Available Projects

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:
- Image segmentation, region and geometry detection in 2d/3d images,
- Analysis and statistics of geometries and shapes,
- Finite element modeling and meshing of evolving surfaces,
- Shape and topology optimization,
- Image-based meshing,
with applications in material science, biology and forensics. These projects involve knowledge of different mathematical areas, such as variational models, energy minimization, free boundary problems, meshing, mesh adaptivity and smoothing, continuous and discrete optimization, dynamic programming, and machine learning.

Disciplines: Applied Mathematics, Geometry, and Probability and Statistics

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Gaithersburg, MD

Project Description:

We are developing efficient physics-informed neural network reduced order models (NNROMs) to accelerate complicated, large-scale physical simulations. Currently, our physics-informed NNROM can reduce the dimensionality of an advection-dominated 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 machine-learning black box approach. We plan to extend the ROM to large-scale problems, such as advection-dominated hydrodynamics, transport problems, turbulence, and Rayleigh–Taylor instability simulations. We expect our NNROM will achieve a higher speed-up when it is applied to larger-scale 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 shock-moving hydrodynamics, pore-collapse 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

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.

Rapid progress in machine learning has engendered numerous applications across the sciences. Deployment of modern ML systems have increased our ability to validate and automate the scientific process, broadening the space for discovery. However, these advances come with their own associated challenges and risks. For example, optimization schemes incorporated during training are necessarily opaque, leading one to question if the algorithm has learned features of nature or artifacts of the data. A recent trend emerging from these issues is the desire to make ML systems more explainable, robust, and overall more trustworthy. Trustworthy ML is particularly important for further development of scientific fields related to national security, such as the Earth system sciences.

Students will learn about the cutting edge methods in the rapidly developing field of trustworthy ML, and their current applications within the Earth systems predictability space. The students will then deploy modern techniques to garner novel insights into AMOC. Students will also be encouraged to work on the development of the mathematical theory necessary to push forward the current state of trustworthy ML.

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

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 information-theoretic connections has enabled probabilistic inference on large-scale models. 

This project would involve research with novel information-theoretic and sparse Bayesian deep learning techniques for supervised and continual learning approaches tailored to the unique needs of scientific data. Specifically, the sparsity-inducing priors (building on [1, 2]) will be developed and applied for incorporating structured sparsity into the latent-variable models and deep architectures. Additional considerations such as efficient implementations with probabilistic programming languages, and probabilistic neural architecture search (building on [3]) will be explored. The participant will be part of a multidisciplinary team and will work on problems from different domains such as high-energy physics [4] and fusion energy sciences [5].

[1] Sparsity-Inducing Categorical Prior Improves Robustness of the Information Bottleneck. arXiv preprint arXiv:2203.02592.
[2] Sequential Bayesian Neural Subnetwork Ensembles. arXiv preprint arXiv:2206.00794.
[3] Unified Probabilistic Neural Architecture and Weight Ensembling Improves Model Robustness. ML Safety Workshop at NeurIPS 2022.
[4]A modular deep learning pipeline for galaxy-scale strong gravitational lens detection and modeling." arXiv preprint arXiv:1911.03867 (2019).
[5] Model Order Reduction of the Plasma Equilibrium Reconstruction framework EFIT with Deep Neural Networks. 64th Annual Meeting of the APS Division of Plasma Physics

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL

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 long-term 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 large-scale complex dynamical systems.

The method will be deployed in the U.S. DOE software library PETSc to enhance the capabilities of PETSc's time integrators. The student will obtain experience with machine learning algorithms and production-level ODE solvers that run on DOE’s supercomputers.

Disciplines: Applied Mathematics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL

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 data-driven approach to identify and incorporate latent dynamics. Quantum dynamics are often modeled by Schrödinger’s and Liouville-von 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

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 multi-parameter sensing or identify structural features of systems under test. For example, large datasets can be obtained from real-time 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)

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 gas-solid) 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 simple-blob detection of individual particles in dense particle-laden flows with a significant computational savings.

This project will focus on the application of the YOLO accelerated particle detection method for PTV to a high-speed video database collected at PSRI (Particulate Solid Research, Inc.) of horizontal air jets into a marginally fluidized, semi-circular bed. Emphasis will be placed on accuracy and bias of the YOLO detection method against hand labeled training data and the comparison of YOLO against the simple-blob detection method in test data. Potential extension of the project (time permitted) would seek to use the results to approximate the particle concentration field.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

National Energy Technology Laboratory (NETL)

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 ab-initio 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

Project Description:

The goal of this project is to develop and analyze an optimization framework for minimizing multi-modal 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 black-box optimization. In this project, the student will gain experience on high-dimensional 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

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

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 post-Moore’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 NSF-MSGI intern will depend on intern interests and background. Our current projects include:

1. An exploration of techniques from arithmetic combinatorics for integer problems, with application to novel devices.
2. Applications of machine learning to Boltzmann machines using an Ising model, and in particular, investigations of the fault model and detection and correction methods (perhaps using machine learning techniques) that may mitigate such faults.
3. Approximate matrix factorization for use in novel hardware.
4. Machine learning as applied to non-convex quadratic optimization problems.

>We encourage publication of results. LANL has a wide range of compute systems, and students will have access to cutting-edge devices of interest. If on-site 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

Project Description:

• The student is required to have preliminary fundamental knowledge about deep learning concepts and PyTorch.
• During the internship, the student is expected to regularly interact with strongly motivated research staff members at ORNL who develop ANN models for scientific applications.
• The student is expected to familiarize with the fundamental concepts of ANN models.
• The student is expected to familiarize and assimilate basic soft skills and apply them in a dynamic environment within a team of highly motivated scientists.

Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

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 high-frequency high-resolution dynamic data and high-dimensional functional data collected at DOE's user facilities; (2) develop mathematical foundations for neural network--based dynamics discovery models and stochastic back-propagation algorithms for training the neural network models; (3) develop goal-oriented 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 self-driving user facilities in the near future.

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL or Virtual

Project Description:

Disciplines: Algebra or Number Theory, Applied Mathematics, and Computational Mathematics

Hosting Site:

Fermi National Accelerator Laboratory (FNAL)

Internship location: Batavia, IL or Virtual

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Algebra or Number Theory, Combinatorics, and Geometry

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or Virtual

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 direct-air capture devices. This project aims to generate high-fidelity data-driven models to improve the accuracy of lower-fidelity models. Specifically, the recently developed exascale-capable CFD-DEM (discrete element method) code MFIX-Exa is being used to create a particle-laden flow database spanning a range of solids concentration and Archimedes number. MFIX-Exa’s Particle in Cell (PIC) is the lower-fidelity model targeted in this work. Unlike CFD-DEM 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 CFD-DEM data to construct a machine learning-based solids stress model that improves PIC predictions. Though beyond the scope work, the ML-enhanced PIC model may be considered for inclusion in the MFIX-Exa, providing credible data-driven prediction at a significantly reduced computational cost.

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

National Energy Technology Laboratory (NETL)

Project Description:

• The student will learn basic concepts of graph theory, along with software capabilities provided in PyTorch and PyTorch-Geometric.
• The student will be exposed to high-performance computing (HPC) challenges that involve deploying GNN models on large scale platforms for incorporation in production codes.
• The student will familiarize with state-of-the-art challenges in atomic modeling for material science applications.
• The student will also develop presentation skills by describing the technical outcomes of his work to the ORNL community.

Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

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

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 – so-called glass-box models – have the benefit that the models themselves are relatively easy for humans to interpret. However, these models tend to underperform state-of-the-art models, such as deep neural networks or random forests – the so-called black-box models. Moreover, glass-box models are not always easily adaptable to image data. At the same time, the more complex relationship between inputs and outputs in the black-box models makes them difficult to interpret, limiting their application in areas where human-user understanding of the model output is strictly necessary. While there have been numerous efforts on combining black- and glass-box methods to aid explainable ML in computer vision, the problem of black-box model interpretability remains largely unresolved.

In this research opportunity, we will tackle the challenge of explainable state-of-the-art models by using Explainable Boosting Machines (EBMs). EBMs are models designed to simultaneously be highly intelligible and explainable and to achieve accuracy comparable to state-of-the-art ML methods. Moreover, their modular design makes it easy to reason about the contribution of each feature to the overall prediction, which in turn enables correlational analysis of the effect of individual features on prediction accuracy. However, a fundamental limitation of EBMs is the requirement that the data must be in tabular format. This prevents their use in many important ML application areas, such as Natural Language Processing, Speech and Signal Processing, and Computer Vision, among others. This research opportunity focuses on investigating in what ways EBMs can be adapted to overcome the tabular data limitation so that they can be used more widely. The project will start by exploring ways to extend EBMs so that they can be used with image data and will involve initial experiments using standard image classification datasets, such as MNIST, Fashion-MNIST, and Chinese MNIST. We plan to tackle the various issues in a subsequent series of experiments, with each consecutive experiment focusing on a more complex dataset.

This opportunity is a critical step towards advancing the use of models with state-of-the-art performance for a wide variety of ML applications where the model outputs must be understood by human users to be fielded, e.g., medical diagnosis based on MRI or CAT scans or experimental control.

Disciplines: Probability and Statistics

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Gaithersburg, MD or Virtual

Project Description:

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or Virtual

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

U.S. Citizenship is a requirement for this internship

Project Description:

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

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or Virtual

Project Description:

Disciplines: Analysis, Applied Mathematics, and Computational Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN or Virtual

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Analysis, Computational Mathematics, Probability and Statistics, and Topology

Hosting Site:

U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC)

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

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 non-linear model-based 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 high-dimensional bi-criteria 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 low-dimensional visualization and approximation methods, (ii) abstractions of computational differential geometry over matrix manifolds, (iii) linear and non-linear model-parameter 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

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 model-based methods to identify high-quality 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

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Applied Mathematics

Hosting Site:

U.S. Army Corps of Engineers, Geospatial Research Laboratory

Internship location: Alexandria, VA

Project Description:

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or Virtual

Project Description:

Disciplines: Analysis, Applied Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN or Virtual

Project Description:

Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO

Project Description:

Disciplines: Applied Mathematics, Combinatorics, Computational Mathematics, and Geometry

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Labeled data are expensive and time-consuming to obtain in many real-world 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 deep-clustering 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.

It is expected that the student will gain experience working in a multi-disciplinary team with expertise in statistics, machine learning, and remote sensing. There will be opportunities to interact with other students working in a similar fields.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or Virtual

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Analysis, and Computational Mathematics

Hosting Site:

U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC)

Project Description:

Disciplines: Applied Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Disciplines: Algebra or Number Theory, and Applied Mathematics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA or Virtual

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 non-trivial, can aid the optimization of the high-fidelity simulations.

In this project, your research will focus on developing novel sampling strategies that exploit the multiple fidelity simulations in search of optimal solutions. Your sampling strategies will leverage information about available compute resources (HPC, cloud, edge) and optimally assign the different fidelity simulations accordingly. You will collaborate closely with our application experts and deploy your developments on real world high-impact problems.

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Topology

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

Project Description:

Disciplines: Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or Virtual

Project Description:

Disciplines: Applied Mathematics, Computational Mathematics, and Geometry

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Sandia National Laboratories (SNL)

Internship location: Albuquerque, NM or Virtual

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.

In this project, the student will develop and evaluate mixed-precision solvers for electronic structure calculations, specifically looking at where double precision is required, and where lower precision can be used. The project will involve some coding in C/C++, and possibly some CUDA.

Disciplines: Computational Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN or Virtual

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Applied Mathematics

Hosting Site:

U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC)

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

USDA Animal and Plant Health Inspection Service (APHIS)

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Analysis, Applied Mathematics, Foundations, and Probability and Statistics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

Project Description:

Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

USDA Forest Service, Southern Research Station

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Algebra or Number Theory, Applied Mathematics, and Computational Mathematics

Hosting Site:

National Energy Technology Laboratory (NETL)

Project Description:

Disciplines: Applied Mathematics, Combinatorics, Computational Mathematics, and Probability and Statistics

Hosting Site:

Fermi National Accelerator Laboratory (FNAL)

Internship location: Batavia, IL or Virtual

Project Description:

The goal of this project is to design and analyze structure-preserving 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.

Structure-preserving 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 long-term 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 phase-space 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

Project Description:

Disciplines: Applied Mathematics, Computational Mathematics, and Topology

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA or Virtual

Project Description:

Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

Fermi National Accelerator Laboratory (FNAL)

Internship location: Batavia, IL or Virtual

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 graph-matching 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 Gromov-Hausdorff and (Fused) Gromov-Wasserstein distances, have shown promising results to compare not only on structures but also in attributed graphs.

To this end, in our project, we will focus on designing new algorithms for comparing attributed graphs and developing of optimization algorithm to provide reliable metrics for attributed graph comparison. We will leverage recent updates in optimal transport in structured data, such as POT (https://pythonot.github.io/), to develop new algorithm handling with graph data, and apply them to a wide range of machine learning models, including the classical machine learning and deep learning approaches.

Disciplines: Applied Mathematics, Combinatorics, Geometry, and Topology

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL or Virtual

Project Description:

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Analysis, and Probability and Statistics

Hosting Site:

U.S. Army Corps of Engineers, Geospatial Research Laboratory

Internship location: Alexandria, VA or Virtual

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Computational Mathematics, Probability and Statistics, and Topology

Hosting Site:

U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC)

Project Description:

Disciplines: Analysis, Applied Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN or Virtual

Project Description:

Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

U.S. Citizenship is a requirement for this internship

Project Description:

Remote sensing technologies such as Light Detection and Ranging (LiDAR), Time-of-Flight (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 data-driven 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

Project Description:

Disciplines: Probability and Statistics

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Gaithersburg, MD or Virtual

Project Description:

Disciplines: Applied Mathematics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

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 longer-term 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 multi-stage 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:
1) Power grid operations and modeling.
2) Multi-stage stochastic programming.
3) Time series machine learning and forecasting.
4) High-performance computing.

Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

Project Description:

Disciplines: Analysis, and Applied Mathematics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL

Project Description:

Disciplines: Applied Mathematics, Mathematical Biology, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or Virtual

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN or Virtual

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL or Virtual

Project Description:

Disciplines: Computational Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA or Virtual

Project Description:

Disciplines: Applied Mathematics

Hosting Site:

Pacific Northwest National Laboratory (PNNL)

Internship location: Richland, WA or Virtual

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Gaithersburg, MD or Virtual

Project Description:

Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or Virtual

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN or Virtual

Project Description:

Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

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 many-query analyses such as uncertainty quantification and optimization, lower-cost approximate models are need to make the analysis tractable.

Projection-based reduced-order 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 high-dimensional system with a low-dimensional 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 low-dimensional trial subspace on which the system state can be well approximated. Typically, this process involves solving the original system, i.e., the full-order model (FOM), over time for select parameter instances. In the online phase, pROMs then compute approximations to the governing equations that reside on this low-dimensional trial subspace. The results of this process is a fast approximate model that adheres to the governing equations.

One challenge associated with constructing pROMs is the traditional requirement for a set of spatially global basis functions.  This can prove problematic for solution spaces involving sharp gradients, requiring undesirable tradeoffs between accuracy and efficiency. One potential way to overcome this difficulty is to spatially decompose the domain implicitly requiring the use of spatially local basis functions.  However, an overly decomposed domain can result in stability issues.  In this project, we will explore the accuracy-efficiency-stability tradeoffs involved in constructing pROMs with spatially local bases.

This project will rely on an in-house Python-based framework implementing this approach that leverages Pressio demo apps (https://pressio.github.io/pressio-demoapps/). The intern will test this technique using a variety of physical applications, ranging from heat conduction to compressible flow.  If successful, this opportunity would be appropriate for peer-reviewed publication and would be eventually applied to important national security applications at 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

U.S. Citizenship is a requirement for this internship

Project Description:

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

Project Description:

Disciplines: Analysis, and Applied Mathematics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL

Project Description:

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or Virtual

Project Description:

Disciplines: Computational Mathematics, Mathematical Biology, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or Virtual

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 national-scale 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

Project Description:

Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

U.S. Citizenship is a requirement for this internship

Project Description:

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

U.S. Citizenship is a requirement for this internship

Project Description:

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

U.S. Citizenship is a requirement for this internship

Project Description:

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

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 multi-path 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

U.S. Citizenship is a requirement for this internship

Project Description:

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

Project Description:

We are developing efficient latent-space 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 latent-space 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 shock-moving hydrodynamics, pore-collapse dynamics, particle transport, plasma physics, and earthquake inverse problems. Depending on the results, we will write a journal paper together. Our LaSDI is application-agnostic, 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

Project Description:

State-of-the-art 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 Navier-Stokes 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 high-fidelity, 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 high-fidelity 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

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.

Previous work from our group has demonstrated simulations of viscoplastic fluids using a highly parallelizable structured adaptive mesh refinement method in AMReX. Further developments included modeling solid boundaries in viscoplastic fluids using embedded boundary methods.

We propose to extend this work by incorporating elastic effects through the implementation of elastoviscoplastic (EVP) models in this numerical framework. The robustness of the numerical implementation will be extensively tested in various flow scenarios (such as Poiseuille and Couette flows) for a range Weissenberg and Bingham numbers.  Another potential avenue for development will involve implementing immersed boundary methods (IBM) to model a suspension of solid particles in such complex fluids, which is an important application area that has received significant research interest lately.

This project will involve close 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

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 state-of-the-art scientific problems. Simultaneously they have revealed topological insights by identifying structures that correlate with a particular learning task.

Recently a new approach to the multi-parameter analysis has emerged in TDA. Generalizing combinatorial properties of persistence diagrams, it allows to analyze multi-parameter 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 multi-parameter 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 multi-parameter descriptor compares to learning from multiple single-parameter descriptors.

Disciplines: Applied Mathematics, Geometry, Mathematics (General), and Topology

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

Project Description:

Conventional analysis of neutron reflectivity data involves multi-layer 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 multi-component 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 physics-based 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 multi-component soft-matter and hybrid system is unprecedented and will lead to development of tools for interpreting time-dependent 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

Project Description:

High-order meshes are crucial for an accurate discretization of geometry- and solution-features 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 high-order unstructured meshes. Some notable advancements made under this project include a novel framework for high-order mesh optimization using the Target-Matrix Optimization Paradigm (TMOP), simulation-driven r-adaptivity for Lagrangian Hydrodynamics, and boundary and interface alignment of high-order meshes to level-set functions.

In the ongoing project, we are developing methods for (i) high-order mesh p-adaptivity, (ii) h-refinement strategies for aligning boundary and interfaces to the surface of interest when current mesh topology does not allow it, (iii) automatic differentiation of the nonlinear TMOP-based objective function for r-adaptivity, and (iv) partial assembly implementation of existing TMOP methods. All the implementation of the methods developed in this project are done in MFEM, a highly scalable C++ library for finite element methods.

An ideal candidate will have knowledge of mesh adaptivity techniques and strong programming experience in C++.

Disciplines: Applied Mathematics

Hosting Site:

Lawrence Livermore National Laboratory (LLNL)

Internship location: Livermore, CA

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Analysis

Hosting Site:

National Energy Technology Laboratory (NETL)

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 multi-dimensional arrays, such as time series (1-D), images (2-D), and simulation of weather conditions for the next few days (4-D).

This project brings together a number of mathematical tools to analyze common tasks on these arrays, including finding portions of an array satisfying some user-specified 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 large-scale data analysis.

Disciplines: Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA or Virtual

Project Description:

Disciplines: Analysis, Applied Mathematics, and Computational Mathematics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

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 physics-based 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

Project Description:

In this project, novel deep learning algorithms will be constructed to learn solutions to the Fokker-Planck equations for stochastic dynamical systems. The key challenges to overcome include the possibility of non-locality, i.e., when such systems are driven by Levy noise; high-dimensionality, and non-Markovian characteristics. Potential data-driven 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, IIT-Chicago, 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

Project Description:

In this project, we will explore the development and application of algorithms that can learn the time-evolution 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 high-dimensional 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 real-world 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

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 high-performance 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 high-fidelity and noise-robust 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 real-world problem-solving 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 post-graduate life. The student is encouraged to participate on-site 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)

Project Description:

This project aims to develop machine-learning-assisted models to create efficient and noise-robust 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. Offline-optimized electromagnetic pulses are often used to control the device. The numerical simulations of these large quantum systems are conducted on high-performance 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 time-consuming, resource-intensive, 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 learning-assisted Hamiltonians, 2) Evaluate optimal control tool performance, and 3) Identify system parameters and correlations using advanced computational tools. The intern will develop machine-learning-assisted models by combining the “known” Hamiltonian-based 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 machine-learning-assisted 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 post-graduate life. The student is encouraged to participate on-site 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)

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, complex-terrain impacts, and wake-atmosphere interaction. As the industry moves offshore, of particular importance is the capability to model wake-atmosphere interaction accounting for mesoscale weather phenomenon and understanding the associated impact on a wind farm's power output.

This project will focus on exploring meso-micro (weather-farm) 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 high-fidelity wind farm simulation software to perform and analyze large-eddy 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

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 mid-century. 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, socio-cultural, institutional, and geophysical.

The overarching aim of this project is to look at the energy transition from a multi-dimensional 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 machine-learning model is built to predict power-generation project failure and success using a large dataset on historic and planned power plants for Africa combined with a host of project-specific and country-level indicators.

The NSF-MSGI 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 build-out; estimating the likelihood of geoengineering deployment by various state and non-state actors based on historical analogs; evaluating the potential of residential solar PV installations and home energy efficiency upgrades based on neighborhood-level socio-demographic and economic characteristics; informing the net-zero 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 on-site 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

Project Description:

Disciplines: Computational Mathematics, and Probability and Statistics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL or Virtual

Project Description:

Disciplines: Computational Mathematics, and Probability and Statistics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL or Virtual

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 petroleum-based transportation energy system to one that is more sustainable, intelligent and energy-diverse. 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 decision-making 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 Run-down 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

Project Description:

The proposed project aims to improve the current multinomial logit method-based 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 data-driven 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, state-specific constants and group-specific 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 5-8 minutes per scenario simulation, acceptable for most application contexts but not suitable if parameter and input stochastics, large-batch inputs and outputs and non-technical users are considered. This study aims to develop “ML-aided 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 on-site internship.

Disciplines: Analysis, Applied Mathematics, Computational Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

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 quasi-real-time grid measurements, geographical, weather, and other information. The proposed research and development (R&D) tasks include i) DT-based high-fidelity 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 rules-based attack mitigations by integrating individual local models with a master global; iv) Data management and experimental evaluation in a cyber-physical testbed environment with multiple use-case 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 cyber-attacks.

Disciplines: Analysis, Computational Mathematics, Probability and Statistics, and Topology

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO or Virtual

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 hydropower-integrated distributed energy resources (DERs). We propose an artificial intelligence (AI)-driven methodology coupled with model and signature-based approaches to develop intrusion detection and mitigation system while considering the participation of hydropower with other DERs in the frequency-regulation market. Based on the industry guidance, this user-friendly tool will integrate a cloud-based data analytics platform to support grid monitoring, events visualization, and management of heterogenous datasets to enable plug-and-play 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 hardware-in-the-loop (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

Project Description:

The damaging impacts of the Earth's changing climate are widespread and include sea-level 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 multi-institutional endeavor (https://paescal-scidac5.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 multi-disciplinary 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 multi-institutional 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

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 derivative-free (zeroth-order) 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

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 inter-regional 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 at-scale, solving it and improving approaches further considering the range of uncertain input parameters that define the problem. In this, informed solutions to inter-regional 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

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 state-space 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.

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

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

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

Project Description:

Our group has decades of experience on developing and using automatic differentiation, which is known as back-propagation or autodiff in the Machine Learning frameworks. We are developing alternatives to back-propagation that take a more flexible approach on how to compute gradients, inspired by techniques developed in the context of differential equations and related problems.
In this project, you would help us develop new methods for gradient computations, and apply them to a variety of neural networks. If successful, this research could enable faster and more energy-efficient ways of training neural networks on GPUs, AI accelerator hardware, and other devices.

Disciplines: Applied Mathematics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

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.
In this project, you would help us develop the theory and software to perform these computations even faster, more reliably, or on different hardware platforms including GPUs or other accelerators. If successful, this work can improve the building blocks that are used by developers of scientific computing, engineering, and machine learning applications.

Disciplines: Applied Mathematics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

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 state-of-the-art predictive models for accelerating scientific progress. Despite recent successes, however, designing DNNs for scientific and engineering applications remains a challenging task, requiring time-consuming 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 end-to-end 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

Project Description:

Mission-critical data-intensive 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 data-intensive scientific machine learning applications.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

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 over-represented 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

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.

In this project, we will develop a stochastic gradient-based batch-wise learning procedure to construct an optimal transport map. We formulate a  learning problem inspired by the Hausdarff moment problem to match the moments of the transformed source distribution and the target distribution.  We will generalize this procedure for generic parametric maps  including neural networks and develop efficient algorithms to demonstrate efficiency in practical scientific machine learning tasks.

Disciplines: Applied Mathematics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

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 multi-temporal 3-D laser scanning (LiDAR), infrared and color video, 3-D 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

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, NP-complete problems etc. and use state-of-the-art quantum computers to solve them. This project would provide a unique experience of running jobs on adiabatic quantum computers like D-Wave 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 state-of-the-art 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

Project Description:

We are interested in developing efficient computational methods for synthesizing specific qudit gates necessary for quantum simulations of high-energy and many body physics problems. A qudit is the N-level generalization of the well-known 2-level 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

Project Description:

As scientific experiments and High-Performance Computing (HPC) infrastructure evolve, data capture rates continue to exceed the available storage, network, and compute infrastructure for subsequent post-processing. 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 large-scale scientific data.

Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

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 real-world 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 real-world 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