Past Projects

Project Description:

Collocation to solve the electronic Schreodinger equation is very attractive but has not been widely used in practice. The method replies on having a good set of trial functions to expand the unknown solution but does not require the calculations of matrix elements which can be very difficult for many basis sets. If one samples the solution on a 3D grid, the result is a matrix equation which can be rectangular in structure. Approaches such as the QR decomposition, the SVD and/or least squares can be applied to get the unknown coefficients in the trial function. The choice of grids can play an important role in a practical implementation of this approach and for molecules the design of an appropriate grid is not totally obvious. The student would be required to develop and perform numerical experiments that would look at appropriate basis sets and grids for some relatively simple diatomic molecules to ascertain whether the collocation approach can be made practical to compute the energy levels of these molecules. This could have important consequences for more complex systems where the difficulty lies in the evaluation of the Hamiltonian matrix elements using complex trial functions.

Disciplines: Applied Mathematics

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Gaithersburg, MD

U.S. Citizenship is a requirement for this internship

Project Description:

The construction of a three dimensional grid which respects the local and global symmetry of a polyatomic molecule is not a trivial task. Near each atom, there is approximate spherical symmetry. Outside the bonding region, things begin to look spherically symmetric in a coordinate system whose origin is near the center of charge. At intermediate distances one gets contributions from the atoms and the central grid. There are approaches which divide space into "fuzzy" cells which use these different grids weighted by some function which divides the mesh into separate meshes for the atoms and the central grid and then carries out integration over each subregion summing at the end to get the final integral. The construction of the weighting function is a critical aspect to achieve efficiency. In this project, we would like to examine various weighting functions to find one that results in minimum number of points to achive chemical accuracy. Some work along these lines has been done by Axel Becke and others but they did not deal with cses where the electrons can escape the atoms as in scattering problems. It is these problems in which we have the most interest.

Disciplines: Applied Mathematics

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Gaithersburg, MD

Project Description:

Constitutive models require derivations and experimental calibration that may be prohibitive as scientific applications demand increasing model complexity. Scientific machine learning provides new data-driven tools for model identification that embed physical laws in the learning algorithm, resulting in physically-consistent learnt models. This project is focused on the discovery of constitutive laws in the context of multiscale modeling and simulation. To achieve this goal, we will use a wide range of techniques including physics-informed neural networks, operator regression algorithms, and neural operator approaches. Applications of interest include transport in heterogeneous materials, mechanics, turbulence, and bio-medicine.

Disciplines: Applied Mathematics, and Mathematics (General)

Hosting Site:

Sandia National Laboratories (SNL)

Internship location: Livermore, CA

U.S. Citizenship is a requirement for this internship

Project Description:

For an electromagnetic pulse (EMP) application, the MCNP code is used for photon and neutron transport in air and to compute the energy deposition rate and photocurrent density. MCNP estimates these quantities as a function of space and time. The MCNP calculations are time consuming and can take weeks to complete. This project seeks to build and train deep neural networks to estimate the energy deposition rate and photocurrent density as a function of space, time, source particle type (neutron or photon), source particle energy, and source height. The neural networks will be trained on MCNP results for photon and neutron transport in the atmosphere. The students will focus on  building and training the neural networks and not on running MCNP to construct the training and  testing data set. However, the students will be introduced to the topics of MCNP and EMP, and will learn to run MCNP for a few problems.

Specific activities on the project include:

1. Generate training and testing data for machine learning predictors using the existing set of 1500 MCNP runs.
2. Build machine learning predictors for the energy deposition rate and electron current density for photon and neutron sources.
3. Build physics-based regression models that provide an intuitive understanding and compare the results with general machine learning approaches.
4. Learn to use MCNP and an understanding of EMP.
5. Analysis of MCNP and regression results. Python is currently used and this is the preferred language.

Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

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:

Full physics simulation-based optimization plays a critical role in geo-energy system design and management (e.g., carbon storage, oil/gas production). Often, thousands of simulations may be needed to achieve an optimal solution, which lead to unaffordable computational costs especially when the dimension of reservoir model is large and geologic uncertainty is considered. In this project, we will develop a computationally efficient framework based on deep learning algorithms (e.g., convolutional neural networks) associated with novel optimization algorithms for optimal carbon storage reservoir management including injection/extraction well placement optimization and well operational control optimization.

Disciplines: Applied Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Complex computations typically require the interaction of a large number of subnetworks which must coordinate communication and computation. Intriguingly, considerable mounting evidence has shown that the brain can exchange information on an “as needed” basis and reconfigure computation “on the fly”. It is hypothesized that the prevalent oscillatory in the brain provide a substrate to flexibly coordinate computation.

We have shown (Kirst et al., Nature Communications, 2016, TEDx Talk 2019) that brain-inspired coupled oscillator networks can indeed dynamically coordinate information exchange. Using appropriate feedback they can be turned into self-modifying systems which effectively reprogram themselves (Kirst et al., COSB 2017). In this framework, information is flexibly routed and processed when encoded in fluctuations that ‘surf on top’ of intrinsic oscillatory dynamic reference states akin to how radio signals are broadcasted via amplitude or frequency modulations of electro-magnetic waves (AM or FM).

Building on our theory, we aim to develop a brain-inspired analog computing framework that employs collective network dynamics to coordinate large scale distributed computation and enable flexible and adaptive processing in dynamically self-reconfiguring neuronal networks.

These tools will have a broad range of applications, including dynamic scene understanding, attention guided computation, belief propagation based inference, as well as the coordination of large scale computation in ensembles of neuromorphic expert systems.

The project will expose the students to mechanisms for flexible computation combining analytical tools form information theory and stochastic dynamical systems (information dynamics), computational modeling as well as novel approaches to large-scale machine learning.

Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

Project Description:

The topic of this project is the development and study of events in dynamic systems that are able to deal with causal reasoning. Learning systems need to behave desirably in always changing environment settings, so they must gain causal understanding of their environment. This project has two aims (1) to use causal inference to model causality to help understand better causes, impacts and relationships so the system can make better decisions and (2) to advance the underexplored intersection of machine learning and causality. We will apply the methods in real-world data and evaluation.

Disciplines: Analysis, Applied Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

The overall objective of this framework is to enable complex interactions between physics-based and data-driven systems to be accounted for in real-time decision-making while retaining credibility in mitigating rare events. This project will develop a data-driven surrogate model-assisted deep reinforcement learning (DRL) framework to achieve fast and uncertainty-aware decision-making. It has the following tasks: (1) Data-driven surrogate modeling and chance constraints reformulation: We will develop a sparse Gaussian process (SGP)-based surrogate model to describe the relationships between uncertainty sources and the chance constraints. In particular, the SGP surrogate will be decomposed into two stages: the statistical-moment-based, i.e., the mean and standard deviation, rough approximation, and the error processing strategy to reduce the learning complexity. This allows us to achieve an accurate reformulation while retaining useful statistical moment information. Note that no prior distribution assumption is needed for uncertain variables. (2) Integrated SGP surrogate model and DRL algorithm for fast decision making: to enable a good performance, nonlinear SGP is usually required, yielding non-convex chance-constrained optimal power flow (OPF). This significantly increases the difficulty of nonlinear programming methods in getting reasonable solutions and achieving fast decision-making. We will develop new safe DRL algorithms, i.e., a safe actor-critic network that can continuously interact with the SGP surrogate model and train an agent to learn optimal control strategies. Direct interaction with the surrogate model instead of the original complex physical model significantly improves the training speed. Once the training is done, the agent can make fast control decisions with new input variables, i.e., forecasted DERs and loads.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Livermore National Laboratory (LLNL)

Internship location: Livermore, CA

U.S. Citizenship is a requirement for this internship

Project Description:

How do animal groups adapt their movement decisions to a changing environment of obstacles? Engineers have so far failed to create movement algorithms for autonomous groups that can successfully negotiate a potentially infinite set of environmental encounters. It is therefore extraordinary that nature has solved this problem with seemingly simple organisms whose behaviors are driven primarily by the need for food, to escape predation, or to reproduce. This presents a tantalizing opportunity to better understand the fundamental nature of communication between the individuals of a moving group that needs to sense, respond, and adapt to challenges and obstacles in their environment.

This internship will involve developing simple agent-based models of obstacle navigation, simulating those models computationally, and devising/testing various statistical metrics drawn principally from information theory to quantify inter-agent communication as obstacles are encountered and circumnavigated. These metrics will eventually be applied to trajectory data from experiments using both dermestid beetles and simple, non-interacting robots in order to ascertain the extent to which social interactions enhance navigational capabilities.

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: Vicksburg, MS

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

Project Description:

This project is focused on modeling and simulation of nonlocal equations in the context of multiscale/mechanics problems. One of the most important open problems in this field is the identification of ``kernel functions’’ characterizing nonlocal operators. This non-trivial and ill-posed problem raises many mathematical and computational challenges. We plan to tackle model identification by combining 1) powerful tools of machine learning and physical principles and 2) versatile surrogates (e.g. neural networks) and a generalized nonlocal vector calculus that provides a universal definition of nonlocal operators. More specifically, we plan to develop a data-driven generalized tool based on approximations of the kernel function with neural networks, radial basis functions, or other complex surrogates. The outcome is a unified framework for new-model discovery.

Disciplines: Applied Mathematics, and Mathematics (General)

Hosting Site:

Sandia National Laboratories (SNL)

Internship location: Livermore, CA

Project Description:

The internship will entail activities with the Athens Fire Lab of the Southern Research Station of the USDA Forest Service, in Athens, GA. The intern would gain experience collaborating with several Forest Service scientists, graduate students, and interns in Wildland Fire Science. This research is critical as wildfires are expanding and prescribed fires are becoming more important for mitigating wildfires and maintaining ecosystem health. An important part to understanding fire, is understanding the role of fuel or in this case vegetation, for driving fire behavior. We hope to utilize the intern’s mathematical expertise to advance our analysis, predictions, or modeling approaches for characterizing 3D forest vegetation structure and how it relates to physical properties of wildland fire, such as heat transfer and interactions with wind and fuel moisture properties. We aim to understand the mechanistic links between vegetation and fire to more accurately predict fire effects and feedbacks with fire-atmosphere dynamics. Mathematical relationships between multi-dimensional information, i.e. spatial and temporal changes in fire spread and vegetation (before, during and after fire) are also of interest. Ultimately, we will collaborate with the intern’s skills and interests to design an achievable goal for the internship within the Lab’s scope of work. The intern would likely utilize remote sensing data, such as 3D laser scanning (LiDAR: Light Detection And Ranging), infrared thermography and hyperspectral imagery, and use their associated instruments in a laboratory or field setting. There will be opportunities to visit forested field sites in the southeast to learn about wildland fire management, forest and fire ecology, prescribed burning practices and experimentation, or deployment of remote sensing instrumentation. During this internship, all safety standards are set high and COVID restrictions may limit in-person interactions and field experience.

Disciplines: Analysis, Applied Mathematics, and Mathematics (General)

Hosting Site:

USDA Forest Service Southern Research Station, Athens Forestry Laboratory

Internship location: Athens, GA

Project Description:

The study of low-magnitude earthquakes (M < 5.0) may serve as good indicators of where seismic hazards exist along an active fault zone should a larger magnitude earthquake occur. We have developed a new technique that combines Interferometric Synthetic Aperture Radar (InSAR) estimates of crustal displacement with a Deep Learning method to extract a signal from low magnitude earthquakes. The technique is being applied to the Nacimiento-Gallina fault system of northern New Mexico given the high number of low magnitude earthquakes that have occurred in this region and proximity to critical infrastructure of Los Alamos National Laboratory. The technique was successfully applied to the July 30, 2020 event (M = 3.7) and progress is underway for application to the stronger and more recent event (M = 4.2) that occurred on July 12, 2021. The goal of this project involves using the crustal displacement signal extracted from this technique within an earthquake deformation model1 to detect more detailed information on the depth, length and width of the fault plane, as well as the amount of fault slip for each event under study. A script for the targeted model has already been developed and successfully applied to investigate properties of a deformation field caused by geothermal activity in northern Nevada. Successful application of the model to the Nacimiento-Gallina fault is expected to reveal more information about this fault system that could be used to better assess the potential for hazards in the vicinity of the fault including critical infrastructure at the nearby Los Alamos National Laboratory.

It is expected that the student will gain experience working in a multi-disciplinary team with expertise in remote sensing, computational modeling and Machine Learning. They will also be able to contribute to research being used in development of a manuscript for submission to a peer-reviewed journal, as well as the Probabilistic Seismic Hazard Analysis (PSHA) report update that will be submitted to the Department of Energy (DOE). There will be opportunities to interact with other students working in a similar field as well as for presenting findings to a professional scientific audience.

Disciplines: Applied Mathematics, and Mathematics (General)

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

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:

Challenges to determine optimal (i.e. most stable) crystal surface configurations stem from several different factors; these include, notably: the need to use large supercells, which slows down the calculation, the need to include reconstruction effects, which implies several steps until converging to an optimal geometry, and the need for accurate forces, which implies going beyond simple classical potentials [1]. Here we propose to use a Density Functional  based tight-binding method (DFTB) as implemented in the LANL LATTE code for a fast calculation of the energy surface [2]. We will couple this code with an in-house slab generator which will explore several Miller indices for a better search. Either a Simulated Annealing or a Simplex method will be used to minimize surface energy across the Miller space. The coupling with the LATTE code will be done using the MDI library to parallelize the computation of the energies [3]. LATTE will be compiled using BML[4] and PROGRESS[5]  libraries which enables the use of GPUs such as the new A100 Nvidia GPUs recently incorporated on LANL’s Darwin HPC cluster.

The student will develop many different skills such as complex geometry calculations involved in the crystal structure research, and the HPC techniques involved in memory distributed calculations and GPU acceleration. The student will also learn to develop a scientific code using best software practices, including version control method and regression testing. We will use this code to produce a catalog of the most optimal crystal surfaces of High-Explosive (HE) crystals such as HMX. This is critical to be able to model and predict HE crystal growth and shape, notably. Some previous experience with HPC and Fortran programming is recommended, as well as a fair geometry and linear algebra math background.

Disciplines: Applied Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Many practical applications can benefit from building accurate, stable and efficient dynamical system surrogates from multimodal data using scientific machine learning (SciML). Many systems that arise from such applications have a large fraction of their interesting dynamics constrained to a low-dimensional manifold. However, low-dimensional data-driven dynamical system surrogates exhibit poor performance when used for long-time predictions, even when interpolations and short-time predictions seem reasonable. State-of-the-art large-scale dynamical system training relies almost entirely on cost-function minimization with simple stability promoting extensions, such as ad-hoc constraints on the Jacobian, or regularizations of the neural network, to promote smoothness. Unfortunately, these methods do not address the limited stability of data-driven surrogate models. For long-term predictions, low stability manifests itself as solutions that explode or converge to unphysical hyperbolic sets. This project aims to address the issue of stable long-time prediction from massive datasets of high-dimensional dynamical systems. A particular attention will be focused on stability-enhanced structure-preserving neural network. As a complementary focus, the project will also investigate the mathematical foundations and rigorous approximation properties of proposed ML architectures.

Disciplines: Applied Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

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

U.S. Citizenship is a requirement for this internship

Project Description:

Representing continuous, real-world entities in discrete, digital form is one of the most significant constraints in exploiting computational power. Data dimensionality issues accompanying hyperdimensional, complex datasets quickly overwhelm static, Euclidian representation systems and may entangle or hide different explanatory factors of variation behind the data. This research seeks to understand if a non-Euclidian geometry-based model, in conjunction with a dynamic geometry query algebra, can extract more intuitive concepts and relationships from large, hyperdimensional data by varying inter feature distances, covariance, and feature importance. The model will significantly enhance the ability to extract meaning and relationships from complex data by functionally projecting it onto dynamic, spherical, hyperbolic, or mixed surfaces. Relationships will be extracted from a spectrum of data projections similar to flat planes intersecting a changing hyperbolic surface using a novel query algebra.

The student intern will collaborate with a team of researchers at the U.S. Army Engineer Research and Development Center. By the conclusion of the project, the student intern will be familiar with techniques for projecting complex, real world data onto hyperbolic, spherical, and mixed surfaces, measuring changes in inter-feature distances and resultant covariance and feature importance variances. The student intern should have introductory coursework in numerical methods and be proficient in a higher-level programming language, such as Python or R, for implementing numerical methods.

Disciplines: Geometry, Probability and Statistics, and Topology

Hosting Site:

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

Internship location: Hanover, NH

U.S. Citizenship is a requirement for this internship

Project Description:

The Coastal Hazards System (CHS) is a national coastal storm hazard data resource for probabilistic coastal hazard assessment (PCHA) results and statistics, storing numerical and probabilistic modeling results including storm surge, astronomical tide, waves, currents, and wind. CHS is an up-to-date and easily accessible environment for development, storage, and rapid access to PCHA hazard results, additional information such as tides, wind and rainfall, and documentation of the results. Based on high-resolution numerical modeling of coastal storms that spanning practical probability and forcing-parameters, PCHA results directly support probabilistic design or risk assessment.

Disciplines: Analysis, and Probability and Statistics

Hosting Site:

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

Internship location: Hanover, NH

Project Description:

Wind energy science relies heavily upon computational fluid dynamics modeling to understand the wind-plant operating environment. High-fidelity modeling—first-principles atmospheric simulations requiring supercomputers to run—can deliver detailed information about the wind-plant environment, from relatively large atmospheric scales (> 1 km, “mesoscale”) down to wind-turbine scales with resolved turbulence (< 100 m, “microscale”). Flow data from these simulations are used to develop physical insights and improve engineering tools. Combined, these insights and tools inform the design and optimization of next-generation wind turbines and wind plants, development of wind-turbine controls and wind-plant operational strategies, and evaluation of how wind energy integrates with the other renewable-energy technologies on the grid. The end goal of this research is to enable technological advances that reduce the cost of energy.

Funded by the US Department of Energy, the Mesoscale-to-Microscale Coupling (MMC) project addresses modeling challenges encountered when simulating realistic wind-energy inflow to a wind plant. Earlier high-fidelity modeling efforts focused on simulating the microscale environment with canonical atmospheric conditions. In a real atmospheric boundary layer, however, wind and temperature fields vary over time and space, driven by the solar diurnal cycle or weather events. To represent more realistic conditions for the microscale simulation, additional large-scale flow information is needed for initial and boundary conditions. This flow information may come from field measurements or mesoscale weather models.

The MMC team has recently developed a profile assimilation technique for coupling mesoscale weather and microscale wind-plant simulations to provide more accurate information about the wind-plant environment than ever before. The approach, which uses mesoscale time–height data to drive the microscale solver through source terms, has been validated and applied to a variety of case studies in different environments. However, there are two challenges in applying profile assimilation. First, field measurements of wind speed and temperature are in general neither complete (data are missing due to limitations of the technology or measurement noise) nor span the entire computational domain (up to 1-2 km). Second, mesoscale simulations provide complete data but have substantial uncertainty arising from a wide array of modeling choices. Therefore, the accuracy of the coupled simulations is limited by the accuracy of the mesoscale data and, ideally, would require either a well-designed field campaign with optimally performing instruments or high mesoscale model skill.

To develop a more robust coupling approach, the intern will evaluate a variety of strategies for calculating microscale source terms based on arbitrary mesoscale data. The new strategies will address the current shortcomings by allowing the microscale solver to correct potential errors in the input data that may arise from data infilling or low mesoscale model skill. To this end, the intern may explore a variety of statistics and controls-theory approaches to more realistically represent the source terms. These strategies will be compared against benchmark simulations from one or more ongoing studies.

An expected outcome of this work is one or more journal publications detailing the new simulation strategies and detailing MMC best practices. Over the course of the internship, the intern will have the opportunity to interact with wind energy and atmospheric science researchers engaged in model development, validation, and applications, from NREL as well as partner institutions such as the National Center for Atmospheric Research. The ideal candidate should have knowledge of fluid dynamics, partial differential equations, numerical methods, and C++ programming.

Disciplines: Applied Mathematics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO

Project Description:

We are developing efficient latent-space dynamics identification (LaSDI) learning algorithm to accurately accelerate 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, 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

U.S. Citizenship is a requirement for this internship

Project Description:

This project develops and tests underwater acoustic deterrents systems (UADs) for Invasive Carp (IC) control throughout the Great Lakes and Mississippi River basins. The project goal is to determine the most effective and efficient combination of sound technology for preventing the IC from becoming established in the Great Lakes by discouraging their upstream movement. This year focuses on three evaluations of underwater acoustics as a deterrent technology at pinch-points (Lock No. 19), a soft bottom reach (HMS East Pit, Morris, IL), and lab-based sound profile development for IC. In addition, providing a framework for deploying and testing uADS. Tasks for this year that may be of interests to students are the development of sound mapping code for challenging shallow water approach channels or working with animal movement data and tema to develop predictive responses to several fish deterrents (i.e., acoustics, electrical, CO2, air bubble curtains).

Disciplines: Analysis, and Applied Mathematics

Hosting Site:

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

Internship location: Hanover, NH

Project Description:

Deep Learning (DL) models are increasingly used in DOE-relevant science applications for prediction, classification, and decision support. Navigating the zoo of DL models and identifying the best architecture for successful application on a science problem that has previously not been addressed with DL models is a challenge.

In this project, your research will focus on applying LBNL-developed DL model architecture optimization methods to a problem in high-energy physics. In particular you will identify highly accurate DL models that can be used to replace modules in high energy physics simulations with the potential of significant reduction in simulation time. There is an opportunity to contribute to further development of the architecture optimization algorithm.

Disciplines: Applied Mathematics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

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:

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

U.S. Citizenship is a requirement for this internship

Project Description:

Microorganisms can release electrons by breaking down organic compounds in soil. The microbial fuel cell (MFC) technology has been developed to harvest electrons from this process. Traditionally, MFCs have been made with wastewater, soil, or sediments as an alternative power source. More recently, they have been used as sensors in the environment. Our recent work determined that voltage changed when a soil was exposed to a contaminant. We seek to further analyze the response of the voltage signal to the introduction of contaminants through statistical and machine learning approaches. 

The candidate will join an interdisciplinary team focused on understanding terrestrial signals and sensing. The candidate will be expected to present her/his/their findings to the larger team on a weekly basis. 

The candidate should have experience using multivariate statistics on biological datasets, linear mixed effects modelling, and/or machine learning. The candidate should have experience using statistical analysis programs such as MATLAB, R, or something equivalent, as well as have familiarity with coding in Python.

Disciplines: Mathematics (General), and Probability and Statistics

Hosting Site:

U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL)

Project Description:

Berkeley Lab’s National Energy Research Scientific Computing Center (NERSC) has an opening for a Data Scientist intern. NERSC operates a sampling framework that takes measurements continuously across all compute nodes in Cori. Currently there are multiple petabytes of this data available. The person in this position will help analyze this data to help increase application performance and throughput and characterize the NERSC workload and analyzes the characteristics of scientific application codes and their usage on HPC systems and monitors NERSC system utilization and capability usage. He/she is responsible for managing user data collected from NERSC High Performance computational and data systems and assisting with operational and system-level data.

What You Will Do:

• Participate in a team that collects and stores data collected from NERSC HPC systems relating to applications and their performance, job scheduling, and systems operations.
• Apply statistical methods to data collected from NERSC HPC systems to draw inferences (e.g. detect anomalies, identify correlations, optimize scheduling and job placement) that guide how NERSC configures systems, makes policy decisions, and acquires systems.
• We have time series data of all compute nodes of Cori. We are looking into extracting insight from this data using Time Series Analysis, Signal processing.
• Implement and maintain application performance monitoring methods and detect and report anomalies and changes.

• Statistical methods for data analysis, including machine learning and time series analysis
• Ability to work with databasesAbility to produce insightful inferences from data and produce clear reports and summaries.
• Strong communication and interpersonal skills are required as is an ability to work productively in groups.

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

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

U.S. Citizenship is a requirement for this internship

Project Description:

Engineering and application-oriented mission science aim to alter system behavior to achieve specific objectives, or to make optimal decisions/predictions regarding system behavior. Many real-world applications involve highly complex systems which are computationally expensive to simulate and whose dynamics are substantially uncertain. Effective predictive science must often resort to surrogate models that represent a reduced form of the system dynamics, in order to explore the space of uncertainties in a more computationally tractable manner.

AI and Machine Learning (ML) have made data-driven models, such as deep neural networks, widely popular for learning such surrogates, which can be used for making predictions or decisions regarding highly complex real-world systems and problems. However, complex systems are often highly nonlinear, while data for learning the surrogates are typically scarce and costly to acquire. Many “big data” models in the ML literature fall short of serving as adequate surrogates in this setting, and further fail to quantify scientific uncertainties in the system and their impact on the attainment of the scientific/engineering objectives at hand.

This project aims to develop Scientific ML techniques that enable objective-driven uncertainty quantification (UQ) for data-driven models in a Bayesian paradigm. Especially, we will focus on deep generative models that can be used for molecular design – e.g., materials design or drug discovery – and develop theories and algorithms that can ultimately lead to an effective uncertainty-aware learning procedure of effective surrogates for complex systems. Specific research topics of interest include effective strategies for integrating ODE/PDE/mechanistic models with data-driven models and multi-objective/high-dimensional Bayesian Optimization (BO) in the latent space.  Potential applications of this methodology will be discussed with the student but may focus on generative molecular design (GMD) for scientific discoveries in materials and biomedical sciences.

Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics

Hosting Site:

Brookhaven National Laboratory (BNL)

Internship location: Upton, NY

Project Description:

Randomized sketching has been used in our work on finding low rank structures in various dense and sparse matrices. We mostly use dense i.i.d. Gaussian in sketching. But the cost of traditional matrix-multiplication often becomes the bottleneck. In this project, we would like to experiment with alternative random sketching operators, including the structured sketching like Sparse Johnson-Lindenstrauss transform (STLT), or Subsampled randomized trig transform (SRTT), or SRFT.  They are faster than dense Gaussian but research is needed to understand whether they provide acceptable quality, and what are the time and accuracy tradeoffs. The research will be conducted in the context of STRUMPACK (https://portal.nersc.gov/project/sparse/strumpack/) and ButterflyPACK (https://github.com/liuyangzhuan/ButterflyPACK).

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

U.S. Citizenship is a requirement for this internship

Project Description:

Battle damage assessment involves assessing the physical damage to buildings and infrastructure from satellite images taken before and after an event. This project has focused on developing automated methods of doing so using neural networks. However, several factors such as adverse weather, the variation in appearance of damage, lack of generalization from one geographic region to another, limited labeled data, and the need for a confidence measure make this a complex problem. An intern on this project will have the opportunity to explore one of these factors (or another related aspect). We are seeking candidates with experience in programming (preferably python) and an interest in applying mathematical or statistical principles to computer vision and machine learning.

Disciplines: Mathematics (General), Operations Research, and Probability and Statistics

Hosting Site:

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

Project Description:

This project focuses on extending a loosely coupled multi-physics scheme for fluid-structure interaction [Journal of Computational Physics 373 (2018): 455-492] to high-order finite elements. The extensions are two-fold: a continuous FEM-based loosely coupled scheme with high-order accuracy up to boundary and a monolithic scheme that is accelerated by the physics-based preconditioning which is motivated by the loosely coupled scheme. As a first step and proof of principle, we will consider the coupling between incompressible Navier-Stokes equations and a beam equation or a moving rigid body. The proposed algorithms will be implemented and optimized as an efficient and accurate computational framework for solving general FSI problems through MFEM (mfem.org). This project will be conducted through close collaborations with the MFEM developing team.

Disciplines: Applied Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Deep Learning (DL) models are becoming increasingly popular for use in DOE-relevant science applications, including earth sciences, high energy physics, and network science. Optimizing DL model architectures by tuning hyperparameters is challenging and suffers from the curse of dimensionality. Moreover, it is not well understood how individual hyperparameters impact the predictive performance of DL models.

In this project, your research will focus on developing sensitivity analysis (SA) methods specifically for DL models architectures. You will implement SA methods that are able to take into account the distinct challenges posed by evaluation DL model performance (integer constraints, prediction variability). Finally, there is an opportunity to try out your developments on a real-world application.

Disciplines: Applied Mathematics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

U.S. Citizenship is a requirement for this internship

Project Description:

The Arctic is rapidly changing as the climate warms. For instance, as permafrost thaws, aspects of the landscape are subsiding, while others are flooding.  Microorganisms within the soil are also affected by climate change, and in turn, permafrost thaw.  These microorganisms mediate important reactions for plants and animals.  We have empirical data from laboratory and field studies measuring soil biological processes under a range of soil temperature and moisture combinations.  We seek a candidate who can develop models describing the soil biological processes. 

The candidate will join an interdisciplinary team focused on understanding microorganisms in cold regions.  The candidate will perform data analysis, modelling, integration, and validation. They will develop and validate models to predict biological processes through data inputs such as soil texture, soil moisture, and soil temperature. The candidate should have experience developing algorithms and/or applying statistical methods to complex datasets.  Experience using MATLAB, Python, or R is preferable.  The candidate will be expected to present her/his/their findings to the larger research group on a weekly basis.

Disciplines: Mathematics (General), and Probability and Statistics

Hosting Site:

U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL)

Project Description:

The project is to develop an autotuning software framework via statistical and machine learning techniques, such as multitask and transfer learning using Gaussian process.  The goal of this work is to help the HPC codes (including parallel mathematical libraries and simulation codes) to choose the near-optimal parameters setting on a large-scale parallel machine, which take into account the characteristics of the input problems. The typical minimization metrics are runtime and memory usage.  Since each execution (“function evaluation”) of the HPC code is expensive and takes a lot of resources, it is not feasible to use a brute-force approach (e.g., grid-search) to search for optimal parameters.  Therefore, it is critical to “learn” some knowledge from the limited number of executions with certain input instances and build a prediction model for the unseen tasks. The research will be conducted in the context of GPTune (https://gptune.lbl.gov/).

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

U.S. Citizenship is a requirement for this internship

Project Description:

High-amplitude acoustic wave propagation in a porous medium can exhibit two types of nonlinearity: convective and Forchheimer. Convective nonlinearity is a departure from a constant wave speed due to finite wave amplitude. Forchheimer nonlinearity is a departure from the Darcy drag law due to high Reynolds number flow within the porous structure. When combined at the interface between a homogenous fluid and porous medium, these two nonlinearities result in a nontrivial boundary condition. We propose to investigate the relative significance of convective and Forchheimer nonlinearity at this interface by deriving one-dimensional weakly-nonlinear jump boundary conditions, accurate to second order in the acoustic perturbations. As a starting point, the student intern will use the volume-averaged jump conditions due to Ochoa-Tapia and Whitaker [Int. J. Heat Mass Transfer, 1995, 38(14), 2635–2646] and extended by Mößner and Radespiel [Computers & Fluids, 2015, 108, 25–42] for compressible flow. The student intern will then apply principles of dimensional analysis to obtain uniformly accurate second-order relations. To examine the implications of the obtained boundary conditions, the student intern will implement a numerical solution for a Burgers equation in the homogeneous and porous media, and study the reflected and transmitted waves with respect to various parameters for both convective and Forchheimer effects.

The student intern will collaborate with a team of researchers at the U.S. Army Engineer Research and Development Center on this project. By the conclusion of the project, the student intern will be familiar with the principles and applications of volume-averaged homogenization, analytical properties of acoustic wave fields, principles of Darcy- and Forchheimer-type flow resistivity, and dimensional analysis. The student intern should have introductory coursework in continuum mechanics and numerical methods, and be proficient in a higher-level programming language, such as Python, for implementing numerical methods.

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

Hosting Site:

U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory (CRREL)

Internship location: Hanover, NH

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

U.S. Citizenship is a requirement for this internship

Project Description:

Ocean waves are directionally distributed, but inferring the directional distribution from measured wave properties is not a straight forward task. A directional distribution can be thought of in terms of a Fourier series. Measurements provide some information about the directional distribution, but not all the information. Buoy measurements are known as single-point-triplets because they measure 3 complimentary aspects of the surface waves at a single point in space. Single point triplets give the low order moments of the directional distribution - a1, b1, a2, b2. A so-called data adaptive method is used to estimate the remaining degrees of freedom. A powerful alternative to a single-point-triplet measurement is a spatial array. At the Field Research Facility (FRF) in Duck, N.C., there is a unique spatial array of 15 pressure sensors in a cross-like pattern located in the the nearshore at about 9 m depth. While arrays can give a much higher resolution directional distribution, i.e. more Fourier coefficients, an estimator is still required to give the full directional distribution. Since its inception in the early 90s, the 8-m array has been processed with an Iterative Maximum Likelihood Method. This method can produce high quality data, however, the array is susceptible to errors of various flavors and requires a lot of human intervention. There has been a lot of progress in the directional estimators since 1990, so we are motivated to test alternative methods.

Testing different methods will be the goal of the internship, but the intern will need to learn a lot of fun things along the way, including the directional properties of ocean waves, how these properties are measured and how what is measured is related to the directional distribution. The intern will learn about directional estimators and perform literature survey. The intern will gather and curate pre-existing code to implement a number of these estimators and perhaps write code implementing existing methods. The intern will develop a framework for testing these methods. Specifically, we want a method to be 1) more robust (to our typical errors), 2) to improve the estimated directional distribution (closer to truth), and 3) to improve the processing (e.g. code readability or processing time).

The location of the project will be at the FRF in Duck, N.C. There the Intern can interact with a number of other interns and scientists in that work in the fields of ocean waves, coastal engineering, nearshore processes, remote sensing, robotics, and machine learning. Strong programing skills in either MATLAB or Python is preferred.

Disciplines: Applied Mathematics, and Mathematics (General)

Hosting Site:

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

Internship location: Duck, NC

Project Description:

Computing Wasserstein distance (also known as Kantorovich--Rubinstein distance) arises in many contexts; we are primarily interested in applications to Topological Data Analysis, where the distance is computed between so-called persistence diagrams --- descriptors that capture the shape of data at different scales.

The auction algorithm (developed by Bertsekas in the 1980’s) is quite efficient in practice, despite having high worst-case complexity (but even with it, computation of distances between diagrams that we get from large-scale simulations is still infeasible). The algorithm belongs to a class of primal--dual algorithms, and the dual variables can be interpreted as prices. While the algorithm converges for any initialization of the dual variables, if the initial values are close to the optimal values, the convergence is much faster.

The idea of the project is to predict close-to-correct prices, by approximating the base metric by sampling many random trees on the union of the inputs. The reason is that the tree metric --- a graph metric on the tree with edge weights given by the distances between points --- allows for a very efficient computation of the Wasserstein distance. We will use the prices from the exact solutions on trees to approximate the prices for the original dual problem.

Before starting to implement this idea and run experiments with it, it will be necessary to:

• have basic knowledge of primal and dual problems in linear programming
• understand how the original auction algorithm for assignment problem works
• read the paper about exact solution of the optimal transportation problem in tree metric
• learn algorithms to sample random trees
• have C++ programming skills (the experiments will be using the existing software to compute Wasserstein distance)

While none of these items requires going too far into theory, if the student is new to all these topics, it is probably not a good option. No knowledge of Topological Data Analysis is required, but it helps to motivate the problem (yet, there are many other reasons to try to accelerate the computation of the Wasserstein distance).

Disciplines: Applied Mathematics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

Project Description:

Hierarchical  Temporal Memory (HTM) is one model of how the neocortex in the human brain memorizes sequences using sequential sparse activation of  pyramidal neurons.  There are three key features of HTM:  (i) a sparse data representation and sparse spiking of neurons,  (ii) a Hebbian  learning rule (neurons that fire together, wire together),  and (iii) the sequential (rippling) activation of neurons for encoding and retrieval analogous to the traditional  recurrent neural network model. These features allow HTM to perform online learning and accurate prediction even in the presence of noise. Recently, the contextual sequential encoding and retrieval of sequence have been demonstrated in the human brain. Experimental studies have shown that when retrieving memories, the human brain replays the neural patterns that were encoded when experienced at the first time.  The goal of this research is to build a mathematical framework that be used to understand how the features of HTM impacts its ability to memorize sequences, its tolerance to noise, how it is different from traditional  Recurrent Neural Network in its ability to generalize, and how these different models can be integrated.

Disciplines: Operations Research, Probability and Statistics, and Topology

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

Project Description:

Among the many recent advancements in machine learning and artificial intelligence, operator learning has emerged as one technique for learning mappings between function spaces -- see, for example, [1] and references therein.  One promising application of such methods is the construction of neural operator networks as surrogate models for dynamical systems.  In this project we will study the performance of such neural operator networks as surrogate models for time-dependent systems exhibiting complex dynamical behavior. Dependence on model parameters (for example, fluid viscosity) will also be taken into account. 

By participating in this project the student will gain experience with emerging scientific machine learning techniques for solving problems governed by differential equations.  Use of the Linux operating system and programming in Python and PyTorch will be required to carry out the necessary computational experiments.

References
----------
[1] Lu Lu et al., "A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data", 2021. arXiv:2111.05512v1

Disciplines: Applied Mathematics, and Mathematics (General)

Hosting Site:

Brookhaven National Laboratory (BNL)

Internship location: Upton, NY

U.S. Citizenship is a requirement for this internship

Project Description:

As part of this project you will learn to apply cutting edge numerical simulation tools to gain understanding of how fluids move through the earth in response to a nuclear blast.  The simulations are highly coupled, with feedbacks in pressure, flow, temperature, and rock damage. Part of the project requires reduced order models relying on probability and statistics that would allow you to work with the CCS division (COMPUTER, COMPUTATIONAL & STAT SCIENCES) at Los Alamos, a group of world class mathematicians.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Emerging spatially explicit coupled fire-atmosphere models of wildland fire behavior are revolutionizing both fire research and fire management. The framework of these models, specifically QUIC-Fire, shows great promise for linking to existing fire effects prediction systems or building new spatially explicit ecological models of fire effects and ecosystem processes affected by fire. The successful applicant would have the opportunity to explore and development new ways to predict fire effects from QUIC-Fire outputs of fire energy and heat transfer on soils, vegetation, and forest dynamics, or other topics of interest. The intern would have access to both a state of the art combustion laboratory and an interdisciplinary team of physicists, meteorologists, fire ecologists and social scientists whose work focuses on understanding and managing wildland fire. The topic is meant to be flexible and will be tailored to the successful applicant's skills and interests.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

USDA Forest Service, Southern Research Station

Internship location: Knoxville, TN

U.S. Citizenship is a requirement for this internship

Project Description:

The goal of the Machine Assisted Mission Engineering Project (also known as Thunderdome) is to improve the Army's warfighting capability through novel machine learning techniques to find tactical advantages in simulated engagements.

The candidate will work with a small team of researchers to either (a) investigate reinforcement learning techniques for both real-time strategy games and combat simulation or (b) investigate machine perception methodology for machine learning.

The candidate should have experience using the Python language.

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

Hosting Site:

U.S. Army Corps of Engineers, Information Technology Laboratory (ITL)

Internship location: Hanover, NH

Project Description:

This project is focused on modeling the behavior of complex fluids, specifically fluid-solid flows. One of the open problems in the field is how to model the migration and behavior of suspensions of polydisperse particles. We plan to address this by using multifidelity physics-informed neural networks with simulation and experimental data to determine closures to continuum-scale mathematical models of particle migration. This research will allow for fast computations of particle migration at a continuum level, without the need for costly experiments or computationally expensive codes.

Disciplines: Applied Mathematics

Hosting Site:

Pacific Northwest National Laboratory (PNNL)

Internship location: Richland, WA

Project Description:

This project involves designing new methods to train generative neural networks (NNs). Generative NNs are trained, using a given data sample, to learn the underlying distribution and sample more datapoints (with similar statistical properties). Such networks have applications in several areas of science, including high energy physics and astronomy.

In this project, we want to create and study a new statistical distance metric between probability distributions, which can be used as a cost function for training generative NNs. We will study the training efficiency and the quality of generative networks trained using the new distance metric in a variety of applications. In addition to standard benchmarking applications of generative networks, we will also explore the usage of this technique to learn the distribution of quantum data (data produced from simulations of quantum computers). Students will be involved in a combination of theoretical work (e.g., deriving the properties of the distance function, including proving its metric-ness) and practical work performed using modern machine learning and quantum computing tools. The entire project may be performed remotely, with periodic virtual meetings.

Students will work in collaboration with researchers at the Fermi National Accelerator Laboratory (Fermilab). Fermilab is a premier national laboratory overseen by the U.S. Department of Energy, with a primary focus in the fields of particle physics and quantum information science. It is the home of several ongoing high-profile experiments and collaborations, including LBNF/DUNE, Muon g-2, SQMS, and LPC. Fermilab's Tevatron was a landmark particle accelerator, where the top quark was discovered in 1995.

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

Hosting Site:

Fermi National Accelerator Laboratory (FNAL)

Internship location: Batavia, IL

Project Description:

The Computational Earth Science (EES-16) group at Los Alamos National Laboratory is looking for a highly motivated student with a strong background in applied mathematics, statistics, or scientific programming to join us as we develop computational and machine learning tools to understand the hazards associated with explosive volcanic eruptions. The computational models used to simulate transport of ash from erupting volcanoes are often quite expensive and not readily amenable to probabilistic hazard analyses because of the sheer number of simulations that would be required, especially in areas with a high density of volcanoes. Recent work has shown that Gaussian process emulators are able to capture some of the predictive capability of higher fidelity models, while providing robust uncertainty quantification that is needed for hazard analysis. However, they generally have not been taken beyond the proof-of-concept phase for specific application purposes. In this work, the student will assist in developing a Gaussian process emulator for volcanic ash transport based on high fidelity computational fluid dynamics models and apply the model to specific sites to understand the impacts of volcanic ash deposition. The student will collaborate directly with LANL scientists and will be given freedom to pursue topics of their choice within the bounds of the project scope. Furthermore, there will be opportunities to interact and work with other students and group members. No prior knowledge of volcanoes is required, but an interest is preferred. Proficiency in either Python or R is required.

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:

An increase in bombing attacks using conventional explosives or more sophisticated vehicle borne improvised explosive devices (VBIED) or personnel borne improvised explosive device (PBIED) has led to an increase interest in understanding blast-induced loads on structures. The main focus of those investigations usually centers on designing structures which can sustain these blast induced loads. But in this study, the researchers want to take a fundamental step backwards and focus on properly characterizing the blast load in the near field. Within the near field, a combination of the detonation products from the explosive energy contributes to the highly nonlinear nature of the air shock. The near-field blast is characterized by the sudden increase in high-amplitude pressure and short-duration pulses with highly nonlinear waveforms which is visualized when plotting the pressure-time history. The current state-of-practice for mathematically describing blast waveforms found in the open literature is the Modified Friedlander. Although the Modified Friedlander is used in blast design manuals, the assumptions does not include the rate of pressure decay within its mathematical form to properly account for anomalies observed in the near-field. This over-simplification within the mathematical form opens the door for new equations describing the decay coefficient as well as other near-field anomalies. 

Student researchers will review the technical literature and understand expressions that describe the blast phenomena for relevant comparisons to be made. The objectives will include developing new blast wave form equations for describing a given initial set of historic ERDC generated data. Determine best practice equation or optimized mathematical fits to describe the pressure-time history. Additional sets of data will be introduced into variable space to examine the robustness of the optimization technique used to fit the parameter space. The student researcher will fulfill all responsibilities for the completion of this project under the guidance of senior researchers. The responsibilities of the student researcher includes communicating weekly updates to senior researchers, managing large datasets, developing novel optimized mathematical expressions to fit the dataset and summarizing key findings in a written technical report which will be submitted as a draft at the end of the summer.

Disciplines: Analysis, Applied Mathematics, Logic or Foundations of Mathematics, and Probability and Statistics

Hosting Site:

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

Internship location: Hanover, NH

U.S. Citizenship is a requirement for this internship

Project Description:

Imagery of the coast can be exploited qualitatively and quantitatively to provide information on coastal processes such as shoreline evolution. USACE-ERDC has helped develop this technology for over 30 years at the Field Research Facility in Duck, NC using stationary camera systems (i.e. Argus, Holman 2013). In this process, a camera with precise empirically derived calibration parameters such as focal length, pose, and position (otherwise known as extrinsics and intrinsics) capture images every hour. Using these calibration parameters, images are georectified to produce mapped imagery where features are measured in real world units (meters versus pixels) and can be used for engineering design. This methodology is and can be employed operationally, as long as the camera does not move or focus changes.

With the ubiquity of high quality cell phone imagery, particularly at highly populated coastal areas, it is desired to apply this technology to crowd sourced imagery. Without needing to install physical camera hardware, many more coastal sites can be quantitatively monitored with reduced cost and infrastructure. CoastSnap, developed by Harley et al. (2019) has spearheaded this movement. Citizens can take cell-phone imagery on a pre-installed mount and via signage or cellphone application send image to a centralized location for processing. However, while the processing has been streamlined, it is still not operational. Due to the different intrinsic and extrinsic calibration parameters of various cell phone cameras and vantage points, a singular or even prescribed list of calibration parameters cannot be used. Users have to manually calibrate each image.

For this 10 week project, the applicant would develop an algorithm to co-register CoastSnap images to operationalize calibration and georectification processing via either feature recognition or machine learning methods. Challenges include changing lighting conditions, beach topography, non-fixed features (waves, people), and various camera resolutions and focal lengths. MATLAB or Python coding experience is required. At the end of the 10 week internship, a working algorithm will be used in the USACE-ERDC CoastSnap operational workflow that will be utilized for USACE district CoastSnap Stations across the country. The work also has potential for journal publication due to the high demand for coastal imagery co-registration (moved fixed stations, web cameras, etc). In addition, the applicant will have opportunities for community outreach via the CoastSnap program if desired.

This project would be carried out at the Field Research Facility (FRF) in Duck, NC, otherwise known as the Outer Banks where numerous CoastSnap and Argus Coastal Imaging stations and subject matter experts reside. In Duck, NC the applicant will have access to CoastSnap stations for algorithm development (test imagery, etc) as well as a host of remote sensing technology to test georectification accuracy (terrestrial lidars, etc).  The FRF is a premier coastal oceanographic research center focused on advancing the communities understanding of coastal processes research through continuous observation and development of novel measurement techniques.  Any applicant would have opportunities to learn about other coastal monitoring techniques (amphibious vehicles, etc) as well as Machine Learning algorithms on remotely sensed data currently being developed there.

Disciplines: Applied Mathematics, and Topology

Hosting Site:

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

Internship location: Duck, NC

Project Description:

With heterogenous GPU-CPU architectures becoming the new normal on HPC systems, along with a rise in machine learning (ML) applications begin executed, the problem of scheduling HPC resources is being revisited. ML applications require high volumes data and are composed of smaller tasks, often utilizing GPUs. In contrast, HPC job schedulers were designed to handle monolithic MPI-based jobs leveraging dozens to thousands of CPUs in parallel for a fixed time period. Beyond just GPU-based ML tasks, there are many examples of HPC workflows utilizing CPUs for computationally intense simulations, using the resulting data to train a ML model utilizing GPUs, and then revisiting the CPU-based simulation to gather more training data, if needed. Such hybrid GPU-CPU workflows represent a new scheduling problem for HPC systems: the mapping of hybrid workflows to hardware must consider I/O, memory, and computational requirements. Therefore, obtaining optimal application performance requires a novel scheduling approach. This project will focus on mathematically defining the problem of scheduling hybrid GPU-CPU workflows on an HPC system and developing algorithms for its solution. This is an emerging problem in the field of exascale computing that is rapidly gaining attention but has yet to be formalized mathematically. This is a relatively open field with significant opportunities for future work and publication.

Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO

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

U.S. Citizenship is a requirement for this internship

Project Description:

The coastal environment is a very challenging environment to operate. This drives traditional data (in-situ) collection to be very expensive and often limited to a single point or limited spatial coverage. Remote sensing techniques (e.g. satellite, electro-optical imagery, radar, lidar, etc.) are often used to supplement/compliment. Fusing these data into a synoptic, noise-reduced state estimate leads to challenges as the in-situ data are often more precise while at times more sparse and out of date while the remotely sensed data are more synoptic (in space and time) but contain more noise.

The US Army Engineer Research and Development Center's Field Research Facility, located in Duck, NC is a coastal observatory focused on studying coastal dynamics with the end goal of better understanding how to protect the nations coastlines. The FRF is the most studied beach in the world and is responsible for a rich long-term data-set of bathymetry, waves, and currents combined with some of the most state-of-the-art and novel measurement techniques available today. The methods researched here are commonly used across the world.

This now-state estimate is to be used for numerical modeling studies, and analytical coastal processes science. The measured bathymetry changes between the monthly surveys -- measured with amphibious vehicles. Complimentary to that, 15 locations have bottom measurements at high frequency (sub-hourly), and are sparse in space.  Additionally, hourly measurements of beach topography are made with lidar scanners and are highly resolved in space and time, capturing a lot of spacio-temporal beach change that the aforementioned measurements do not, leaving unrealistic gradients and discontinuities in traditional fusion methods. Complimentary to these are Machine Learning and wave kinematic approaches to estimating depths from imagery providing high spacio-temporal coverage in the daylight with general skill, but noise associated with the perceptions. The spatial coverage of the aformentioned disparate datasets inherently produce discontinuities or non-physical gradients that are a combination of real physical change and error in state estimate.

This project will explore addressing these potential problems through traditional assimilation-based techniques as well as recently developed Machine Learning approaches. The intern will get good experience with geomorphologic and hydrodynamic processes, handling field data, developing data fusion methods for a real world application, and gain valuable experience in a government lab. An expected outcome is to publish and implement the newly developed method into operation. The ideal candidate is proficient in python.

Disciplines: Analysis, Applied Mathematics, and Probability and Statistics

Hosting Site:

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

Internship location: Duck, NC

U.S. Citizenship is a requirement for this internship

Project Description:

Complex surface topographical features (e.g., dunes, structures) and roughness elements (e.g., vegetation, rocks) attenuate near-surface wind flows, and often lead to turbulent airflow patterns generated by the interaction between a multitude of dynamic processes at different spatial and temporal scales.

The proposed study is part of a large-scale effort to explore near-surface turbulent flow phenomena by interrogating multi-fidelity data collected in controlled-laboratory (wind tunnel) and field settings using emerging techniques in data-driven machine learning and computational modeling. Through the project the applicant will gain exposure to a diverse set of multidisciplinary problems and hopefully write at least one paper depending on research outcomes.

The particular topic of study will be chosen based on the applicant’s interests and area of expertise. Opportunities include (a) verification, validation, and uncertainty quantification for high-fidelity simulation of complex airflows, (b) exploration of recently developed machine learning (ML)-based techniques for turbulence closure, (c) global reconstruction of system variables from potentially scarce and noisy observations, and (d) model reduction and data assimilation in near-surface flows.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

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

Internship location: Hanover, NH

Project Description:

Fluids with complex equations of state (EoSs) have become increasingly important in energy systems.   Examples of interest to NREL’s High Performance Algorithms and Complex Fluids (HPACF) Group include the use of supercritical carbon dioxide in high-efficiency energy systems that enable carbon separation, utilization, and storage (CCUS), liquid sulfur for energy storage, biomass for energy applications, and low-temperature helium for energy-efficient cooling of quantum technologies.  NREL is currently implementing these equations of state in a broad range of computational fluid dynamics (CFD) solvers, ranging from commercial codes to the high-fidelity open-source Pele combustion solver being developed as an application for exascale computing.  The relative complexity of the equation of state used varies not only with the fluid, but with the application, and the temperature and pressure range of the system.  

This project will involve studying the impact of EoS choice on the stability, solution time, and physical accuracy of the solutions obtained from CFD solvers for realistic energy systems simulations. The student will build fundamental physical understanding of the behavior of complex fluids, tying the equation of state used to determine the density to other key properties such as internal energy.   Research will be tied to actual energy system applications.  This is a relatively open field with significant opportunities for future work and publication.

The intern can expect to build skills in the following areas:

1) High-performance computing.
2) Numerical analysis including computational fluid dynamics.
3) Energy systems modeling.

Interns in our group generally present at the Rocky Mountain Fluids Symposium, held every August in Boulder, and are encouraged to present elsewhere.

Disciplines: Applied Mathematics, and Mathematics (General)

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO

U.S. Citizenship is a requirement for this internship

Project Description:

African swine fever (ASF) is a highly contagious and fatal disease that affects swine. The U.S. swine industry markets 115 million hogs annually, with a gross income of $20 billion. USDA Veterinary Services has several ongoing analytical projects devoted to quantifying the risk of entry of ASF and applying the products to target surveillance for African Swine Fever. The participant may select from any of these projects that best fits their interest and career development:

• Data analysis and development of new, automated weekly reports to Veterinary Services leadership on how the inspection activities in the U.S. Protection zone reduces the likelihood of entry of ASF.
• Development of a Bayesian model of air passenger destination data that predicts domestic hotspots of entry for swine products. This product informs targeting of swine surveillance.
• Data analysis and research to identify pathways for smuggling of meat products into Florida for the purpose of targeting interdiction activities.

The participant will have the opportunity to design their own analyses, impact decision making with regard to U.S. preparedness activities, and safeguard agriculture from the threat of foreign animal disease. There are opportunities for collaboration with different federal agencies, analytical units within Veterinary Services, and team members. There will be opportunities for the participant to learn about different operational and research activities within Veterinary Services. The participant may have any level of mathematical/statistical skill, as there are several projects with a wide range of skill needed from statistical summaries to simulation modeling. Familiarity with R/R Studio is desired.

Learning Objectives:

• applied analysis in a regulatory setting
• knowledge of disease epidemiology and spread mechanics
• effective communication of analytical products and data visualization
• how to collaborate across different disciplines of expertise (epidemiology, statistics, ecology, economics, entomology, etc)

Disciplines: Analysis, Applied Mathematics, and Probability and Statistics

Hosting Site:

USDA Animal and Plant Health Inspection Service (APHIS)

Project Description:

Tremendous opportunities exist to increase the efficiencies of Vertical Open Display Refrigerators used commonly in grocery vendor settings. Proposed new designs incorporate novel radiative, convective and conjugate cooling approaches coupled with integrated thermal energy storage.  Computational fluid dynamics simulations that incorporate display case air flow and product shelving details can be used to inform reduced order models (ROMs) which can be integrated into advanced optimization strategies for system design.  In this project, we will develop 2D and 3D models of these complex systems, incorporating many of the required design and operational constraints, and work with vendors to develop ROMs that engineering teams can use for the technoeconomic analysis necessary for new product development.  Given the broad usage of these devices across grocery and convenience stores and the opportunity for efficiency gains, this project has considerable potential for significant impact in nationwide energy consumption and greenhouse gas emissions.

Disciplines: Applied Mathematics

Hosting Site:

National Renewable Energy Laboratory (NREL)

Internship location: Golden, CO

Project Description:

In this project, the student will learn about numerical integration methods that are tailored to ordinary differential equation (ODE) models of biochemical mass-action kinetics, which are expected to be more efficient than general-purpose methods. The student will also learn about different methods of sensitivity analysis: finite-difference methods, forward sensitivity analysis, adjoint sensitivity analysis, and automatic differentiation. The student will contribute to development of a software package that implements integration and sensitivity analysis methods. The goal of this project is to develop computational infrastructure that will facilitate Bayesian inference of biological model parameter values using gradient-based Markov chain Monte Carlo methods.

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:

The project will focus on application of neural networks in the area of physical modeling. Participants will have the opportunity to learn about, design, and test neural networks. Previous experience is not required. Being comfortable with Python or willingness to learn about Python is required.

Disciplines: Analysis, Applied Mathematics, and Operations Research

Hosting Site:

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

Internship location: Hanover, NH

Project Description:

This project concerns modeling steady state and kinetic responses of stomata (the little holes in plant leaves that control carbon dioxide uptake for growth and water loss impacting plant drought stress) under different environmental conditions. The data set was collected to determine and potentially set secondary air quality standards for the state of California. The species is a widespread, economically important pine species. You would be joining a functional team consisting of Dr. Nancy Grulke and Dr. David Levin in 1) identifying drivers of stomatal conductance (to CO2 and O3); 2) constructing a model of stomatal behavior under steady state and dynamic environmental conditions; and 3) statistically comparing different O3 metrics (ambient O3 concentration; O3 dose; O3 uptake) during daylight hours as well as daytime + nighttime hours to determine whether there are analog or threshold plant responses to O3 metrics. Data collected was funded by US EPA and meets US EPA QA/QC standards. The intern can expect to submit a manuscript of the findings to a peer-reviewed journal as the senior author at the end of the 4 month internship.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

USDA Forest Service (USFS), Pacific Northwest Research Station

Internship location: Corvallis, OR

Project Description:

This project seeks to achieve significant breakthroughs at the interface of neuroscience and machine learning.  Our team has recently worked with Intel to implement the first verified LASSO solver for convex optimization problems on a spiking neuromorphic processor.  We hypothesize that good solutions to non-convex quadratic unconstrained binary optimization (QUBO) problems can be obtained by exploiting the unique dynamics of spiking neural networks.  The proposed project will test this hypothesis by applying our existing neuromorphic implementation to physiologically-relevant regimes in which spikes are only summed over short integration time windows so that single spikes are functionally equivalent to binary spins.

Disciplines: Applied Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Protein protein interactions (PPI) play a crucial role in cellular functions and biological processes in all organisms. Biochemical studies on PPI have been limited by experimental throughput. Deep mutational scanning (DMS) is a new experimental technology that allows surveying amino acid mutational space of proteins and their impacts in PPI by generating, in a single experiment, the activity of 10^5 or more unique variants of a protein. We plan to further develop a machine learning (ML) model from our group using existing DMS data to predict combinatorial mutational effects on PPI, including virus and therapeutic antibodies. We will also look into potential methods to incorporate protein structure into the ML model to improve the model explainability.

By working on this project, students will be able to learn how to apply some of the latest ML concepts into solving real world problems.

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:

Microreactors are compact, transportable nuclear reactors aimed to be used solo at remote sites, or in conjunction with renewables to provide 24-hour power throughput. The project relies on using advanced artificial intelligence, and machine learning techniques to solve physics-based design challenges. A successful execution of project can lead to proceedings or journal paper.

Disciplines: Applied Mathematics, Geometry, and Probability and Statistics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Study of the predictability of a complex system (think climate) deals with characterizing what aspects of the system are predictable and why. For example, the nature of instabilities and nonlinearities of the dynamics that govern the complex system could lead to a finite prediction horizon even as uncertainties are driven down to zero. The project seeks to use probabilistic machine learning (ML) techniques to advance the characterization of system predictability.

From a computational physics perspective, prediction errors can be traced back to their imprint on prediction of (irreducible) uncertainties in the estimation of the state of the system (initial condition uncertainty) and inevitable errors in the model used to make the prediction (model uncertainty). (The latter includes effects of truncation of a multiscale system, uncertainties associated with the parameterization of subgrid or poorly known physics, etc.)

The dynamics of the growth of such errors are just as relevant and important to the data-driven, system modeling approach.  Recent developments in probabilistic ML such as generative modeling (adversarial networks, variational autoencoders, etc.), (parametric and non-parametric) variational inference, Bayesian neural nets, reservoir computing, etc. present the possibility of developing a diverse set of ML-based ensemble prediction systems that can then be analyzed, possibly with the use of explainable AI methods, to advance the understanding of system predictability.

Students who choose this project can opt to to work on one of a few well-defined questions proposed by the mentor or develop an idea that the student may have.

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

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

This project seeks to use tools from machine learning to quantify uncertainty in numerical simulations. Numerical simulations are a cornerstone of modern engineering. Tasks related to optimization, control, and prediction all rely on the ability of various computer codes to produce accurate approximations of governing physical systems. This is the case across a wide swath of engineering disciplines in physics, biology and chemistry; modern settings include climate prediction, tokamak design, and drug discovery. However, these computer codes are often computationally expensive: a single simulation might take weeks or months, even with high performance computing resources. Further, it is often the case that not one, but many, simulations are required: engineering design must be robust to uncertainty, and compensating for this uncertainty usually involves running many independent simulations over the distribution of possibilities. This presents a real challenge: how are we to explore the full space of possibilities needed for engineering design when doing so necessitates an amount of simulation time that is infeasibly large?

This project seeks to address this challenge by using tools from machine learning and optimal experimental design to build surrogate models that are computationally inexpensive to evaluate, and require fewer simulations to construct than a naive sampling of the design space. As such, this project presents a unique opportunity for a motivated student to learn a lot in fields that are very topical in data-driven science and engineering. The student will work together with us to implement, train and test various neural network architectures (e.g., variational autoencoders, or physics-informed neural networks) to predict the state evolution of a given computer model. He/she will learn about and explore using various active learning techniques (e.g., active subspaces, or adaptive probing of the neural network's latent space) to avoid the "curse of dimensionality" and adaptively select for evaluation only those computer simulations which are most informative and useful for building the neural network surrogate. Once constructed, this surrogate will be an inexpensive alternative to the original computer code, and can be used in its place for computationally affordable engineering design. How well this design process -- based on machine learning models learned from a sparse set of adaptively, intelligently selected simulations -- will work is still poorly understood, and is an exciting topic of research that the student will gain direct experience with. There are many possibilities available with respect to the specific application; we envision climate prediction, given the suitability of the problem and the mentors' prior experience with DOE climate codes (e.g., E3SM).

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Brookhaven National Laboratory (BNL)

Internship location: Upton, NY

Project Description:

The goal of this project is to use applied mathematics techniques (numerical methods, machine learning) and computational science approaches (e.g., parallel computing) and build methods to perform machine learning on data streams while constraining physics. Our team works on applications related to porous media flow that are of interest to the national energy problems. The student will learn numerical methods and machine learning and some parallel computing techniques. In addition, the student will work have an opportunity to learn and network with 10-15 students that internship with our group.

Disciplines: Applied Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

U.S. Citizenship is a requirement for this internship

Project Description:

Direct simulations of turbulent flows, such that all dynamically relevant scales are resolved, are only possible for a very restricted set of flows. For most practical applications, including those of interest at LANL, numerical simulations can only be performed on coarse meshes, which in turn require turbulence modeling. While there have some attempts to include memory in such models (most notably in Kraichnan’s DIA), current turbulence models are constructed using only the current time information. On the other hand, the Mori–Zwanzig (MZ) procedure can be used to derive formally closed evolution equations for the resolved physics. In these equations, the unclosed terms are recast as a memory integral involving the time history of the resolved variables. While this procedure does not reduce the complexity of the original system, these equations can serve as a mathematically consistent basis to develop closures based on memory approximations. Current MZ applications to turbulence are based on nonlinear projection. In this case, unravelling the memory kernel requires solving the orthogonal dynamics, which is a high-dimensional partial differential equation that is intractable, in general. Ling et al [1] proposed an MZ procedure based on a finite-rank projection operator, and derived closed formulas for extracting the memory kernel from data that are computationally feasible. Tian et al [2] used these formulas to examine the memory kernel corresponding to different sets of real space observables and filtering widths in the context of homogeneous isotropic turbulence. They showed that the memory kernel adds non-negligible effects, but its magnitude decreases to small values on scales smaller than the turbulence integral scale. The application of the procedure to the spectral space would allow connection to fundamental turbulence theories and extending these theories to include non-Markovian effects. Thus, the project would allow the student to learn about data-driven algorithms, Mori-Zwanzig formalism, and turbulence theories, as well as turbulence modeling. The student would also interact with experts on dynamical systems, turbulence, and machine learning techniques.

References:

[7] Lin YT, Tian Y,  Livescu, D. and Anghel M. Data-driven learning for the Mori-Zwanzig formalism: a generalization of the Koopman learning framework. arXiv. 2021; 2101.05873v2 (in press Siam J. Appl. Dyn. Syst.).
[8] Tian Y, Lin YT, Anghel M and Livescu D. Data driven learning of Mori-Zwanzig operators for isotropic turbulence. arXiv. 2021; 2108.132882021 (in press Phys Fluids).

Disciplines: Applied Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

To advance our understanding of climate change and to support impacts assessments, there is an increasing demand to provide quantitative measures of skill and uncertainty in high-resolution climate projections. As an effort to support systematic evaluation of these climate simulations, NASA provides tools and web services that enable climate scientists to perform many basic data manipulations, such as subsetting data and calculating averages, needed to process NASA’s satellite observations suitable for climate model evaluation. However, it should be noted that existing toolkits have limited capability to conduct the quantitative analysis of spatial structures in observational and model datasets. To date, a scalable climate data analysis framework dedicated to evaluating spatial structures of key variables from climate models at various spatial resolutions does not exist.       
Recognizing this gap and need, we propose to develop a novel software toolkit for evaluating climate models against NASA’s satellite and suborbital observations. We will introduce the concept of multi-resolution investigation and topological data analysis (TDA) to evaluation of climate models. In particular, we will focus on assessing the aerosol optical depth (AOD) simulations from the Aerosols and Chemistry Model Intercomparison Project (AerChemMIP) using satellite observations from the Multi-angle Imaging SpectroRadiometer (MISR) and the MODerate resolution Imaging Spectroradiometer (MODIS).
The overarching scientific goal of applying topological approaches to multi-resolution evaluation of climate models is to demonstrate the value added by high-resolution simulations in projecting future climate changes. Our three specific goals and associated tasks are to:
G1. Integrate a cross-disciplinary algorithm for multi-resolution investigation
The climate models participating in the AerChemMIP have different spatial resolutions. We will leverage the hierarchical data analyzer (HDA) based on the Hierarchical Equal Area isoLatitude Pixelization (HEALPix) to evaluate the AOD simulations against state-of-art level 2 (L2) AOD products from MISR and MODIS.
G2. Assess the shape of AOD datasets
We will develop topological descriptors that summarizes spatial structures of the AOD datasets from climate models and satellite observations. The key step is then to measure similarity of the spatial structures between the datasets without regridding them into common grids and to use the similarity as a model performance metric.
G3. Provide a software package and web service
Our project aims at enabling as broad an audience as possible to reproduce our results and apply the multi-resolution topological evaluation to their own datasets. As such, we will publish the proposed software as an open-source Python package and visualize the model evaluation capability through a web service developed for the NASA Earth eXchange (NEX; https://www.nasa.gov/nex).

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

Hosting Site:

National Aeronautics and Space Administration (NASA)

Project Description:

A series of upcoming High Energy Physics neutrino experiments will be using liquid argon time projection chamber (LArTPC) detection technology. This technology enables high resolution neutrino interaction imaging in a three-dimension setting. When neutrinos interact within these detectors, the resulting charged particles leave energy deposits which can be measured (at millimeter resolution) and recorded as 3D point clouds. The 3D point cloud can be used to accurately reconstruct the neutrino interaction that occurred within the detector.  To do this reconstruction process, we need to infer the trajectories of the all the particles that appeared during the interaction, along with and the hierarchical relationship of those particles to each other.

Graph-based methods are well suited for reconstructing from LArTPCs because particle physics interactions are naturally graph structured. For instance, a tau neutrino may interact in the detector producing a tau lepton and a proton. The tau lepton may further decay into a chain of other unstable particles, ultimately producing a set of stable particles which can produce either a linear pattern of energy deposits (tracks) or a cluster of energy deposits (showers). We are part of the Exa.TrkX project, which has successfully developed message passing graph neural networks to infer particle trajectories. This works by constructing an initial guess at a graph where nodes are energy deposits and edges are causal connections representing the trajectory of the particle that created the nodes. Then, the message passing algorithm learns to deemphasize edges which do not correspond to true trajectories. However, this algorithm does not determine the hierarchical relationships between individual reconstructed trajectories.

Hierarchical graph neural networks provide a framework for understanding data-containing communities. For LArTPCs, this could be used to find collections of nodes and edges which correspond to tracks and showers, collections of tracks and showers that correspond to the decay of unstable particles, and the separating the collections of particles coming from the interaction of the neutrino itself, the reaction of the nucleus to the interaction, and external activity. A crucial ingredient to building a hierarchical graph neural network is developing community detector for constructing an initial plausible graph which will be refined using message passing. Techniques like the Louvain algorithm are unlikely to be capable of uncovering physically meaningful communities, but other options like spectral clustering or metric space embeddings may be feasible.

As an intern, you will together with high energy physicists to help define methods and algorithms for locating and identifying particles trajectories in data obtained from state-of-the-art 3D detectors using graph theory and related machine learning techniques.  This trajectory information is a critical aspect of obtaining precision measurements needed to further neutrino science, so results must be highly accurate.  You will have the opportunity to see some of the extensive simulation capabilities in high energy physics for generating good training data.

Disciplines: Applied Mathematics, and Operations Research

Hosting Site:

Fermi National Accelerator Laboratory (FNAL)

Internship location: Batavia, IL

Project Description:

Forensic evidence evaluation often involves comparison of patterns (fingerprints, footwear impressions, firearm and toolmark striations, DNA electropherograms, mass spectra for drug analysis, and so on). Using either their subjective, professional judgement or a computer algorithm, experts are often asked to assess correspondence between the crime sample (e.g., fingerprint recovered at the crime scene) and a reference sample (e.g., fingerprint obtained from a person of interest).  The expert communicates their findings to lawyers, judges, and jurors in written reports or courtroom testimony.  Several groups from the broader scientific community, such as the National Academy of Sciences and the President’s Council of Advisers on Science and Technology, have issued prominent reports raising questions regarding the validity of methods used by various forensic disciplines, which has led to a continually increasing focus on method validation. 

Crime labs conduct validation experiments using ground-truth-known, casework-like samples. Data from such validation experiments help stakeholders assess the reliability of the method used. However, such experiments are very expensive, and it is impractical for each crime lab to extensively study their method’s performance across the spectrum of scenarios encountered in real casework.  Even within the same lab, there are often updates to a given analytical workflow (e.g., updated software version, a new reagent supplier, a new analyst or instrument).  Any of these changes could affect workflow output in a given case, but it is impractical to entirely redo validation from ground zero each time something changes. There are strong potential efficiency gains to pooling validation results across labs and across minor workflow variations, but it must be done in a manner that takes into account potential differences and depends on demonstrated correspondences between workflows.

In this project, we develop experimental design strategies and analytic methods to efficiently predict the validation results of one workflow (say, A) given the validation results from a second workflow (B).  The basis for the predictive model will be a designed collection of comparisons analyzed by both workflows.  For validation samples analyzed with workflow A and not workflow B, the predicted values from the model will be used as pseudo-data (down weighted in accordance with each prediction’s uncertainty) during the validation of workflow B.  Some experimental designs will lead to better predictive power between workflows than other experimental designs. This project will compare the efficiency of different experimental designs using both theory and computer simulation.  Crime scene like pattern evidence samples will be used for evaluation of the methods developed. The participating graduate student will have the opportunity to learn how experimental design objectives should be formulated to directly benefit the application area. She/he will also learn how to design and conduct statistical simulation studies to compare the performances of different design strategies based on  application focused performance metrics.

Disciplines: Biometrics and Biostatistics, and Probability and Statistics

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Gaithersburg, MD

U.S. Citizenship is a requirement for this internship

Project Description:

In $q$-calculus, which is a difference calculus, the $q$ to 1 limit connects with standard differential calculus. We describe a $q$-calculus treatment of orthogonal polynomials in the $q$-Askey scheme of hypergeometric orthogonal polynomials which are closely connected with Jacobi polynomials. These were introduced by Dick Askey, are called continuous $q$-Jacobi polynomials. We are able to compute special values for the continuous $q$-Jacobi polynomials in terms of $q$-Racah polynomials. Then by starting with Gasper and Rahman's Poisson kernel for these polynomials and the special values, we compute new generating functions and summation expressions for these polynomials and for orthogonal polynomials in their subfamilies, such as for $q$-ultraspherical polynomials and in the $q$ to 1 limit, for Jacobi polynomials.  One can show how one can use these special values by utilization with the Poisson kernel for continuous $q$-Jacobi polynomials to obtain a 4x4 grid of transformation formulas for single nonterminating basic hypergeometric functions. We will extend scheme to more general hypergeometric orthogonal polynomials such as the Askey--Wilson polynomials.

Disciplines: Analysis

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Gaithersburg, MD

Project Description:

Since the Transformer architecture was introduced in the Natural Language Processing (NLP) area, this deep learning approach has been successfully applied to a diverse set of problems. Visual Transformers is a variation of the original model targeting images as input. This project aims to explore Transformer-based architectures for the analysis of image-based scientific data. There are several different types of Transformers proposed in the literature, however, little research has been done towards using and developing similar architectures for the analysis of large scientific datasets.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

Project Description:

This research project will focus on the development of novel physics-informed machine learning methods and computational techniques for forward and inverse differential equation problems. The aim will be to develop methods that are more computationally efficient than current models, while still retaining accuracy. This project will use cutting-edge research in machine learning within the context of applied mathematics (including applications to dynamical systems). This project will also include a focus on optimization, exploring new machine learning procedures, and different approaches to add physical constraints to machine learning problems (such as through utilizing the structure of numerical integration techniques or control theory).

Recommended prerequisites (by start of internship): A strong background in Python programming, as well as familiarity with machine learning frameworks such as PyTorch or JAX. General familiarity with dynamical systems and constrained/unconstrained optimization.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

Project Description:

In this project, we will try to explore and create algorithms that 'tensorizes' neural networks [https://arxiv.org/abs/1509.06569] for the purpose of memory usage reduction and performance improvement. The project generally assumes a hands-on approach. Specific activities include setting up benchmark neural network models, designing layer compression algorithms using tensor decomposition methods, and training and comparing the performance of the original and compressed networks. Software development and contribution to open-source ML packages are also encouraged.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

Project Description:

This research is aimed at the implementation, evaluation and optimization of novel HPC codes based on task-based programming models as solution for the upcoming computing architectures. The project includes studying the design of novel numerical algorithms based on LU factorization and their implementation on the available software and hardware platforms. Learning objectives for the applicant include: i) studying HPC codes based on task-based programming models, such as OpenMP tasking, on current HPC and heterogeneous (CPU+GPU) architectures, ii) acquire skills in both, numerical and HPC codes implementation, iii) gain experience in performance and numerical analysis on HPC architectures.

Disciplines: Algebra or Number Theory, Analysis, Applied Mathematics, and Mathematics (General)

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

## Project description

Over the last two years, in a collaborative effort between researchers at Fermilab and Old Dominion University, we have produced two highly efficient multidimensional integration algorithms: PAGANI and m-Cubes. We have implemented each algorithm for use on GPUs. PAGANI is a deterministic adaptive integration algorithm that applies the Genz-Malik cubature rules to estimate the value of the integral and to provide a measure of the uncertainty in the estimate. m-Cubes is a Monte Carlo algorithm based on the venerable VEGAS algorithm but adapted to use a mapping of workloads to processors that allows efficient implementation on a GPU. It also produces a statistical error estimate.

We use these algorithms to integrate complex functions for which symbolic integration is not possible. We have observed that for some integrands PAGANI is the faster algorithm, while for others m-Cubes is faster.

In this project, you will investigate these algorithms to find a method by which we can characterize the integrands to allow us to identify which algorithm would be better for use with that integrand. This will involve both performing computer experiments to evaluate the algorithm performance and study of the mathematical basis of the algorithms to characterize their expected performance on different types of integrands.

## Learning opportunity

The participant will learn about the application of numerical integration techniques in a hard-science domain, and obtain experience using the same kind of computer hardware -- GPUs -- that power the fastest supercomputers in the world. He or she will also have the opportunity to work with the researchers who have developed these cutting-edge algorithms.

Disciplines: Algebra or Number Theory, Applied Mathematics, and Probability and Statistics

Hosting Site:

Fermi National Accelerator Laboratory (FNAL)

Internship location: Batavia, IL

U.S. Citizenship is a requirement for this internship

Project Description:

This project develops mathematics description of objects.  Equations, and Matlab code will be needed to construct image of object in 3D space. There are several such problems in NETL’s research challenge list. The researcher of this project will be asked to work on one or more of them based on their own interests and background. One group of problems comes from the need to supply 3D printer an algorithm and/code with which an object can be manufactured through 3D printing. One of the objects would be a screw, and the other would be a hollow circular tube with arms at three different locations with each orientated differently around the tube. The other group of problem is represented by the image of a long rod in a curved tube. This is a simulation of the bending status of drill string in directional well, as commonly occurred in drilling an oil and gas well.  The validation of the mathematic description of the object is expected to be conducted by providing 3D imaging of the objects with a series of cross section images staking over one and another. If time allow, the objects will be made to perform certain motion. For example, the motion can be rotating the screw or moving the rod downward simulating the drilling progress.

Disciplines: Geometry

Hosting Site:

National Energy Technology Laboratory (NETL)

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

U.S. Citizenship is a requirement for this internship

Project Description:

The need to simulate coupled, nonlinear multiphysics systems can be found across engineering and is of critical importance to the Corps of Engineers’ civil works mission.  In particular, coupled wave-circulation models that can accurately model nearshore phenomena characterized by the interactions among surface gravity waves, wind and wave driven storm surges, and astronomical tides are essential for the reliable prediction of coastal processes and flood risk.
 
Over the last several years, we have been exploring and developing projection-based non-intrusive reduced order models (NIROMs) to accelerate large-scale simulations governed by nonlinear shallow water hydrodynamics while preserving a desired level of accuracy. To this effect, we have achieved significant speed-up by developing NIROMs using classical kernel-based methods, linear dimension reduction methods, and modern data-driven machine learning (ML) algorithms.
 
This study aims to extend these existing NIROM approaches and develop new physics-aware, operator learning-based ML methods to model multiphysics problems in environmental hydrodynamics. Through the project, the student participant will be exposed to a diverse set of challenging real-world problems in coastal processes and nearshore hydrodynamics, gain expertise in high-fidelity computational modeling of large-scale flows, and explore the extension of existing NIROM approaches to a wider class of problems. 
 
Additionally, they will have the opportunity to pursue the development of robust, generalizable ML methods based on deep operator networks (DeepONets) in order to augment and accelerate existing coupled nearshore wave-circulation models. Depending on the results, the work will lead to a potential journal article, and the student will also be encouraged to contribute to our Python-based, open-source software package for NIROMs.

Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics

Hosting Site:

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

Internship location: Hanover, NH

Project Description:

The student will learn about cell signaling systems, specialized methods used to model these systems, and ways to estimate model parameter values from data. The cell signaling systems of interest will be networks downstream of immunoreceptors (e.g., the T cell receptor) or receptor tyrosine kinases (e.g., the epidermal growth factor receptor). These systems play a role in immunity and/or cancer.

Disciplines: Applied Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Disciplines: Applied Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Image reconstruction is essential in several data acquisition pipelines happening at DOE data facilities such as the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory (LBNL). Image modalities such as micro computed tomography for example, rely on the acquisition of a projection image for each angle while a sample is being rotated. In order to obtain a final 3D image representation of the targeted sample, these projections need to be processed by an image reconstruction algorithm. This project aims to develop efficient reconstruction algorithms using mathematically grounded approaches and deep learning methods. Moreover, we aim to explore the problem of finding the optimum minimum number of projections necessary to achieve acceptable reconstruction quality.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

Project Description:

Quantum computing is a research area that has received a great amount of attention in the last few years. In this project, we aim to take advantage of quantum computing theory to develop quantum image processing tools suitable to the analysis of scientific data. This includes the development of new quantum circuits for quantum image representation and for analysis algorithms (feature extraction, template matching). We aim to develop concrete proof-of-concept tools that run on NISQ devices. We will use our own preliminary framework for quantum image representations (QPIXL) available at https://github.com/QuantumComputingLab/qpixlpp.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

Project Description:

Abstract: This proposal aims to develop a high-throughput methodology enabling rapid discovery, inverse design, and optimization of novel organic fluorophores with exceptional properties. Fluorescent molecules are used in the key formulation of: (i) Photonic-engineered inks and tags, in the form of paints, stickers or appliques, for encoding information placed on objects and subjects, and decoding them using a hyperspectral camera; (ii) Near infrared fluorescent dyes attract intensive attention for biosensing and imaging in cancer and neuron sciences, however only a few of them are readily available owing to poor photostability and hydrophilicity, and difficulties of signal capture in heterogeneous tissues in vivo; (iii) Organic light-emitting diodes and lasers: substitution of rare metals such as iridium and platinum in molecular complexes is a key step toward increased quantum efficiency. These are critical for applications in high quality near eye displays (for energy efficient mobile applications).

Therefore, it is crucial to discover ad design new organic fluorescent molecules for the electronic and optoelectronic applications. The aim of this proposal is to develop an efficient virtual screen (HTVS) and inverse design approach incorporating theoretical insight, quantum chemistry, chemo-informatics, machine-learning, with synergistic efforts on high throughput organic synthesis, molecular characterization, device fabrication and optoelectronic testing that compliment to current industrial expertise and design of experiments.

Proposed approach:
Our proposed approach is to develop an integrated organic multifunctional material design process aimed large-scale HTVS capabilities towards the successful discovery of novel organic fluorophores. This proposal is designed in three steps, which are described in the next paragraphs.

Step I: Extracting existing data from databases and texts, library generation and high-throughput DFT calculations: We will create our library by extracting data from open datasets. In the next step, we will extract knowledge from the literature on molecular structure diagrams, chemical equations, tables, and figures using different techniques. The quality of the data will be checked and the all the outliers will be removed from the library. We will do DFT calculations to generate the data for the molecules, which are not listed in the open data sources.

Step II: Developing of surrogate machine-learning models for target properties of interests: Using the data from Step I, we will develop machine-learning (ML) models based on physically-inspired descriptors (both, composition based and structure-based, such as Coulomb matrix, bag of bonds, molecular graphs, etc.) to predict structure stability, and accordingly the physical properties including spectral signature (e.g., infrared/Raman), charge-carrier lifetimes, etc.

Step III: Validate ML models for pre-screening the combinatorial space of possible molecules and build a list of potential candidates with the best performance: Validate ML models for pre-screening the combinatorial space of possible molecules and build a list of potential candidates with the best performance. Application of the predicted properties by DFT and experiments. ML models will be applied for pre-screening of the combinatorial chemical space of possible molecules to figure out which molecules are likely to have good outcomes, and prioritize the molecules to be studied next. We will carry out experimental syntheses and characterization and benchmark our ML models with predicted properties from DFT calculations. This Step will illustrate the performance of our developed models and the possibility of their use in real situations.

Potential impact:
The proposed approach can lead to develop and validate 3D collective models to explore the plasmon-exciton Rabi oscillations and Fano-resonance, and create high-performance novel quantum devices.

Disciplines: Analysis, Applied Mathematics, and Probability and Statistics

Hosting Site:

National Energy Technology Laboratory (NETL)

Project Description:

A neural network model promises a universal approximated function without laborious feature engineering and complete problem formulation. Despite its huge success in many learning tasks, the advantages of neural network models come at a price: the inability to interpret and understand the model behavior, creating a fundamental barrier to optimize and evaluate the model. Due to this barrier, it is an open research question to systematically design/diagnose a novel neural network model for the target dataset. To address this challenge, the most important gap is the ability to compare similarities between neural network models in order to correlate their prediction accuracy differences with model architectures. This project fills this gap by developing a scalable graph kernel-based method that can measure similarities between neural network models across multiple scales (e.g., a whole model and submodules in each model.) With being able to measure similarities, we can interpret the difference between neural network models, and, in turn, we can systematically design/diagnose neural network models.

Through this project, a student will obtain experience about graph-based machine learning algorithm. For example, a student will learn: 1) graph kernels to map the graph-represented neural network in a vector space; and 2) graph similarity metrics to compare neural network models in the vector space. Specifically, a student will gain experiences with the application of functional analysis and non-parametric distance metrics such as maximum mean discrepancy (MMD).

Disciplines: 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:

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:

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:

Developing quantum information science (QIS) capability is one of the most urgent tasks the DOE faces to make sure the U.S. wins the quantum race. To address QIS for energy applications, we must take action to participate the 2nd quantum wave to advance our computational capability. QIS is creating a potential transformative opportunities to exploit the intricate quantum mechanical phenomena in new ways for obtaining and processing information to advance many areas of science and engineering. The QIS contains four pillars: quantum computing, quantum simulations, quantum sensing, and quantum networking. To apply QIS in energy related applications, the key is to develop the capability of quantum computing & simulation tools. It is a great opportunity for NETL to support DOE in this quest of quantum race, while enabling the development of pathbreaking applications of QIS in energy technology development, particular to the decarbonization in fossil energy.

Existing quantum algorithms are still in early stage of their developments for electronic structure predictions. There is an opportunity to collaborate on the existing efforts to optimized and develop improved algorithms for efficient calculations of electronic properties and reaction kinetics. In this project, we propose to enhance the capability of quantum algorithms for molecular property calculations of system of molecules such as CO2, NH3, and CH4. In addition, we further propose to implement quantum algorithms to predict the chemical properties of other hydrocarbon systems. We will begin with benchmarking the available quantum algorithms and computational resources by using simple molecular systems. The targeted systems under study will be chosen from the NETL’s use case problems. We will implement state-of-the-art quantum simulator (e. g. IBM qiskit, QC-DMET) installed at the NETL supercomputer to simulate the environments of quantum computer. At the end of this project, trainee will be able to conduct quantum computing research for electronic and chemical property calculations of simpler molecular systems.

Disciplines: Applied Mathematics

Hosting Site:

National Energy Technology Laboratory (NETL)

Project Description:

Abstract: The generation of pure oxygen is of great importance for different kinds of applications including solid oxide fuel cells, wastewater treatment, and in particular, cleaner fossil fuel combustion. Design and discovery of high-performance oxygen carrier materials play a crucial role in such applications. Perovskite-type ABO3-δ oxides as oxygen carriers are receiving much attention recently due to their high thermal stability, good mechanical properties, and ability to reversibly and rapidly uptake and release oxygen. Furthermore, the flexibility in choosing the elemental composition of the A and B sites allows for the synthesis of many different perovskite-structured materials with inherently distinct oxygen storage properties. In addition, the level of chemical and structural disorder can be controlled through doping, and variable stoichiometry provides the ability to probe the material’s phase space. The current proposal aims to develop a machine learning method to accelerate discovery of effective doping in A1-xRxB1-yMyO3-δ (R: A-site dopant, B-site dopant) perovskites with develop a structure-property relationship.

Approach: The effect of A and B site doping, both individually and in combination with different concentrations, on the oxygen ion diffusion considering oxygen vacancy formation energy was investigated utilizing DFT calculations. Accordingly, we developed a database for NETL-ABO3 perovskites of interest for a range of cationic dopants including alkali, alkaline earth metals, 3d, 4d, and 5d transition metal elements with and without an adjacent O vacancy. In the current research, a predictive machine learning (ML) model will be developed based on our developed database to develop a structure-property relationships, leading to the rational materials design and discovery by establishing a relationship between dopant features and the oxygen formation energy of a doped oxide. The properties of interest are oxygen vacancy formation energy, mechanical stability, electronic and optical properties, and catalytic behavior.

Impact: The findings of this research will identify trends and correlations between the dopant features and the discovered materials’ properties including oxygen vacancy formation energy, mechanical stability, and electronic, optical and catalytic properties. It is hoped that this work will spur future experimental studies of such doped oxides and open avenues for the development of high performance ABO3 based oxygen carriers and catalysts.

Disciplines: Analysis, Applied Mathematics, and Probability and Statistics

Hosting Site:

National Energy Technology Laboratory (NETL)

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 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

Internship location: Lemont, IL

Project Description:

This project will explore efficient solutions methods for solving a Bayesian inverse problem (i.e. recovering model parameters from observations) in systems modeled by stochastic PDEs with high-dimensional input data.  The solution methods will rely on surrogate models of the PDE solver - a cheap-to-evaluate function that maps a sample of the stochastic input to the dependent variable in the PDE.  In order to efficiently construct a surrogate with limited data, we leverage several several key building blocks from state-of-the-art deep learning that encode desirable inductive biases into the model. Additionally, we will also explore sampling methods such as Normalizing flows to sample from the high-dimensional posterior distribution.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

Many critical decision and design problems relevant for DOE must be made with partial information, under uncertainty, and quickly.  We will develop new models and algorithms for the sequential robust optimization problems, leveraging synergies between traditional optimization and machine-learning.

Disciplines: Applied Mathematics, and Operations Research

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

At Argonne National Laboratory, we have developed ParMOO, a Python library for solving multiobjective simulation optimization problems, while exploiting available structure in the problem.  We are seeking a candidate to add new features to ParMOO via the following research and engineering activities:

1. Design and analysis of a novel structure-exploiting algorithm or technique for optimization, scalarization, surrogate modeling, or Pareto front modeling;

2. Implementation of this method in the existing ParMOO framework; and

3. Empirical comparison between the newly implemented algorithm and baseline methods, for synthetic and/or real-world multiobjective simulation optimization problems.

Disciplines: Applied Mathematics, Mathematics (General), and Operations Research

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:

This project focuses on developing theoretical metrics quantifying the compressibility of scientific datasets for lossy compressors. We will explore various statistics of the data for correlations and multiscale aspects, and their relationships to compression ratios through functional models. This consists of a first step towards evaluating the theoretical limits of lossy compressibility used to eventually predict compression performance and adapt compressors to correlation structures present in the data. In particular, we will perform the analysis on synthetic Gaussian fields providing a proof of concept and on user scientific dataset.  Several of the leading lossy compressors will be used and compared in the light of their response to various descriptive statistics of the datasets.

The perspective student is expected to get hands-on experience of the use of data compressors, statistical analysis of scientific datasets such as the extraction  of correlations and multiscale patterns in scientific datasets. This perspective student will be part of an existing inter-disciplinary team.

Disciplines: Probability and Statistics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

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:

Often a computationally expensive simulation is replaced by a surrogate model in common inference procedures such as calibration, uncertainty quantification etc.. Building a Gaussian process (GP) based surrogate using large simulation data is equally expensive and can be challenging in the presence of  factors like high-dimensional output (and input), input dependent noise and incomplete/failed simulation runs. A common approach to deal with some of these challenges is to approximate the true (global) surrogate by cheaper (local) model(s).

The goal of this project is to conduct a comprehensive comparison among existing methodologies for different simulation scenarios and to extend the ensemble partitioned GP approach(https://doi.org/10.1007/978-3-030-77977-1_19) in a full Bayesian set up. The final outcome will be comprised of a review of existing and new methods in the form of a manuscript. Applications from cosmology and epidemiology will be used as test-beds. Participants should have basic knowledge of Bayesian inference, MCMC, and Gaussian processes. R or python will be used for numerical experiments.

Disciplines: Applied Mathematics, and Probability and Statistics

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:

We will develop algorithms and theory for randomized approaches to zeroth-order optimization that test variance reduction different techniques for adaptive sampling. 

Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

Deep Neural Networks (DNNs) have demonstrated promising results for inverse maps that are capable of solving inverse problems (e.g., see arXiv:2107.14346). An inverse problem is encountered when one is interested in estimating parameters in partial and ordinary differential equations, where the effects of parameters are only indirectly observed through solving the differential equations. Various open questions remain regarding accuracy of the DNN-based inference with inverse maps, such as, the incorporation of prior knowledge about the parameters, and how to quantify uncertainties in the recovered parameters.
In this project, we will focus on applications in which inverse problems exhibit computational challenges arising from a highly nonlinear and nonconvex loss function, with sharp gradients and multiple local minima; and when the loss cannot be regularized by a convex additive term since this would largely eliminate the information from data and model. Specifically, we will target inverse problems for differential equations used in neuroscience.

During the internship, you get the opportunity to work at the intersection of classical mathematics, neurosciences, and modern machine and deep learning. You will be guided to find your preferred research directions and then encouraged to pursue self-driven advancements in these directions. You will be part of a welcoming team of computational scientists from Argonne.
The goal of the project is to creatively explore machine and deep learning techniques to solve challenging inverse problems, for instance, in neurosciences.

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

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

Due to the ill-conditioned characteristics of natural processes and environments where a single solution rarely exists, this project involves solving the inverse problem in x-ray science  following a multi-objective fashion that simultaneously optimizes  objectives from multimodal datasets, and provides a way to  reduce ambiguity/non-uniqueness of understanding comparing to single acquisition/modality method. As proxies, we single out the applications of X-ray fluorescence and coherent diffraction image reconstructions. 

Disciplines: Analysis, Applied Mathematics, and Operations Research

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

Identifying the causal relationships between precursors to extreme events in spatiotemporal applications such as climate forecasting is a difficult task. These extreme events are influenced not only by local, short-term dynamics but also global and long-term dynamics. To that end, we will develop a deep-learning-based causal discovery framework to understand the relationship in high dimensional spatiotemporal data while accounting for global connectivity. We will build an attention-based graph neural network to uncover new connections between extremes and potential drivers over a vast geographic area. We will evaluate the efficacy of the developed method on large scale snowstorm data across the globe.

Disciplines: Analysis

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

This project investigates the spatiotemporal extents of intensity, duration, and frequency of climate extremes. Specifically, this project will explore the use of ML based algorithms to identify and characterize climatic extremes such as droughts.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

The goal of the project is to study the implementation of quantum temporal convolutional networks. Temporal convolutional networks (TCNs) are recent sequence models that received a lot of attention in recent years. Inspired by convolutional neural networks (CNNs), TCNs extract temporal features in a temporal translationally invariant manner. Prior the development of TCNs, sequence modeling is typically done using recurrent networks such as recurrent neural network (RNN), gated recurrent units (GRUs) and long short-term memory (LSTM). These models suffer from short memory of past data and the need for backpropagation through time due to their recurrent nature. The development of transformers introduced an attention mechanism and removed the recurrent architecture. They achieved longer range memory and superior performance. However, the quadratically complexity in sequence length make it very expensive to implement. TCNs are far more efficient than transformers, and perform better than recurrent networks.

Recently, the impact of quantum computing on machine learning is explored. Many work use variational quantum circuits (VQCs), where there are quantum rotation gates whose rotation angles are learnable and optimized for various tasks, as substitutes for classical neural networks. Variational quantum circuits are used in quantum approximate optimization algorithms, variational quantum eigensolveres, and other optimization algorithms. Many attempts to connect machine learning and VQCs include quantum convolutional networks, quantum LSTM and more. It is a great opportunity to explore the potentials of QTCNs because of the potential in both TCNs and VQCs. The proposal is to use the MNIST handwriting digit data set for benchmarking. The image information can be condensed to a sequence of travel directions of a pen that writes these digits, greatly compressing the size of the data, which is necessary for our quantum simulation work to be tractable.

Disciplines: Applied Mathematics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

This project focuses on developing advanced algorithms and numerical software for applications of efficient high-order numerical discretizations across the DOE energy-science spectrum including reactor analysis, internal combustion engines, electromagnetics, and ion transport. Our goal is to enable the 500+ users of Nek5000/RS (for thermal fluids) and NekCEM (for electromagnetics and other multiphysics problems) to leverage the highly scalable performance of these methods across a variety of platforms.  As our algorithms are driven by by application needs, the project will include close interactions with domain
scientists and engineers.  A solid understanding of numerical methods for PDEs on unstructured meshes, numerical linear algebra, and high-performance computing, as well as advanced programing skills in software such as MPI and CUDA would be useful.

Disciplines: Applied Mathematics, and Mathematics (General)

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

Quantum computing and simulations play central role in the quantum information science (QIS), and several quantum computers have already been used to model chemical reactions, and as this technology continues to develop it may have transformative implications for material design and discovery. From the other side, the advancement in developing novel and high-performance quantum magnetic sensors is intimately intertwined with progress in magnetic materials and devices. Since the state-of-the-art sensors for characterizing bulk magnetic materials are insensitive (signals are too weak to be measured) to nano-spintronic devices and thin magnets, we are, in the current proposal, going to develop a quantum computing approach that can accelerate the design of novel nano-scale quantum sensors with intrinsic quantum mechanical operation to address such challenges.

In this research, we propose to design quantum sensors based on an isolated single alkali-metal atom in the solid hydrogen supercells. Solid hydrogen possesses BCC structure, and exhibits semiconducting behavior and promising quantum mechanical properties [J. Chem. Phys. 153, 204107 (2020)]. Upadhyay et al. [Phys. Rev. A 100, 063419 (2019)] showed that rubidium atoms in solid hydrogen have properties that make them extremely sensitive magnetic field sensors. In this research, we will first embed a single atom inside the solid hydrogen supercell. The quantum mechanical properties (structural, electronic magnetic, and optical properties) of the developed systems in both pristine and with embedded single atom configurations will be then calculated. The spin-electron interactions will also be taking into consideration in the computations. All the calculations will be done using IBM qiskit, as a quantum computing simulator. Based on the current available quantum algorithms (i.e. variational quantum eignesolver (VQE), and quantum phase estimation (QPE)) for quantum chemistry, we will develop our own quantum computing codes to perform quantum simulation focusing on the development of novel single atom quantum sensors. In the second step, instead of single atoms, we will put a range of small molecules inside the hydrogen supercell and compute the quantum mechanical properties to develop structure-property relationship, which can result in the design of quantum sensors with optimized properties.

We believe that the findings of this research not only can provide insights for better understanding of the physics atoms and molecules inside of the quantum solids, but also can lead to develop novel sensors for characterizing both the static and dynamic magnetic properties of ultrathin magnetic materials.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

National Energy Technology Laboratory (NETL)

U.S. Citizenship is a requirement for this internship

Project Description:

Position: Student Intern in the U.S. Army Engineer Research and Development Center (ERDC) Mobility Systems Branch (MSB)

Overview:
The student will collaborate with MSB engineers and scientists (E&S) to analyze autonomous ground vehicle performance in software-in-the-loop (SIL) simulations using the Virtual Autonomy Navigation Environment (VANE) (M&S) tool suite. This will include using MSB VANE tools to create virtual worlds (i.e. scenes) with parametric content (e.g. vegetation density, obstacles) and environmental conditions (e.g. rain, time of day), conducting co-simulations with VANE sensor and vehicle M&S tools, processing the autonomy performance data, and writing a report about the experiments and results.

Responsibilities and Duties:

• Learn how to create VANE scenes and conduct VANE SIL simulations from MSB E&S
• Collaborate with MSB E&S to integrate a new autonomy stack into the VANE SIL
• Help with experimental design for autonomy performance study
• Generate parametric VANE scenes
• Run SIL simulations and collect autonomy performance data
• Assist with data analysis and presentation
• Lead effort to write a draft report for publication in a peer-reviewed journal, as an ERDC technical report, or both

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

Hosting Site:

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

Project Description:

As both the quantum hardware and software communities continue to make rapid progress while our understanding of quantum computers continues to mature, the immediate role of quantum computing for quantum chemistry becomes much clearer. The challenge is that to advance the quantum algorithms for quantum chemistry requires the synergy of quantum information theory and classical quantum chemistry techniques. Currently, the existing quantum algorithms are still in early stage of their developments for predicting the electronic structures and properties of molecules. Hence, this project will involve development of a module for benchmarking, implementing, and validating the developed quantum computing (QC) codes to simulate vibrational spectra and thermodynamic properties of molecules on noisy quantum simulators for the energy applications at NETL.

In addition to electronic energies of chemical systems, many chemistry applications need properties beyond electronic energies, such as vibrational property measurements for identifying fingerprints of molecules, adsorbates, reaction intermediates, etc. The framework for the calculation of ground and excited state energies of bosonic systems such as the vibrational structures of a CO2 molecule has been recently demonstrated with the Qiskit QC code and near-term quantum devices (P. J. Olltraut et al. Chem. Sci. 11(2020)6842-55; E. Lötstedt et al, Phys. Rev. A, 103(2021)062609; M. Majland et al, arxiv: 2102.11886). Development of QC code for calculating vibrational properties of chemical systems of interests can be a parallel task in addition to the electronic energy calculations (N. P. D. Sawaya et al, arxiv: 2009.05066). In this project, by developing QC codes, the vibrational spectra and thermodynamic properties of various relevant molecules (e. g. CO2, NH3, CH4) and building blocks of larger molecules will be simulated and will further extend to anharmonic systems or more complex systems (e. g. polymeric chain and MOFs), which will further expand the capability of the QC code for simulating chemistry systems of interests at NETL. At the end of this project, the trainee will be able to build a framework to calculate the vibrational properties of bosonic systems and conduct quantum computing on the electronic and thermodynamic properties of small molecular systems.

Disciplines: Applied Mathematics, and Mathematics (General)

Hosting Site:

National Energy Technology Laboratory (NETL)

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

Project Description:

The aim of this project is to develop quantitative assessments of resilience that capture how the various scales of a complex ecosystem respond to changes in climate. In this project we will make use of probabilistic dynamics and notions of information theory to capture how the resilience of the complex ecosystem changes under forcing and with these, develop an understanding of quasi non-equilibrium states of the ecosystem itself. We will be using machine learning tools to capture inter-scale interactions and the changes in the probabilistic states to inform our proposed notion of resilience.

Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

An executive summary is a reduced dimension representation of a time series that contains all of the important causally-important aspects of the original signal. The type of time series are those from the stock market, the load on an electric grid, among others. If this executive summary is subtracted from the original time series one hope that what is left can be easily captured using a simple stationary stochastic parametrizaiton. This executive summary is particularly challenging to synthesize in data that is non-stationary and has a time dependent spectral distribution. We will use diffusion maps to sift out the summary and develop explainable artificial intelligence notions of surrogate model interpretability. This project will use these diffusion maps to create a time series decomposition from which the executive summary will be generated. The student will be involved in the theoretical and algorithmic development of the decomposition as well as the formulation of an interpretable summary.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

The goal of the project is to develop machine learning models to create quantum gates to be used in quantum simulations. With the realization of highly coherent quantum devices, such as the quantum computer developed in Fermilab, interacting quantum systems storing many computational states (d-level qudits, a generalization of 2-level qubits) can be successfully built. Pulses are used to control the device optimally. Simulations of these large systems are done in high-performance computers (HPC).

We study gates at the pulse-level to gain precise control of the quantum computer. Pulses have underlying parameters (“pulse parameters”). For example, consider the gate U(theta), where U is a matrix and theta is a gate parameter. We could train pulses for every value of theta -> U(0), U(0.1), U(0.2), etc, but training each value is hard and expensive, and there are infinite values to train. In this project, the interns will be involved in developing numerical algorithms that find families of pulses which can represent any U(theta), so we only train a few theta and are then able to generalize to all U(theta). One avenue for this generalization is the use of machine learning models, such as neural networks.

The interns will develop neural networks, train them on optimized pulses, and then use the trained neural networks to generate optimal pulse parameters for new gate parameters, theta. They will compare performance of the predicted pulse parameters to fully optimized pulse parameters, as well as deriving analytical results to bound error and optimality. Given that we will need to generate many optimized pulses as training data, our investigations will also help determine the best settings and best numerical optimizers to use for our quantum simulators and their limits. Time permitting, we will test our parametrized gates on quantum hardware.

The students will collaborate with researchers at the Fermi National Accelerator Laboratory (Fermilab), HRL Laboratories, Argonne National Laboratory (ANL) and Northwestern University. The entire project may be performed remotely, with periodic virtual meetings. For the numerical research, we will share computing notebooks with students to set things up. Supercomputer clusters will be available for this project, and their use is expected early on in the project. Previous knowledge on quantum hardware and quantum programming is not required.

** Learning opportunity

We are in the new era of quantum computing and HPC simulations. Fermilab is building a quantum computer with a novel approach. Aurora, a next-generation exascale supercomputer, is being built at ANL. It is a great opportunity to explore the intersection of several fields in one project and be part of a team with various backgrounds. The students will be able to network with researchers from universities, national labs and private research labs (HRL Laboratories) and get multiple perspectives on post-graduate life.

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

Hosting Site:

Fermi National Accelerator Laboratory (FNAL)

U.S. Citizenship is a requirement for this internship

Project Description:

Peridynamics is a nonlocal reformulation of classical continuum mechanics suitable for material failure and damage modeling, which has been shown to be highly effective in the computational simulation of fractures in many application problems. However, the predictive capability of peridynamics depends on the proper choice of constitutive relations and the appropriate selection of corresponding model parameters, which may be difficult to attain in complex scenarios. Current developments in machine learning (ML), such as deep learning, provide unprecedented opportunities to learn models directly from data. This project will explore the use of ML methods (especially neural networks) to advance the learning of novel peridynamic models.

Disciplines: Analysis, Applied Mathematics, Operations Research, and Probability and Statistics

Hosting Site:

USDA Forest Service (USFS), Center for Forest Watershed Science

Project Description:

Peridynamics is a nonlocal reformulation of classical continuum mechanics suitable for material failure and damage modeling, which has been shown to be highly effective in the computational simulation of fractures in many application problems. However, the predictive capability of peridynamics depends on the proper choice of constitutive relations and the appropriate selection of corresponding model parameters, which may be difficult to attain in complex scenarios. Current developments in machine learning (ML), such as deep learning, provide unprecedented opportunities to learn models directly from data. This project will explore the use of ML methods (especially neural networks) to advance the learning of novel peridynamic models.

Disciplines: Applied Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

Learning objectives: i) opportunity to collaborate on a real-world problem, ii) mentorship from statisticians and an environmental scientist, iii) freedom to pursue model approaches within the scope of the project and iv) the opportunity to first author or co-author a manuscript.

This project will study the properties of an estimator of missing values of a predictor variable X, X>=0. The outcome variable R is ordinal. X and R will be measured using one-stage cluster designs—where X will often be missing. In measurement units where X is nonmissing, X and R are measured synoptically. Interest is in predicting X where R but not X is measured. X (and so R) may be assumed to be spatially correlated among measurement units within the same sampling unit.
 
This study is motivated by interest in predicting aquatic vegetation biomass at measurement units where a relatively inexpensive, ordinal estimator of that biomass is obtained. The ordinal outcome may be assigned scores of 0, 1, 2, …, 5, with 0 denoting no observed biomass. The sampling design envisioned would approximate that of a two-phase sampling design (i.e., R would be obtained at all measurement units and X at a fraction of those units within a fraction of sampling units). A difference from a two-phase design is the focus on predicting X rather than in a population estimator of a mean.
 
Models will need to address that X may arise under two states: one where X = 0 (representing an unvegetated state) and another where X > 0 (representing a vegetated state). Given an assumption of no false positives, Pr(R = 0 | X = 0) = 1. A potential approach would assume ordered outcomes (conditional on X > 0) with a Bernoulli component to address the two states (i.e., X = 0, X >0). Interest is in E[Xi], Pr(Xi > 0) and potentially E[Xij|Rij], where ij denotes the jth measurement unit, j = 1, 2, …, nj within the ith sampling unit, i = 1, 2, …, n. Code to fit this model has been tentatively explored.

The project would entail developing models using contemporary methods with real and simulated data. Real data derive from n = 67 sampling units, where Xij and Rij were obtained jointly at each of six measurement units (i.e., X not deliberately missing under this design). Simulations would need to be designed to evaluate estimator performance under different mean, covariance, sample size and missingness assumptions.

In the above, X is treated as the predictor. However, the student might consider alternatives (e.g., inverse regression). Students will have the help of statisticians and a PhD environmental scientist and will also be free to consult with others of his/her choosing. (Students and faculty who choose to contribute substantially to the project would be eligible for coauthorship.) As the study, including computer code, will ultimately need to be described for a wider audience, the student will need to author or coauthor draft methods and results sections of a manuscript with initial target arXiv.

Disciplines: Probability and Statistics

Hosting Site:

United States Geological Survey (USGS) Upper Midwest Environmental Sciences Center

Internship location: La Crosse, Wisconsin

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:

Recent applications of Long Short-Term Memory (LSTM) recurrent neural networks have shown great promise toward streamflow prediction, significantly surpassing the performance of pure physics-based models in head-to-head tests. One of the strongest barriers toward adoption of LSTM modeling for streamflow lies in the community's reluctance to accept the "black boxiness" reputation commonly attributed to machine learning. We therefore seek ways to translate internal LSTM information into physical understanding via established or new methods. As an example, a recent publication demonstrated how an LSTM internally learns long-term effects of snowmelt on streamflow: https://link.springer.com/chapter/10.1007%2F978-3-030-28954-6_19.

You would collaborate closely with a team with expertise in hydrology and are not expected to understand the details of streamflow modeling. You will ideally have some experience in applying, developing, or interrogating machine learning models. This project will provide you with the opportunity to learn about streamflow and flooding while exploring and/or creating new techniques for interpreting models. Our team has developed a platform that readily serves the data needed to build and train LSTMs for watersheds globally, which means that you will be able to spend more time on model building and exploration and less time on data manipulation. We prefer to use Python; take a look at the neuralhydrology Python package for a sense of the kinds of models you would use. We collaborate with the authors of this package which includes members of Google's AI For Good Initiative, which, in addition to the LANL scientists you will collaborate with, will provide ample opportunities for growing your professional network.

This project ultimately hopes to provide global flooding projections under various projected climate scenarios, but we are also intent on providing a deeper understanding of the models that generate these projections. Your activities will contribute to cutting-edge, impactful science to help anticipate and guide flood-related management and mitigation.

Disciplines: Applied Mathematics, and Mathematics (General)

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

U.S. Citizenship is a requirement for this internship

Project Description:

In the design of hydrologic infrastructure (such as dam, levees, bridges, culverts etc.), the probability of failure over the lifetime of the structures due to flooding is perhaps the most important piece of information an engineer can communicate to water resource planners and the public. Traditional probabilistic approaches make use of an average return period, the (conditional) interval between two flood events for defining risk of infrastructural failure from flooding that may not reliably represent the time to the next flood event. More importantly, this leads to an over-simplification of a far more complex scenario that is driven by non-stationarity in climate, and multi-dimensional nature of risk. For those reasons, the usage of conditional return periods is not recommended, and is generally not applied in areas of major water resources planning. Accordingly, a most recent literature recommended to replace the term risk with ‘‘reliability’’ that not only takes account of the planning horizon but also is a more robust estimate as compared to the average return period in both stationary and non-stationary cases. Reliability is defined as the probability that a system will remain in a satisfactory state during its lifetime, which also means that an exceedance event will not occur within a project’s lifetime. It is also in par with the modern definition of risk used in environmental and water resource planning where both the magnitude and frequency of the event plays an important role in defining the life of hydrologic infrastructure within the planning horizon. However, so far, the concept of reliability has not been extensively exhausted, in the realm of advanced statistical theories, for assessing the design life of hydrological infrastructures already in place. This study aims to develop advanced statistical modeling approaches using the long-term climate data and geo-morphological information from three different study sites of USDA Forest Service for exploring the concept of reliability and for quantifying the associated long-term risk of infrastructural damage due to future flooding events. The observations and statistical inferences would, then, be extrapolated to long-term datasets and geo-morphological information of the other study sites across the globe. The study's tasks include training the graduate student on Mathematical and Statistical modeling using R/Python; Data Mining, Analysis, Visualization, and Interpretation; Remote Sensing and Geographic Information System (RS & GIS); and Decision Making. The incumbent will be using the existing knowledge of computer programming, statistics, and engineering mathematics to enhance the skills to address the dynamic issues associated with the hydrological cycle and its components. The student will also learn about field experimental studies, forest hydrologic processes represented by mathematical equations, real-time monitoring technology, geospatial data, and managing and analyzing the long-term data sets using statistics, applied mathematics, analysis, and statistical/mathematical modeling.

Disciplines: Analysis, Applied Mathematics, Biometrics and Biostatistics, Operations Research, and Probability and Statistics

Hosting Site:

USDA Forest Service (USFS), Center for Forest Watershed Science

Project Description:

Nonlocal models have been proposed as effective alternatives to classical (local) models, which are based on partial differential equations (PDEs), due to their ability to overcome challenges of their PDE-based counterparts in many scientific and engineering applications. However, the significant increase in computational cost of nonlocal models can sometimes hinder their use, especially in practical large-scale computations. Local-to-nonlocal (LtN) coupling is a strategy to combine local and nonlocal models, so that the usage of the more expensive nonlocal representation can be restricted to critical regions, while remaining regions can be modelled with a more efficient local model. Even though many LtN coupling methods have been proposed, unfortunately, model coupling often results in spurious coupling effects, in particular around coupling interfaces. Although many studies consider LtN coupling for static problems, only a few studies focus on dynamic coupling artifacts. This project will study dynamic LtN coupling artifacts with a particular focus on interfacial wave reflection.

Disciplines: Analysis, and Applied Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

This project will explore the potential computational advantages of discrete event simulation techniques applied to cellular automata models of grain growth and other problems in computational materials science. Among the main aims of this research are reductions in execution time, the elimination of numerical errors that stem from truncating random variables in a stepwise model, and leveraging high performance computers via parallel discrete event simulation techniques. Although the focus of this project is on problems related to materials, there is a broad interest in examining analogous problems, particularly in the area of agent based simulations, for which modeling methods, simulation techniques, or both could be usefully translated between domains of application.

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:

The National Animal Health Monitoring System (NAHMS) is a United States Department of Agriculture (USDA) program that performs national-level surveys of U.S. livestock and poultry management and health. Please check out our data products at https://www.aphis.usda.gov/nahms.

This project focuses on the NAHMS Swine 2021 and Feedlot 2021 national-level surveys that were administered to producers in 2021. Our team is currently cleaning and validating the data in preparation for data analysis to begin over the summer.

The intern will help analyze national-level survey data from the NAHMS Swine 2021 and/or the Feedlot 2021 studies using SAS and a SAS-callable software package called SUDAAN. The analysis involves calculating survey-weighted point estimates and associated standard errors as well as the use of SAS macros to format the data output. The data output is then used to create Tableau dashboards, which will be published on our website. Our data analysis process involves two main roles: one analyst writes the entire analysis code, and a second analyst independently reviews the code for correctness and identifies potential issues; the intern may be involved with one or both roles of this process. While the main objective is the data analysis in SAS, the intern can also assist with Tableau dashboard development in their time with us if the intern is interested.

A NAHMS mathematical statistician will mentor the intern throughout their time with us. The statistician will provide a detailed description and background as to how the intern’s projects fits into the broader NAHMS study process, review associated statistical methodology (e.g. survey weighting, stratification, etc.), and be readily available to answer any questions or provide assistance with SAS coding, statistics, etc. to the intern.

Knowledge of statistics, particularly some exposure to survey statistics, is preferred. Experience in SAS is preferred but having experience in other coding languages (e.g. R, Python) and a willingness to learn SAS would suffice.

We are a dynamic and friendly team composed of veterinary epidemiologists and statisticians who very much enjoy working with new students and teaching new skills. We regularly have students and recent graduates researching with us.

Disciplines: Analysis, Applied Mathematics, and Probability and Statistics

Hosting Site:

U.S. Department of Agriculture, Animal and Plant Health Inspection Service (APHIS)

U.S. Citizenship is a requirement for this internship

Project Description:

Help to automate the creation of national-level USDA animal health reports with the National Animal Health Monitoring System (NAHMS). NAHMS, a non-regulatory unit of the USDA, completes national studies that provide essential information on livestock and poultry health and management to decisionmakers, including producers, researchers, and policymakers. For more information please visit our website: www.aphis.usda.gov/nahms

Recently, NAHMS has worked to provide study results through innovative software, including tableau dashboards, pdfs, and informational briefs.  In order to meet the needs of our diverse set of data users, we are looking to create a set of data products from one set of statistical outputs. The data product that we would like to develop next is a pdf report using either Rmarkdown or SAS code to translate a long-form dataset of statistical data into a human-readable report that can be consumed digitally or printed out and used or distributed. This process will replace a predominantly manual process of developing pdf versions of these reports. The pdf report will accompany a Tableau dashboard presenting the same statistical data. The project will likely cover reports for cattle, goats, and swine.

Knowledge of R (especially Rmarkdown) or SAS is preferred, but willingness to learn would suffice. The applicant would interact regularly with USDA statisticians and would work with confidential data and national-level statistical summaries of animal health and management data. There would be ample opportunity to get experience with coding in statistical software, with the aim to produce a pdf report to accurately communicate the story behind the statistics so that it is easily digestible by the general public. The reports would be shared on the NAHMS website.

Join our team and make a difference in the agricultural industry. These reports are used by many stakeholders to support research and growth in the studied agricultural commodities. The team is very dynamic and willing to teach and learn from students. We look forward to collaborating with you!

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

Hosting Site:

U.S. Department of Agriculture, Animal and Plant Health Inspection Service (APHIS)

Project Description:

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

This is an exploratory project to investigate whether low rank methods can be used to recover multiscale features of physical flows.  In this project, the student will design and implement methods and will assess the potential of the approach.  The student will learn about fluid dynamics and tools for (multi)-linear algebra as well as presentation and writing skills.  Opportunities will also be provided to interact with lab staff, postdocs, and other interns.

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

The goal of this project is to develop hybrid algorithms for the numerical simulation of complex particles systems. These algorithms combine fluid and kinetic models in order to construct highly efficient simulations that incorporate non-equilibrium kinetic effects only when necessary for simulation accuracy. In this project, the student intern will develop numerical methods, perform numerical analysis, and implement methods numerically using modern software tools.

Disciplines: Applied Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

Deep learning models are gaining wide interest within the scientific computing community due to their role in detecting and explaining underlying correlations between the different physical quantities that characterize a complex system. In particular, graph convolutional neural networks (GCNNs) have been showing great potential to describe the behavior of materials at microscopic scale by accurately capturing and describing interatomic interactions.

The predictive performance of GCNNs is very sensitive to the choice of the architecture for multiple hyperparameters such as the number of neurons per layers, the number of convolutional layers, the number of fully connected layers, the radius cutoff, the activation functions at each hidden layer, the learning rate and the batch size to iteratively train the model. All these hyperparameters strongly impact the predictions made by a GCNN model and GCNNs with different hyperparameter setups may produce vastly different predictions for the same input data. In particular, some choice of hyperparameters may lead to a poor predictive performance due to numerical artifacts such as overfitting or underfitting. Therefore, identifying an appropriate setting of hyperparameters is essential to ensure the model’s accuracy and generalizability.

Identifying a hyperparameter configuration that would make GCNN both accurate and robust requires performing an exhaustive search over a high dimensional space, which, in general, is computationally expensive. High performance computing can be leveraged to alleviate the computational burden of hyperparameter optimization (HPO) by concurrently exploring several hyperparameter configurations with distributed computing resources.

In this work, we will develop and implement scalable HPO algorithms for GCNNs. We will use the RayTune library for hyperparameter tuning and we will integrate the RayTune functionalities into an existing implementation of GCNNs. The performance of the HPO procedure will be assessed in terms of: (1) scalability attained by distributing the hyperparameter search over hundreds of compute nodes on supercomputers at the Oak Ridge Leadership Computing Facility (OLCF) and (2) validation accuracy of the trained GCNN model on 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