters at Fermilab. Time admitting, we will study implementing these computational methods in real quantum hardware. Previous knowledge on quantum hardware and quantum programming is not required. This project will be conducted in a team setting under the primary direction of researchers at Fermilab. The entire project may be done remotely, with frequent video meetings and the use of other communication tools (e.g., Slack, email). Disciplines: Applied Mathematics Hosting Site:Fermi National Accelerator Laboratory (FNAL) Internship location: Batavia, IL Mentors:
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No  ORNLCHOI1  01/11/2023  1673413200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:As scientific experiments and HighPerformance Computing (HPC) infrastructure evolve, data capture rates continue to exceed the available storage, network, and compute infrastructure for subsequent postprocessing. The scientific data challenge is similar but distinct to many of the “Big Data” challenges we see in the commercial space. The trend from the newest diagnostics and exascale computations clearly shows that advanced machine learning techniques are necessary to manage, reduce, refactor, and extract information. The project will focus on applying various machine learning and deep learning techniques for analyzing scientific data. The main research goals are i) how to analyze scientific data and apply machine learning algorithms for performance improvement, ii) researching advanced machine learning techniques for faster and more accurate models, and iii) how to automate science machine learning and deep learning workflows. The project will provide the following learning opportunities; i) develop a basic understanding of scientific data processing workflows, ii) acquire skills in applying machine learning algorithms, and iii) gain experience in managing largescale scientific data. Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:
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No  ORNLKOTEVSKA1  01/11/2023  1673413200000  Oak Ridge National Laboratory (ORNL)  Oak Ridge, TN  Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:The number of intelligent systems around us is growing rapidly. These Internet of Things (IoT) devices include smart home devices, health monitors, autonomous vehicles, and the smart grid, collecting data about our home activities, our health, where we visit, and our electricity usage, respectively. These technical means are constantly growing in power and sophistication and will likely see even more rapid development with the widespread deployment of 5G wireless networks, which will provide high speed data transfer and more precise location information. However, as these systems scale up, privacy is being left behind. We currently lack the ability to ensure meaningful data privacy guarantees to citizens, institutions, and infrastructure. And, we ask the question of how data privacy should be protected in a world where data is gathered and shared with increasing speed and ingenuity? Differential privacy (DP) is a new model of cybersecurity that proponents claim can protect sensitive data far better than traditional methods. Until recently differential privacy had been a topic of theoretical research without much application to realworld scenarios. So, there is a huge gap between theoretical bounds and practical implementation which opens the possibility for experiments. The aim is to create mathematically provable guarantee of data privacy protection and validate on realworld dataset related to smart grid to address the potential privacy consequences in those systems.
Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Oak Ridge National Laboratory (ORNL) Internship location: Oak Ridge, TN Mentor:
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The name and contact information of the hosting site internship coordinator is provided for further assistance with questions regarding the hosting site; local housing availability, cost, or roommates; local transportation; security clearance requirements; internship start and end dates; and other administrative issues specific to that research facility. If you contact the internship coordinator, identify yourself as an applicant to the NSF Mathematical Sciences Graduate Internship (MSGI) Program.
Interns will not enter into an employee/employer relationship with the Hosting Site, ORAU/ORISE, NSF or DOE. No commitment with regard to later employment is implied or should be inferred.