Past Projects
Below is the list of archived projects from the 2021 summer cohort for the NSF Mathematical Sciences Graduate Internship.
For a list of currently available projects, visit the Project Catalog page.
2021 Projects
Project Title  Citizenship Required  Reference Code  Posted Date  Posted Datetime  Hosting Site  Internship Location  Disciplines  Description 

No  ORNLPASINI1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Probability and Statistics 
Project Description:The goal of this project is to address arising computational challenges in improving performance of Artificial Intelligence and Deep Learning applications on stateoftheart supercomputers. Particular focus is on improving the performance of current optimization algorithms (e.g. Stochastic Gradient Descent, Adam) applied to train statistical models (e.g. neural networks). Standard optimization algorithms update the regression weights of Deep Learning models in a strongly sequential fashion which is the consequence of the data batches successively updating the regression weights of the predictive models. This sequentiality in handling different data batches causes significant bottlenecks for the parallelization. Thus, current algorithms are extremely inefficient and computationally involved when statistical models are deployed and trained on highperformancecomputing architectures. Although attempts to overcome this computational barriers are already underway, the improvements obtained to date are incomplete and limited in the scope of applications. Our project propose to develop generalpurpose communicationavoiding strategies that can improve the scalability for the training of Deep Learning models without compromising convergence rates with respect to standard approaches.
Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


Yes  USACETORRES1*  11/23/2020  1606107600000  U.S. Army Corps of Engineers, Engineer Research and Development Center  Vicksburg, MS  Applied Mathematics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:In the Gulf of Mexico (GOM) and similar large bodies of water surrounded by land, seasonal warming in the summer months induces thermal expansion of the water surface through baroclinic processes. This seasonal variability is prevalent in the tidal signal at most NOAA tidal gages in the GOM region. For storm surge inundation studies, the timing of the tidal signal (flow or ebb stage) can contribute significantly to the overall surge inundation at the time of hurricane landfall. Traditional tidal analysis methods typically account for only the basic tidal signal structure, and tend to underestimate (or overestimate) the magnitude of the daily high (or low) tide. Current solutions in numerical modeling applications involve applying a static water level adjustment to the boundary conditions of the model (e.g., ADCIRC) to account for the variability in circulation. We seek a more universal approach to adjust the tidal signal for storm surge predictions. This project aims to characterize and quantify the seasonal variability in the tidal signal such that variability can be detected and corrected for storm surge numerical modeling applications. The findings of this project are expected to inform continued development of a probabilistic framework for detecting and correcting seasonal variability parallel to traditional tidal analysis methods in a followon opportunity. The prospective student intern will engage in research with mentors to develop an understanding of tidal analysis methods and processes. The intern will assist with determining the best methods/techniques to characterize and quantify the seasonal variability in the GOM region. If successful and/or if time permits, the intern will follow through in the detection and correction methodology. The intern will participate in weekly meetings with mentors to discuss progress, as well as document methodology and showcase results. The intern should have experience with time series analysis, scripting in highlevel languages (e.g., MATLAB, Python), probability and statistical analyses methods, stochastic modeling, as well as interest in coastal water waves and storm/surge modeling. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center Internship location: Vicksburg, MS Mentors:
Internship Coordinator:


No  ANLWILD1  11/23/2020  1606107600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics, Operations Research, Probability and Statistics 
Project Description:We explore different loss functions and formulations of simulationbased calibration and parameter estimation. We are particularly interested in the setting where some of the simulations may fail or yield outliers. We will develop and evaluate optimizationbased and statistical algorithms for such problems.Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  LANLFARRAR1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Probability and Statistics 
Project Description:The process of implementing a damage detection strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). The SHM process compliments traditional nondestructive evaluation by extending these concepts to online, in situ system monitoring on a more global scale. SHM can best be described in terms of a statistical pattern recognition paradigm. In this paradigm, the SHM process can be broken down into four parts: (1) Operational Evaluation, (2) Data Acquisition and Cleansing, (3) Feature Selection and Extraction, and (4) Statistical Model Development for Feature Discrimination. Studies to date suggest that a fundamental axiom of SHM is that all damage increases the “complexity” of a system. This increase in complexity can manifest itself in terms of geometric complexity, material complexity, or information complexity encoded is sensors monitoring the structure’s dynamic response. The challenge is to determine what are the appropriate measures of complexity to be used for a given damage detection problem. This project will focus on studying the various measures of information complexity based on the concept of “entropy”. The student will begin by studying the Shannon Entropy, which was developed for communications theory in the late 1940s. Since then a number of information entropy measures have been proposed in the literature for a variety of applications. They include: KomogorovSinai Entropy, Pesin Formula, Permutation Entropy, Renyi Entropy, Topological Entropy, Transfer Entropy, Spectral Entropy, Differential Entropy, Conditional Entropy, Relative Entropy, Mutual Information. The goal of this project will be to develop an understanding of the relationship between these various entropy measures, their respective sensitivities (e.g to time series length) and demonstrate their relative performance as a damage indicator on numerical and experimental data.Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  LANLLAWRENCE1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Mathematics (General) 
Project Description:This internship is part of project to build scalable statistical inference algorithms that can model large spatiotemporal simulation data and be fit inside the simulation as it is running ("insitu"). Next generation exascale supercomputers will generate huge amounts of data with rich opportunities for scientific discovery. However, these architectures will be storagelimited, so these opportunities will be missed if analysis can only be done offline, after most of the data has been discarded. Our goal is to develop the fundamental algorithms needed to perform statistical inference insitu to the full stream of data those simulations generate. We will be driven by questions from the fields of climate and space weather modeling.To answer such questions, we will develop algorithms to fit Bayesian hierarchical models to spatiotemporal simulation data. An example is to fit generalized extreme value distributions to precipitation data at every grid cell in a climate simulation. The parameters of the distributions would vary smoothly over the spatial domain of the simulation and the posterior distribution would be updated quickly at each time step. The core of this model will be based on sparse Gaussian process models which will describe the change in the parameters over space. To make the models scalable, we plan to consider a number of possible approaches and components. For example:  Globallocal approaches to distributed computation in which models are initially fit on each computation node independently and updated based on limited information sharing.  Estimation with fast approximate Bayesian inference methods such as variational inference.  Deep neural networks to learn approximate sufficient statistics that can be passed between nodes to improve fitting.  Fast, approximate, and distributed linear algebra. The summer internship can be aimed at any part of the overall project. Interested students should contact the mentor to discuss possibilities. Disciplines: Applied Mathematics, and Mathematics (General) Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  LANLMEIERBACHTOL1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Mathematics (General) 
Project Description:Higherorder accurate numerical discretization schemes are often useful, and sometimes required, when modeling vectorized wave propagation on rectilinear grids within large domains. Although yielding superior numerical results wherever applied, they can prove overly burdensome (from a computational efficiency standpoint) if applied uniformly across said large grids. Since higherorder accuracy is not always required throughout the entire domain, more localized methods would ideally be utilized whenever possible. The use of subgrids is one such solution to this problem. However, the correct treatment of their coarse/subgrid boundary, along with their underlying grid structures (not to mention the need to maintain temporal consistency and stability) often make their development and derivation a complex task, to say the least. So while higherorder accurate algorithms on subgrids would undoubtedly prove useful for accurately modeling vectorized wave propagation within large domains, no such generalized algorithm has yet been developed in three spatial dimensions. (Some unpublished work has been previously carried out by the mentor in this area, producing a simple, onespatialdimension formulation.) Thus, this project will investigate higherorder accurate discretization schemes for modeling vectorized wave propagation across sub grids in three dimensions. Specifically, this will involve the development of a numerical algorithm that selfconsistently solves a higherorder formulation of the discretized vector wave equations for regions including a coarse/subgrid boundary. This will necessarily include both spatial and temporal frames, and extend to three spatial dimensions. The developed algorithm should satisfy stability criteria at all times. It may be necessary to concurrently develop a standalone code for testing and proofofconcept purposes.Disciplines: Applied Mathematics, and Mathematics (General) Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  LANLNEUDECKER1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Probability and Statistics 
Project Description:The goal of this project is to utilize machine learning methods to improve the quality of estimates of nuclear reaction cross sections and their uncertainties in nuclear databases. These nuclear data are critical for understanding and modeling nuclear physics in reactors and other scientific applications. These estimates are obtained using a statistical combination of complex nuclear physics models and experiments. They are then tested in the simulation of validation experiments, which integrate many sets of nuclear data into one model of a complex experiment. Using machine learning, we have been able to identify previously unidentified relationships between nuclear data estimates and benchmark bias. This project will focus on further advancing the methodology for machinelearningaugmented search for sources of bias in benchmarks and basic nuclear physics experiments to improve nuclear data evaluation.Disciplines: Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  LANLSEVERSON1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Biometrics and Biostatistics, Probability and Statistics 
Project Description:Infectious disease outbreaks can quickly change course moving into new populations or developing resistance to antimicrobial agents. Likewise, infectious agents can interact with one another in infected persons leading to highly complex nonlinear dynamics as they spread though human populations. Deciding how to adapt policies to the changing and complex landscape of an ongoing outbreak involves optimizing limited prevention resources to both prevent as many future cases as possible but also adapt to the evolving epidemic itself. This project involves continuing work in developing and implementing numerical optimal control methods for optimining the dynamic investment in a suite of different prevention methods over a variable time horizon for infection transmission models. This work is aimed at using mathematical methods to provide real decision support for public health agencies, which involves dealing with hard constraints such as limited budgets and nonequilibrium dynamics. Our long term goal is to integrate mathematical decisions support into the emerging field of near realtime surveillance based on realtime genetic sequencing and moding of infectious disease pathogens.Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  LANLJAFAROV1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Biometrics and Biostatistics 
Project Description:The student will conduct computational modeling work to implement hydrolysis and methanogenesis reaction equations within a processbased computational model. Here, we are attempting to develop a new capability designed to optimize the production of methane within anaerobic gas biodigesters that consume heterogeneous solid waste streams. Once equations are implemented, parameter sensitivity analysis will be conducted given a variety of different inputs to optimize methane production under various environmental conditions. The end goal of the modeling exercise would be to produce similar results to the Anaerobic Digestion Model #1 (ADM1), which is the industry standard for models of this kind. The student would work closely with a small team of three people who collectively have experience in computational modeling and reactive chemistry. Expected deliverables include a presentation of work at the end of the internship to a scientific audience. There will be opportunities to broaden learning experience by attending weekly scientific talks and interacting with other students and scientific professionals.Disciplines: Applied Mathematics, and Biometrics and Biostatistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  LANLSTAUFFER1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:We are building a generic radionuclide transport model of the vadose zone of the northern Negev region to develop capabilities required to evaluate potential vadose zone sites for nuclear waste disposal in Israel. This model will demonstrate the applicability of the Negev vadose zone for nuclear waste disposal, highlight potential limitations and data gaps, and refined at a later date for a specific site or expanded to include deeper geologic layers. The work plan combines experimental and numerical work. It is built in a structured manner and organized into three phases. In Phase 1 – Year 1, a conceptual model has been be built by collecting all the available data on the geology, geohydrology, geophysics and geochemistry of the Negev area. The conceptual model serves as the basis for building the Geologic Framework Model (GFM) grid, used as the basis of the Negev subsurface Hydrogeologic and Flow and Transport process models. In Phase 2 – Year 2, uranium batch sorption and column desorption experiments have been be conducted on rock samples of different lithologies initially using one radionuclide. In Phase 3 – Year 3 of this study (2020), the radionuclide transport model will be completed, as well as the Negev subsurface hydrogeologic model. These will be integrated into a prototype flow and transport model for the Negev potential repository site. Preliminary site recommendations for the Negev area will be provided to the IAEC based on findings, to direct future siting decisions on potential vadose zone waste disposal sites. This project will focus on significant geostatistical analysis and creation of a complex 3D simulation of radionuclide transport. Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  LBNLGHYSELS1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics 
Project Description:Combinatorial algorithms are indispensable in factorizationbased sparse linear equations solvers. Examples include reordering of a sparse matrix to limit the amount of fill in the factorization and scheduling tasks in parallel factorization. Finding an ordering that minimizes fill, and hence memory usage, of the solver is an NPcomplete problem. Finding an optimal scheduling is also NPcomplete. Over the past decades, highquality heuristics have been developed for finding good approximations to some of these combinatorial problems. Traditionally, the development of these heuristics has focused on the quality of the solution. However, due to the everincreasing degree of parallelism, they are becoming serious bottlenecks. Although efficient sequential implementations of the heuristics exist, these techniques are often hard to scale to multiple processing nodes. Instead of trying to come up with new, more scalable heuristics that achieve the same quality, it is time to explore radically new, outofthebox approaches. Deep reinforcement learning (DRL) is such a technique, which promises much more scalable solution. The ability of DRL to learn directly on rules to discover new policies is of particular importance here. The very nature of NPcomplete problems makes training a deep learning algorithm intractable in a supervised way. Without a brute force approach, one cannot compute the optimal solution of a problem, making it impossible to fabricate inputoutput data to train the algorithm. Training with data constructed from known heuristics will limit the achievable quality. Hence, enhancing the policies discovered by the algorithm, corresponding to the reinforcement part of the approach, is crucial. In this project, the candidate will investigate the use of various training reinforcement techniques for several combinatorial problems arising in sparse matrix factorizations, as well as explore configurations of the deep neural network. Disciplines: Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentors:
Internship Coordinator:


No  LBNLLI1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Probability and Statistics 
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 nearoptimal parameters setting on a largescale 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 bruteforce approach (e.g., gridsearch) 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. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LBNLMUELLER1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Probability and Statistics 
Project Description:In many scientific applications, computer simulations are used to approximate complex physical phenomena. These simulations usually have parameters that must be adjusted in order to obtain the most accurate simulations. Accuracy is assessed by comparing the simulation output to observation data. However, these data are often noisy, and therefore parameter inference is needed to determine those simulation parameters that most likely explain the observations. Simulations are often computationally expensive and may require several minutes or hours per run. Thus, during inference, we cannot query the simulation model thousands of times in order to find the desired parameter posterior distributions. Moreover, simulations are often provided as black boxes, i.e., there is no analytic description available and inference methods that are based on adaptive exploration of the sample space are needed. Previously, methods have been developed that exploit Gaussian process models as surrogates of the expensive simulation in Bayesian inference. However, these methods do not scale well with an increasing number of sample points and parameters. In this project, your research will focus on the development of scalable inference algorithms that are efficient and effective for computationally expensive models. In order to achieve this, your work will involve the development of new sampling strategies that adaptively explore the potentially largedimensional parameter space; the use of dimension reduction and sample space reduction methods; the use of Gaussian process models (or other types of surrogate models); and Bayesian inference methods. You will develop a suite of fasttocompute test problems to assess the performance of your developed algorithm and finally apply it to a realworld science problem. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LBNLPERCIANO1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Probability and Statistics 
Project Description:This project explores the use of Probabilistic Graphical Models (PGM) such as Markov Random Fields (MRF) along with deep learning models to tackle image analysis problems at scale. Those two frameworks have been widely used individually with success in the area of image processing. Recent works propose the combination of PGM with Deep Neural Networks allowing: (1) easier and more efficient PGM optimization (2) incorporating learning into the PGM. Research scope will include not only the mathematical modeling behind these approaches, but also code development taking into account optimization for large datasets. Research and development will be applied to datasets obtained from state of the art instruments in one or more fields such as material science, medicine, biology, chemistry, others. Accepted applicants will collaborate directly with Dr. Perciano, who is a Research Scientist with broad expertise in image processing and analysis, computational statistics, high performance computing and machine learning. Interns will also network with and will have the opportunity to collaborate with members of the Data Analytics and Visualization group at LBNL and the Computational Biosciences Group. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LBNLWILLCOX1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics 
Project Description:Accurate models for the time evolution of stellar matter undergoing nuclear reactions are critical for simulating a variety of astrophysical problems spanning a large dynamic range in space and time. These include nuclear burning in turbulent convection, thermonuclear supernovae, corecollapse supernovae, Xray bursts, and many other explosive events. The nucleosynthesis of a reacting volume of fluid can be described by a set of stiff, coupled ordinary differential equations (ODEs) in time that can be expensive to integrate and generally require implicit methods. This project will apply machine learning methods to approximate the time integration of ODEs describing nuclear reactions as an alternative to integrating the reaction ODEs in hydrodynamics simulations. Our ultimate goal is to eliminate the computational expense of insitu implicit integration for nuclear reaction ODEs entirely while preserving underlying physics including energy, baryon number, and lepton number conservation. In this project we will first explore the size and topology requirements for neural networks to reproduce the nucleosynthesis and energy generation from nuclear reactions given the physical constraints above. Your research will determine the optimum neural network configurations for representing a range of different nuclear reaction systems applicable to open problems in astrophysics. We will generate training data sets from existing tools for implicit time integration of these systems of reactions across a range of representative thermodynamic conditions. You will also collaborate with astrophysicists to verify your neural network models in astrophysical burning scenarios where reactions and hydrodynamics are strongly coupled. You will work with an interdisciplinary team of applied mathematicians, engineers, and astrophysicists in the Computational Research Division at Lawrence Berkeley National Laboratory. Disciplines: Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LLNLPAZNER1  11/23/2020  1606107600000  Lawrence Livermore National Laboratory  Livermore, CA  Applied Mathematics 
Project Description:Scientific machine learning (SciML) is a new and rapidly evolving field of research, lying at the intersection of machine learning and scientific computation. SciML focuses on how to incorporate the success of datadriven machine learning models to enhance physicsbased simulations in computational science and engineering applications. In order to apply these methods to largescale problems, efficient and scalable algorithms for highperformance computing platforms are required. Residual networks, a powerful tool often used in deep learning applications, can be interpreted as discretized versions of dynamical systems. This interpretation can lead to new insights about the behavior of these networks, and inform the design of training algorithms. This project will focus on the application of recent advances in parallelintime integration and optimal control to develop training algorithms that are scalable and parallelizable across the layers of the network. Additionally, a goal of this project is to develop novel discretizations for the weights of the network based on spline bases, allowing for deeper networks without increasing the complexity of the corresponding optimization problem. These algorithms will be run on largescale, massively parallel supercomputers, and will be applied to relevant SciML problems. Disciplines: Applied Mathematics Hosting Site:Lawrence Livermore National Laboratory Internship location: Livermore, CA Mentors:
Internship Coordinator:


No  LLNLPETERSSON1  11/23/2020  1606107600000  Lawrence Livermore National Laboratory  Livermore, CA  Applied Mathematics 
Project Description:This project develops an efficient solver for the quantum dynamical control problem, aiming at 1 M degrees of freedom (DOF), corresponding to a 20qubit system. The need for optimal control of quantum systems lies at the heart of several emerging technologies from quantum sensing to dynamical control of chemical reactions and, most significantly, quantum computing. Solving the quantum control problem amounts to finding timedependent control signals that are applied to the quantum computing hardware to guide the quantum states through a prescribed sequence of quantum logical operations. Finding the control signals can be cast into an optimization problem, under the constraints imposed by the time dependent Schroedinger equation, which governs the dynamics of the quantum system. Precise, fast and energy efficient control signals are required to realize the quantum logical gates that constitute the building block for quantum algorithms and to initialize a quantum system from a thermal state. Additional control signals are needed for extracting the information stored in the quantum states at the end of the simulation. In order to meet the demand for this capability we are developing a gradient based optimization algorithm, utilizing the adjoint Schroedinger equation to effectively compute the gradient of the objective function, implemented on a highperformance (classical) computing platform. Disciplines: Applied Mathematics Hosting Site:Lawrence Livermore National Laboratory Internship location: Livermore, CA Mentor:
Internship Coordinator:


No  NISTDOGAN1  11/23/2020  1606107600000  National Institute of Standards and Technology  Gaithersburg, MD  Applied Mathematics, Geometry, Probability and Statistics 
Project Description:The goal of this project is to develop tools for image and shape analysis, by leveraging scientific computing and machine learning algorithms. Various research opportunities exist in the following topics: Disciplines: Applied Mathematics, Geometry, and Probability and Statistics Hosting Site:National Institute of Standards and Technology Internship location: Gaithersburg, MD Mentor:
Internship Coordinator:


Yes  ORNLBRIDGES2*  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Analysis, Applied Mathematics, Mathematics (General), Operations Research, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Vehicles rely on constant communication of many electronic control units (ECUs), little computer, which broadcast messages across a few controller area networks (CANs). Various ports and indirect communications (E.g., Bluetooth, wifi, etc.) have exposed this critical invehicle network to cyber attacks, e.g., the welladvertised Jeep hack, stopping a vehicle remotely while it was driving on a highway. Exacerbating the problem for defensive research is that there is no available translation of the CAN bus packet contents (bits) to the vehicle’s functions (e.g., speed, rpms, brake lights, …), and every model has different encodings. Basically, we can see all the messages, but we do not know what they mean, and it varies per model. The goal of this project is to use data science to aid in understanding and defending the vehicle network communications. We are currently working with regression techniques to reverse engineer signals in the data, and manifold learning and deep learning techniques for building anomaly detectors. We collect and test results on real cars and strive to implement detection capabilities in hardware. This internship seeks folks interested in learning and implementing algorithms to test detection accuracy. Disciplines: Analysis, Applied Mathematics, Mathematics (General), Operations Research, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLDUMITRESCU1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Geometry, Mathematics (General), Probability and Statistics, Topology 
Project Description:Until fault tolerant quantum computers are readily available efficient program encodings minimizing circuit depth and associated errors are needed. This project focuses on the decomposition of a wide variety of Hamiltonian simulation and information processing unitaries into a set of operations physically implementable by manybody analog evolution with transmonbased superconducting qubits. The work will consist of employing unitary decomposition methods to compile hardwareefficient quantum programs. Disciplines: Applied Mathematics, Geometry, Mathematics (General), Probability and Statistics, and Topology Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentors:
Internship Coordinator:


No  ORNLERWIN1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Hanover, NH  Applied Mathematics, Biometrics and Biostatistics, Mathematics (General) 
Project Description:The Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute provides structured and unstructured data from populationbased cancer registries across multiple states. The SEER database provides information about demographics, cancer site, treatment, and follow up status. Leveraging the computing resources at Oak Ridge National Laboratory, the goal of this project is to analyze the SEER data to predict long term cancer outcomes based on socioeconomic status. With unsupervised learning methods, we will first create visual tools (ex. graphical networks with clustering algorithms) to broadly understand the SEER data. From there, we will leverage artificial intelligence and machine learning to develop a predictive model that utilizes multiple variables from the SEER registry. The ultimate goal is to understand which socioeconomic factors are key contributors to the treatment and follow up status of patients. This internship seeks applicants with experience in programming (ideally R or Python), and an interest in applying a multitude of mathematical and statistical skills to solve key problems in health care. Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Mathematics (General) Hosting Site:Oak Ridge National Laboratory Internship location: Hanover, NH Mentor:
Internship Coordinator:


No  ORNLFATTEBERT2  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN 
Project Description:Phase Field Modeling (PFM) is a technique used to track interfaces using a “phasefield” that takes, for instance, a value of 0 on one side of the interface, a value of 1 on the other side, and smoothly varies between the two through the interface. The interface can then be defined by the isosurface where the function takes the value 0.5. This technique is used a lot for modeling solidification in metals, where the phase variable would take the value “0” would correspond to “liquid” and the value “1” to “solid”. A more specific application of recent interest is modeling solidification in metallic alloys during the process of additive manufacturing. In practice, PFM leads to solving a system of coupled partial differential equations to calculate the time evolution of the interface/phasefield, the composition of the alloy, and possibly a coupled temperature field. These equations can be discretized in time using an implicit scheme (backward Euler) and in space using a finitevolume approach. These discretized equations can then be solved using a Jacobian Free Newton Krylov (JFNK) approach. Solving the resulting linear systems iteratively  by GMRES for example  requires a good preconditioner. Geometric multigrid works well in practice to precondition the diffusion equations to be solved for composition and temperature. In this project, we want to extend the general technique described above to the context of a moving “frame”, that is a computational domain that follows the solidification front and moves at the velocity of the interface. Doing that adds a “convection” term to the equations, with a velocity given by the velocity of the moving frame. This has been done before for explicit time discretizations, but not for an implicit timestepping. The difficulty in an implicit approach is to find a good preconditioner that can handle well the diffusion part and the convection part of the operators. The idea to be developed in this project is to use a preconditioner based on an operator splitting idea. This research will require some coding in an open source C++ code developed by mentor and others, which uses the Sundials package for timeintegration. This research is likely to lead to a peerreview publication. Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLHAUCK2  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics 
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 nonequilibrium 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 Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLKAR1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Analysis, Applied Mathematics, Operations Research 
Project Description:The purpose of this project is to predict human mobility patterns following disasters due to failure of critical infrastructures, specifically, transportation networks. Understanding human mobility pattern following a disaster event, such as a tropical storm, is crucial for assessing impacted and displaced population. Given that many communities lack information about how the failure of an infrastructure following a disaster can impact emergency management efforts, it is crucial to understand how failure of critical infrastructures, specifically, roads impact mobility pattern of impacted populations and subsequent origin and destination locations. Given the availability of large volume of heterogeneous location and mobility data, this project focuses on: (i) understanding human mobility pattern during normal conditions using heterogeneous big data (unstructured  social media and other crowdsourced textual and imagery data, and structured geospatial data  infrastructure and disaster data) using activity based intelligence, network analysis and trajectory data mining, (ii) developing reinforcement learning based recommender system to predict mobility pattern during and following a disaster by accounting for damaged and unusable road networks, and (iii) uncertainty quantification of the outputs. Other than being transformative, the scientific impacts of this research include (i) deriving fundamental understanding about human mobility behavior that could be used to develop strategies for humanitarian response and infrastructure planning, (ii) deriving insights into the interaction between human mobility and infrastructure network (i.e., roads) that is pivotal for infrastructure failure planning, restoration and emergency response. The broader impact of this project is the creation of nextgeneration response tools for first responders, decisionmakers and stakeholders to aid with decisionmaking and preparedness activities. We have recently expanded to implementation of activitybased intelligence (ABI) to derive origin and destination matrix that would be used in the reinforcement learner. The ABI will be evaluated in near realtime by accounting for changes in transportation network access and extreme event impact areas such that different sets of origin, destination and network will be determined used the reinforcement learner under different circumstances. Disciplines: Analysis, Applied Mathematics, and Operations Research Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLOSTROUCHOV1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Biometrics and Biostatistics, Probability and Statistics 
Project Description:The Oak Ridge National Laboratory has many parallel computing systems as well as many R language parallel computing tools developed by the pbdR project (pbdr.org). The student’s project will involve either using these tools to perform various statistical analyses on a mutually agreed on large data set or developing more parallel statistical computing tools. While some specific project topics are available (such as parallelizing knockoffs or polynomial regression tools), it is also possible for the graduate student to further own thesis related research with parallel computing on large parallel systems. Ideally, the student will already have considerable experience with R and possibly some exposure to parallel computing. Disciplines: Biometrics and Biostatistics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLSELESON1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN 
Project Description:Peridynamics is a nonlocal reformulation of classical continuum mechanics suitable for material failure and damage simulation. Peridynamic models have been applied to simulate a variety of engineering problems, particularly those involving large deformation and crack propagation. This project will study various numerical methods to advance peridynamic capabilities, in terms of simulation accuracy and efficiency. Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLSELESON2  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics 
Project Description:Atomistic models have been shown to be effective for modeling and simulation of many materials science problems. One of their main drawbacks is a high computational expense, which limits their application to very small systems. Atomistictocontinuum (AtC) coupling is a multiscale modeling technique to attain accurate representation of atomistic phenomena in largescale systems. This is achieved by employing atomistic models only in small critical regions, while coupling those to continuum formulations. Quasicontinuum is a class of AtC coupling methods. This project will investigate a novel highorder quasicontinuum approach based on a blending methodology and study numerically and analytically its performance in AtC coupling problems. Disciplines: Applied Mathematics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  PNNLDEVANATHAN1  11/23/2020  1606107600000  Pacific Northwest National Laboratory  Richland, WA  Analysis, Applied Mathematics, Probability and Statistics 
Project Description:The aim of this project is to identify materials that retain their strength for tens of thousands of hours during service at temperatures in excess of 650 C. We will gather relevant alloy data, assess data quality, and use data analytics and machine learning to identify key factors governing alloy performance. Advanced data computing and data science methods have emerged over the past decade and have the potential to transform the energymaterials sector. There is a need for integrated data solutions, tools and databases, to support materials data analytics to meet end user needs. At present, materials data and information persist in largely disparate and differing forms. There is a need for new data science driven tools to help find, acquire, and transform these existing datasets and put them to work for energymaterials research. Building this data foundation and developing tools and algorithms that will help improve efficiency of data acquisition and transformation is integral to meeting this need. For this effort, a solid foundation of data and information is necessary to understand the types of information about key materials that are currently collected, where that data and information exists presently, and define an approach for transforming data from a range of sources to meet end user needs. This summer, the team will focus on selecting 1 or 2 key materials as a use case to address the needs above, develop a work flow for addressing those needs, and initiating development of cohesive database and data analytics for those key materials where data resources acquired can be integrated. Disciplines: Analysis, Applied Mathematics, and Probability and Statistics Hosting Site:Pacific Northwest National Laboratory Internship location: Richland, WA Mentor:
Internship Coordinator:


No  SNLD'ELIA1  11/23/2020  1606107600000  Sandia National Laboratories  Albuquerque, NM  Applied Mathematics, Mathematics (General) 
Project Description:In this project we continue an ongoing effort focused on the development of a unified nonlocal theory. The ultimate goal is to derive a universal theory of nonlocal operators that spans a broad spectrum of nonlocal processes and has, as special instances, the classical calculus and the fractional calculus. The foundation of such unified calculus is the wellestablished nonlocal vector calculus for "truncated nonlocal operators". This new theoretical framework would provide the groundwork for newmodel discovery and, hence, enable modeling and simulation of intrinsically nonlocal phenomena that have not been studied due to the lack of theory. In this project, we focus on necessary preliminary results: the establishment of equivalences of unified nonlocal operators and common nonlocal operators used in mechanics. Disciplines: Applied Mathematics, and Mathematics (General) Hosting Site:Sandia National Laboratories Internship location: Albuquerque, NM Mentor:
Internship Coordinator:


Yes  SNLQUADROS1*  11/23/2020  1606107600000  Sandia National Laboratories  Albuquerque, NM  Applied Mathematics, Geometry 
U.S. Citizenship is a requirement for this internship Project Description:Goal of this project is to generate series of anisotropic tetmeshes for solution convergence. Initial tetmesh is generated by using Sandia’s geometry and meshing toolkit Cubit. Cubit uses Delaunay based algorithm with geometrically guided controls to generate an initial tetmesh. First step in this project is the extract a tensor field that captures the initial mesh characteristics. The tensor field defines tetrahedral elements’ size, shape and orientation throughout the domain. Next step is to scale the metric tensor field so that desired number of output elements can be obtained. The scaling factor is defined as the ratio of number of elements in the output mesh to number of elements in the initial mesh. This scaling factor is provided by the end user. While the anisotropy of the mesh elements is controlled globally through the applied scaling measure, the resulting volumetric constraint is controlled through the necessary local modifications of the mesh at each iteration of the mesh generation procedure. Such local modifications are contingent upon the notion of the metrics defined at discrete points. In general, the metrics act as controls for the size, shape, and orientation of the generated meshes. We rely on the theoretical foundation of the logeuclidean framework to generate metrics at nodes of a discretized mesh. This framework establishes a onetoone relation between the vector space of symmetric matrices and the vector space of tensors on the computational domain. Nodal metrics are expressed in the form of a weighted geometric mean of the mesh element metrics. Open source OmegaH library will be used to adapt the initial mesh to match the scaled tensor field defined at the nodes in generating output anisotropic tetmesh. Student will work closely with developers of Cubit and OmegaH. As most of the infrastructure is already in place, there is a good possibility to publish the work in a mesh generation related international conference. One of the goals of this internship is to get results from this continued project and potentially publish this research in the International Meshing Roundtable conference. Disciplines: Applied Mathematics, and Geometry Hosting Site:Sandia National Laboratories Internship location: Albuquerque, NM Mentor:
Internship Coordinator:


Yes  USACEGASPELL1*  11/23/2020  1606107600000  U.S. Army Corps of Engineers, Geospatial Research Laboratory  Various Locations  Geometry 
U.S. Citizenship is a requirement for this internship Project Description:The main focus of this project is to utilize low Size, Weight and Power (SWAP) sensors to map and survey building interiors and subterranean environments. One key aspect of this project is sensor fusion leveraging the Robot Operating System (ROS). Another is exploring Simultaneous localization and mapping (SLAM). The optimal configuration (hardware and software) will then be incorporated onto a GVRbot UGV to determine the accuracy of the resulting point cloud. Disciplines: Geometry Hosting Site:U.S. Army Corps of Engineers, Geospatial Research Laboratory Internship location: Various Locations Mentor:
Internship Coordinator:


Yes  USACEMARCHANT1*  11/23/2020  1606107600000  U.S. Army Corps of Engineers, Geospatial Research Laboratory  Hanover, NH 
U.S. Citizenship is a requirement for this internship Project Description:Photoncounting LIDAR systems collect highresolution 3D data from high altitudes across large areas through use of low signaltonoise (SNR) receivers. These devices have larger amounts of noise versus traditional, lowaltitude LIDAR sensors. The two primary noise sources can be characterized as uncorrelated Poisson noise and crosstalk noise correlated with stronger, real detections off of objects in the scene. This project will apply new, untested mathematical methods for denoising and signal processing to raw photoncounting LIDAR datasets. Participant will collaborate closely with the primary signal processing algorithm developer and apply their knowledge of mathematical methods to the problem through algorithm development in either Matlab or Python. Hosting Site:U.S. Army Corps of Engineers, Geospatial Research Laboratory Internship location: Hanover, NH Mentors:
Internship Coordinator:


No  USACEMAYO1  11/23/2020  1606107600000  U.S. Army Corps of Engineers, Engineer Research and Development Center  Vicksburg, MS  Applied Mathematics, Probability and Statistics 
Project Description:Research Objective: What biological factors drive the basic individual interactions in bird flocks or fish schools, causing them to coalesce into larger groups that move fluidly in unison? More importantly, how can such factors enable the contagious spread of an idea or action? We aim to advance our ability to forecast critical transitions by unraveling the building blocks of social contagion in a model system using recent advances in information theory. Evidence strongly suggests that animals may adopt a topological interaction mechanism as a means of coordinating their activity, but is drawn from a statistical mechanics approach that largely ignores the biological origins of the phenomena. Recent discoveries suggest that animal attention to physical cues is a crucial factor in driving collective action, thereby suggesting a flexible biological mechanism which parades as a fixed topological pattern. Hypotheses for the interaction mechanisms driving collective action have been traditionally validated using computer simulation to match grouplevel consequences with qualitative features observed in wild populations. However, there has never before been a means to more directly distinguish which, if any, of these hypothetical mechanisms are used by real animals to selforganize, and empirical evidence to decisively settle the issue is lacking. To address this problem, we propose a novel test of the Weber’s Law perception mechanism—i.e., that perception is driven by a foldchange in the magnitude of sudden velocity fluctuations—using social behavior in fish as a prototype for collective animal motion with stateoftheart information theory metrics that can distinguish between direct influence (A→B) and indirect influence (A→C→B). More specifically, we hypothesize that if animal collective motion is driven by a Weber’s Law selective attention mechanism, then individual fish will always be most directly influenced by local velocity fluctuations that exceed the group average. To test this hypothesis, we will use computer simulation to understand how influence from velocity fluctuations can be inferred from grouplevel data using information theory metrics that distinguish causation from correlation. We will then determine whether velocity fluctuations drive individual attention in fish subjects experimentally using decision trials. We will manipulate key physical features (size, speed, direction) of virtual stimuli and track the reaction of our subjects, both in isolation and in groups. Experiments will determine whether individual dependence on velocity fluctuations propagate beyond pairwise interactions or threebody interactions to drive schooling at the group level. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center Internship location: Vicksburg, MS Mentor:
Internship Coordinator:


No  USDABERGMAN1  11/23/2020  1606107600000  USDA Forest Service Forest Products Laboratory  Madison, WI  Analysis, Biometrics and Biostatistics 
Project Description:We plan to develop a robust machine learning modeling framework to relate biomass properties variability at tissue levels by rapid NIR spectroscopy linked hyperspectral imaging (HSI) system with feedstock handling and conversion performances and to optimize conversionready designer feedstock for a biorefinery. Geospatially sourced corn stover (CS)  hydrolysis target, and southern pine forest residues (SPFS)  pyrolysis target, from various locations will be sampled, characterized, labelled, and screened into various tissue components corn stover5: cobs, leaves, husk, stalks/internode, others; pine forest residues: needles, bark, juvenile wood, chips/branches, others). When a tissue component does not offer improved conversion yield, other conversion pathways such as gasification, combustion or production of biochemical conversion will be explored. For example, juvenile wood contains more than 60% of hemicellulose, which could be an excellent feedstock for producing xylitol rather than pyrolysis. However, the economics of separating and producing juvenile wood should be considered and it will be considered in this proposal. The physical and chemical properties of each tissue component will be determined analytically while developing rapid measurement method by Hyperspectral imaging and sensing techniques to collect quick properties data. The performance metrics for mechanical screening equipment for tissue fractions (e.g. energy use, yield), powder handling characteristics after grinding, and conversion potentials (e.g. yield) of each tissue fractions will be determined at labscale. The tissue properties data will be used to train, validate and test machine learning based predictive models such as Artificial Neural Networks (ANN) with high correlation to feedstock performance metrics. The predictive models can serve as a decision support tool to identify, and/or design and optimize uniform conversion ready tissue fractions at low costs. The intern will collaborate with a postdoc research fellow in reviewing and finding the best artificial neural network (ANN) model to correlate biomass chemical compositions with conversion performances for biorefineries. Disciplines: Analysis, and Biometrics and Biostatistics Hosting Site:USDA Forest Service Forest Products Laboratory Internship location: Madison, WI Mentors:
Internship Coordinator:


No  USDABERGMAN2  11/23/2020  1606107600000  USDA Forest Service Forest Products Laboratory  Madison, WI  Analysis 
Project Description:To obtain parameters for product lifecycle assessments, surveys are sent to the producers in order to obtain necessary inputs for the LCA. From these surveys, values regarding the lifecycle costs and impacts of pallet production can be estimated. The quality of these estimates may be assessed by applying survey sampling principles. The following is a list of concerns and issues to be addressed.
Disciplines: Analysis Hosting Site:USDA Forest Service Forest Products Laboratory Internship location: Madison, WI Mentors:
Internship Coordinator:


No  ORNLARCHIBALD1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Probability and Statistics 
Project Description:Image compression is a very active field of study, with new methods being constantly generated. The need for improvements in image compression quality is growing in the field of HPC simulations because of the exponential trend in data generation. There exists an untapped potential in this situation due to the nature of simulated data that is not currently exploited. Simulation data from numerical systems of partial differential equations exist on a solution manifold. Thus, the manifold hypothesis in machine learningwhich states that realworld, highdimensional data lie on lowdimensional manifolds embedded within the highdimensional spaceis concrete for simulation data. We can therefore expect that identifying this map to the lowdimensional manifold will provide ideal compression for HPC Simulations. This project will focus on designing ideal compression for HPC simulation. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


Yes  LANLARMSTRONG1*  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Operations Research, Probability and Statistics 
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:
Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  LLNLCHOI1  11/23/2020  1606107600000  Lawrence Livermore National Laboratory  Livermore, CA  Analysis, Applied Mathematics, Mathematics (General), Operations Research, Probability and Statistics 
Project Description:We are developing efficient physicsinformed neural network reduced order models (NNROMs) to accelerate complicated, largescale physical simulations. Our current LLNLdeveloped physicsinformed NNROM can reduce the dimensionality of an advectiondominated 2D Burgers simulation to a latent space of 5 with a relative error with respect to the corresponding full order model of less than 1% and accelerate the full order model simulation by a factor of 10, which cannot be achieved by any machinelearning black box approach. We will extend our ROM to largescale problems, such as advectiondominated hydrodynamics, transport problems, turbulence, and Rayleigh–Taylor instability simulations. We expect our NNROM will achieve a higher speedup when it is applied to largerscale problems. A student participating in our research project will first learn what our NNROM can do for the 2D Burgers simulation and then extend it to a turbulence problem by training an autoencoder neural network on 2D turbulence model data and implementing NNROM on the turbulence model. Depending on the results, we will write a journal paper together. Our NNROM will be general enough that by the end of summer, the student will be able to apply the NNROM 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 Internship location: Livermore, CA Mentor:
Internship Coordinator:


No  LLNLBARKER1  11/23/2020  1606107600000  Lawrence Livermore National Laboratory  Livermore, CA  Applied Mathematics 
Project Description:This project focuses on the development of new algorithms for preconditioning highorder finite element operators without explicit matrix assembly. Emerging highperformance computing architectures make highorder finite elements more attractive, because high local arithmetic complexity often allows them to deliver higher accuracy for a similar compute time compared to loworder methods. Efficient implementations of the operatorvector multiply in this context are very fast with a matrixfree implementation, but matrix assembly is not practical at high polynomial order. The lack of an assembled matrix poses a challenge for solvers, where the standard workhorse of algebraic multigrid depends intimately on such a matrix. The goal of this project is to extend the general, automatic nature of algebraic multigrid to a setting where no explicit matrix is available. The project will involve discovering new algorithms for preconditioning and solving linear systems in this context, analyzing their theoretical convergence properties and computational costs, and implementing them in practical software packages.
Disciplines: Applied Mathematics Hosting Site:Lawrence Livermore National Laboratory Internship location: Livermore, CA Mentor:
Internship Coordinator:


No  NISTCOUDRON1  11/23/2020  1606107600000  National Institute of Standards and Technology  Gaithersburg, MD  Analysis, Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:Description: Preferred Prerequisites: Disciplines: Analysis, Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:National Institute of Standards and Technology Internship location: Gaithersburg, MD Mentor:
Internship Coordinator:


No  PNNLDEVANATHAN2  11/23/2020  1606107600000  Pacific Northwest National Laboratory  Richland, WA  Analysis, Applied Mathematics, Probability and Statistics 
Project Description:This project will collect, curate and manage data and information from the literature, processing and characterization experiments, and multiscale simulations. The database by itself will offer enduring value by bringing hidden data to light, preserving it, and making it available for future research. In addition, data analytics will connect the results of simulations and experiments to achieve new scientific understanding of solid phase processing (SPP) of alloys. Recent advances in data science offer an exciting opportunity to advance the science of SPP by identifying correlations in the large volume of data generated during processing and defining the key features that control the microstructure of alloys. Data management and data analytics integrated with physicsbased simulations, validated using data from experimental processing, processscale characterization and advanced in situ and ex situ characterization, are needed to optimize the processing conditions. Connecting the SPP parameters to microstructural evolution and phase stability is a daunting challenge. Data analysis will identify the key processing parameters, out of many, that control microstructural changes. The expense and time of generating data from processing runs and beamline experiments makes it vital to collect and curate the data. In addition, data analysis will help link the physicsbased models at different scales and develop reducedorder models of alloy performance. This project will establish a data management framework and data analytics tools to optimize processing and integrate the strengths of the experimental and modeling efforts. Disciplines: Analysis, Applied Mathematics, and Probability and Statistics Hosting Site:Pacific Northwest National Laboratory Internship location: Richland, WA Mentors:
Internship Coordinator:


No  ORNLFATTEBERT1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics 
Project Description:Using reduced precision floating operations (single or halfprecision instead of double precision) can speedup significantly computer simulations on modern computer architectures, especially for GPUaccelerated nodes. On the other hand, reducing precision can affect the quantitative results of a simulation in a way that is not acceptable. In this project, we will explore ways of taking advantage of mixedprecision algorithms in electronic structure calculations without affecting the physical results of our simulations. Since solvers can be quite complicated to analyze globally and very little research has been done with mixedprecision in that domain, we will focus on simplified problems that involve only a subset of the unknowns of the real problems. We will also examine how the lessons learned from these simplified problems carry to a complete solver on realapplications. This project will require modifying, adding functionalities, and running an existing opensource C++ code. Results may lead to a publication in a peerreviewed scientific journal.
Disciplines: Applied Mathematics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  LANLFRANCOM1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Probability and Statistics 
Project Description:We are interested in exploring the possibility of leveraging the multilayer structure that is used in neural networks to improve other learning methods. Particularly, we are exploring how we can create multilayer multivariate adaptive regression splines (multilayer MARS) that can be used to make predictive models with less complexity in depth at the expense of more complexity in each layer, though perhaps with fewer total parameters. We intend to use these models for building surrogates for complex computer models. Disciplines: Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  LLNLGILLETTE1  11/23/2020  1606107600000  Lawrence Livermore National Laboratory  Livermore, CA  Applied Mathematics, Geometry, Probability and Statistics 
Project Description:Adversarial attacks on neural networks refer to the ability of certain inputs to “trick” a neural network into giving an undesired output. Widely circulated examples include image classifiers that can be fooled into significant misclassifications by seemingly modest perturbations of an image from the training data set. The goal of this project is to explore geometric properties of the data that may help identify what makes an effective adversarial attack. While much of the literature in this area looks at the problem from a statistical perspective, this project will focus more on the geometric perspective, such as the importance of sampling density and the Euclidean distancetohull of an adversarial input. Project tasks will include both mathematical analyses and numerical experimentation, using the extensive computational resources of HPC systems at LLNL. Results from this project have the potential to provide new insight into generative adversarial network design, a field of growing importance in scientific machine learning. This project will be performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DEAC5207NA27344. IM release number LLNLABS816020. Disciplines: Applied Mathematics, Geometry, and Probability and Statistics Hosting Site:Lawrence Livermore National Laboratory Internship location: Livermore, CA Mentor:
Internship Coordinator:


Yes  USDAGRULKE1*  11/23/2020  1606107600000  USDA Forest Service Pacific Northwest Research Station  Corvallis, OR  Applied Mathematics, Biometrics and Biostatistics, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Drought indices based on modeled environmental data, a digital elevation model, and soil characteristics are broadly used to define the degree of hydrological deficits or agronomic drought. However, modeled environmental data are less accurate in high mountain ranges, and many of the soil characteristics are unknowable at any scale in this terrain. Approximately 35 million Californians rely on west and eastside Sierra Nevadan water resources. The impact of the last two droughts (19992002; 20132016) were extreme, and the level of drought was unanticipated. Roughly 135 million trees died in the Sierra Nevada. Water management districts use drought indices and their trends to allocate water resources. We propose modeling environmental drivers of physiological pine drought stress using an existing, 20 year, onsite environmental and biological data that span the two extreme droughts to test the veracity of commonly used drought indices in the Sierra Nevada (USDM;SPEI12;SCPDSI;SPEI12;VegDri). We propose two statistical modeling programs: to identify how tree physiology depends on local environmental covariates, and to test effectiveness of different drought indices in predicting physiological tree drought stress, the 'biological barometer.' Flexible additive models can be used to identify both linear and nonlinear dependence of tree physiology on the environmental covariates, and to estimate the functional form of such responses in the nonlinear case. For the classifier problem, machine learning methods (e.g., treebased classification, kernel methods, and linear classifiers) can all be trained with our data, and their predictive power evaluated. Other potentially useful models include hidden Markov models, since the data is sequential, and underlying but hidden states may be driving the observable responses. The available data lends itself to multiple modeling approaches which the intern will develop and evaluate. Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Probability and Statistics Hosting Site:USDA Forest Service Pacific Northwest Research Station Internship location: Corvallis, OR Mentors:
Internship Coordinator:


No  LBNLGULIZZI1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics 
Project Description:The equations of gasdynamics consist of a hyperbolic systems of partial differential equations (PDEs) which are generally characterized by the presence and evolution of shocks. Their solution has been historically obtained using finitevolume (FV) schemes because of their ability to resolve steep solution gradients. However, despite their robustness, FV schemes require elaborated modifications to reach highorder accuracy and/or to handle complex geometries. More recently, discontinuous Galerkin (dG) methods have become popular for the solution of PDEs because they offer a variational framework where variable order, complexshaped elements are more naturally treated. Highorder dG methods are very efficient in regions of smooth gradients but induce undesirable, and sometimes unacceptable, oscillations in presence of steep gradients and/or shocks. Therefore, dG methods are combined with suitablydefined limiting strategies when employed for the solution of hyperbolic equations. During this internship, you will focus on the development of a numerical solver for hyperbolic PDEs that combines the advantages of FV and DG schemes and limit their shortcomings. More specifically, your research will involve the development of: You will write the solver in AMReX (https://amrexcodes.github.io), a software framework for massively parallel, blockstructured adaptive mesh refinement applications. Disciplines: Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  NRELFRAHAN1  11/23/2020  1606107600000  National Renewable Energy Laboratory  Golden, CO  Applied Mathematics 
Project Description:Device level modeling using unified simulation frameworks of complex energy systems has the potential to increase device efficiencies by enabling design optimization processes and technological innovations. Current modeling strategies rely on passive coupling between solvers at different length and time scales using parameterized representations. These approaches do not account for twoway coupling across the scales (e.g. transport affecting catalyst reactions), stochastic effects at the smaller scales (e.g. dendrite initiation in batteries), and state space exploration of unvalidated parametrized regions. NREL is currently exploring multiresolution multialgorithms frameworks for performing simulations of complex energy systems in the NREL mission space, including electrocatalysis devices, batteries, and biomass feedstock handling. The objective of this project is to develop high fidelity modeling frameworks that can leverage multiresolution representations of the system to deploy algorithms tailored to the length scale under consideration and couple these algorithms in a unified framework. This project will involve studying scale coupling mechanisms for different mathematical models present in physics solvers to bridge scales (e.g. the atomisticcontinuum scale), ranging from continuum solvers with varying physical assumptions to atomistic and particlebased solvers (e.g. DSMC, KMC, MD). Graduate students involved in this project will have opportunities for both publication and future collaboration. Disciplines: Applied Mathematics Hosting Site:National Renewable Energy Laboratory Internship location: Golden, CO Mentor:
Internship Coordinator:


No  LANLJAFAROV2  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Probability and Statistics 
Project Description:Recent observations indicate extensive permafrost thawing everywhere in the Arctic. Permafrost thaw triggers landcover changes, soil carbon release, soil subsidence, and adds to the increasing cost of infrastructure maintenance. Existing numerical models are unable to predict permafrost conditions effectively due to the scale restrictions or the computational burden. There is an urgent need for a new model that can represent the required spatial scale and be computationally effective. This project will require ability to quickly learn and apply numerical models to solve climate change related problems in the Arctic. Knowledge of the optimization theory, sensitivity analysis, and uncertainty quantification is a plus.
Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  LBNLJAMBUNATHAN1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics 
Project Description:Pulsars are rapidly rotating, highlymagnetized neutron stars that were discovered more than half a century ago, yet, we do not understand the fundamental processes driving their electromagnetic radiation. Recent advances in computer architectures as well as numerical methods allow for detailed global simulations of the pulsar magnetospheres. WarpX (https://github.com/ECPWarpX/WarpX.git) is an electrodynamics ParticleInCell code developed as part of the Department of Energy (DOE) funded Exascale Computing Project (ECP). The advanced numerical methodologies implemented in WarpX make it a unique computational tool to extend the stateoftheart modeling techniques employed to investigate pulsar magnetospheres. During the internship, you will focus on exploring meshrefinement strategies to resolve the current sheet region in the pulsar magnetosphere required to study the critical magnetic reconnection phenomena using WarpX. In particular, you will analyze the growthrate of the tearingmode instability in the currentsheets formed in pulsar magnetospheres and compute the energy transfer from the electromagnetic fields to the kinetic energy of the particles. This project will further enable accurate predictions of the spindown rate of the pulsar and comparison with observations for realistic systems as well as uncover the kinetic mechanisms driving the largescale electromagnetic radiation. You will collaborate with an interdisciplinary team of astrophysicists, applied mathematicians, computational scientists in the Center for Computational Sciences and Engineering (CCSE) as well as collaborate with plasma physicists in the Accelerator Technology and Applied Physics (ATAP) group at Lawrence Berkeley National Laboratory. Disciplines: Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LBNLKIRST1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Biometrics and Biostatistics, Probability and Statistics 
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 braininspired coupled oscillator networks can indeed dynamically coordinate information exchange. Using appropriate feedback they can be turned into selfmodifying 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 electromagnetic waves (AM or FM). Building on our theory, we aim to develop a braininspired analog computing framework that employs collective network dynamics to coordinate large scale distributed computation and enable flexible and adaptive processing in dynamically selfreconfiguring 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 largescale machine learning. Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Probability and Statistics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LBNLKLYMKO1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Mathematics (General) 
Project Description:Stochastic thermodynamics is an emerging framework for the description of the thermodynamics and statistical mechanics of stochastic systems far from equilibrium. In particular, the development of fluctuation relations provides analytical results for the statistics of thermodynamic path variables (such as work, heat, and entropy production) in the form of equalities, as opposed to the inequalities of the second law of thermodynamics. Fluctuation relations have generalized Landauer's principle to a variety of physical systems, setting a fundamental limit to information processing. Our group has recently developed a quantum computing algorithm that uses a particular fluctuation relation, the Jarzynski equality, which relates the statistics of work generated during nonequilibrium trajectories to the equilibrium free energy (a thermodynamic function providing information about equilibrium phases). Our method utilizes real time Hamiltonian evolution to drive nonequilibrium protocols, and thus is naturally suited to quantum computing. We propose two directions building on our current method:
This project will involve a combination of analytical activities to develop the algorithms (familiarity with methods to sample rare events and measure complexity bounds could be useful) as well as implementing and demonstrating the algorithms on quantum hardware (some quantum computing experience is helpful but not required). Disciplines: Mathematics (General) Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentors:
Internship Coordinator:


No  LANLWANG1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Geometry, Mathematics (General) 
Project Description:Although the fundamental framework of the nature or the laws of physics are well known, the ability to use them for predictive science remains to be limited, even with the most powerful computers today. Examples of such laws include Boltzmann, Maxwell and Schrodinger's equations. We are looking for a creative mathematician to join our team of interdisciplinary experts to explore the new possibilities of data science (especially DNN) constrained by physics considerations, and search for new insight and implications of these frameworks to plasmas, metamaterials, astrophysics, and quantum science.
Disciplines: Applied Mathematics, Geometry, and Mathematics (General) Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  ANLRAO1  11/23/2020  1606107600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics, Probability and Statistics 
Project Description:"The Bayesian inference paradigm provides a probabilistic formulation for integrating information from complex models from observational or experimental data under uncertainty by updating the model parameters from their prior distribution to a posterior distribution. Solution to a Bayesian inverse problem involves the task of drawing samples from the posterior probability distribution to compute various statistics of quantities of interest. However, this is prohibitively expensive when the posterior distribution is highdimensional; many conventional methods for Bayesian inference suffer from the curse of dimensionality, i.e., computational complexity grows exponentially or convergence deteriorates with increasing parameter dimension. This project will explore Machine Learning based alternatives to mitigate the prohibitive costs associated with solving Bayesian inverse problems."
Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentor:
Internship Coordinator:


No  LBNLWILLCOX2  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Mathematics (General) 
Project Description:Neutron stars are complex astrophysical systems where matter is compressed to extreme densities comparable to the interior of atomic nuclei. A variety of interesting physics may emerge under these conditions, including superfluidity arising from quantummechanical pairing between neutrons in the neutron star interior. We will investigate the astrophysical implications of neutron superfluidity by numerically solving the underlying partial differential equations (PDEs). Superfluidity is a largescale quantum behavior arising from particle pairing that macroscopically manifests as an irrotational fluid. Complex interactions between the superfluid and normal fluid components of a neutron star are thought to underlie mysterious phenomena known as “pulsar glitches,” observed as rapid changes in the angular speed of a spinning neutron star. We will investigate this physics by numerically solving the HBVK PDEs applied to normal and superfluid components in neutron star interiors. With recent computational advances, we are poised to solve these PDEs with unprecedented fidelity, combining high order numerical discretization with adaptive mesh refinement algorithms running on supercomputers. In this project, we will work together to develop and test numerical simulations of superfluidity and you will also learn how PDE solvers are designed, implemented, and run on supercomputing systems. You will collaborate with an interdisciplinary team of applied mathematicians, computational scientists, and physicists in the Computational Research Division at Lawrence Berkeley National Laboratory.
Disciplines: Applied Mathematics, and Mathematics (General) Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentors:
Internship Coordinator:


No  LBNLYAO1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Mathematics (General) 
Project Description:The student will aid in the development of a new exascaleready, multiscale software framework for physical modeling of electromagnetic signals with the flexibility for additional physics coupling, targeted at current and nextgeneration microelectronic devices. Examples include spinbased memory devices and quantum information processing circuits. The goal of this project is to reach into new energyefficient application spaces with the incorporation of new physics, enabling improved design of nextgen devices. The student will leverage the extensive software and algorithmic expertise developed in collaboration with the Exascale Computing Project (ECP) CoDesign Center, AMReX, and related AMReXbased applications, WarpX. Specifically, the student will collaborate on (i) customization of existing algorithms and incorporation of new physics by adding in PDEs; (ii) update current implementation of boundary conditions, excitation, field evolution, etc., to accurately predict the newly added physical phenomena; (iii) explore leadership class GPU/multicore supercomputing architectures that will provide ordersofmagnitude speedup over existing capabilities. The outcome of this position include technical publications, conference presentations, etc.
Disciplines: Applied Mathematics, and Mathematics (General) Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentors:
Internship Coordinator:


No  LANLZLOTNIK1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Operations Research, Probability and Statistics 
Project Description:Optimization is widely used to responsively determine the physical and financial exchange of wholesale electricity in organized markets. The established operations of power grid independent system operators (ISOs) are increasingly challenged by growing dependence on natural gas as a fuel and increasing penetration of uncontrollable renewable energy. This compels advanced methods for optimizationbased gas pipeline operation and optimal allocation of reserve capacity to guarantee secure power and gas transmission function. Such methods require robust optimization for the nonconvex, nonlinear, and spatiotemporally complex stochastic models of network flow physics under uncertainty, which presents mathematical and computational challenges. While formulations for uncertaintyaware power flow have been proposed, the use of dual solutions for price formation in the stochastic setting presents a fundamental conceptual gap. Yet such mechanisms, which apply optimization to synthesize physical models with business processes, are indispensable to incentivize adoption of advanced computational tools in practice. This project will develop a general formal mathematical setting for dual (sensitivity) analysis of nonlinear stochastic physical network flows modeled by partial differential equations on graphs, and create constructive optimization algorithms for computing the economic value of energy network load and production uncertainties and measures used to mitigate them.
Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


Yes  USACEMUSTY3*  11/23/2020  1606107600000  U.S. Army Corps of Engineers, Engineer Research and Development Center  Vicksburg, MS  Analysis, Applied Mathematics, Mathematics (General) 
U.S. Citizenship is a requirement for this internship Project Description:The prospective intern will engage in numerical modeling and mathematical analysis of the hydrodynamic problem at hand. In this project, the intern will have an opportunity to learn how to navigate through and utilize DoD’s HPC machines. He/she will also gain exposure to different caveats of the research and development (R&D) activities within the government research facility/laboratory. In addition, the intern will be directly mentored by leading phaseresolving numerical wave modeling experts in the field. The internship will culminate in a peerreviewed journal, or a conference proceedings publication. An ideal candidate should have a good knowledge of applied and computational mathematics (numerical modeling with both finite difference and finite volume schemes), with emphasis on nonlinear freesurface flows (water waves). It is also desirable, but not necessary, for the intern to be able to read and write code in lower (FOTRAN) and higherlevel (Python) programming languages, as well as have a basic understanding of distributed parallelcomputing paradigms (MPI – Message Passing Interface). Disciplines: Analysis, Applied Mathematics, and Mathematics (General) Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center Internship location: Vicksburg, MS Mentors:
Internship Coordinator:


No  SNLTENCER3  11/23/2020  1606107600000  Sandia National Laboratories  Albuquerque, NM  Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:Recent advancements in projectionbased reducedorder models have enabled the construction of fast and approximate surrogate models for complex, parameterized nonlinear dynamical systems. In this project, we seek to augment these technologies by developing stochastic Petrov—Galerkin reducedorder models (SPGROMs) for uncertainty quantification. Like the stochastic Galerkin method, SPGROMs are promising as a single solve yields the entire posterior distribution for quantities of interest. In the SPGROM formulation, a parameterized dynamical system solution is represented by tensor products of datadriven basis functions in statespace, and polynomial chaos expansions in stochastic space. A reducedorder model is then obtained via orthogonality or residual minimization constraints. This project will focus on (1) development of the SPGROM formulation, (2) theoretical numerical analyses of the approach, and (3) the deployment of the approach to benchmark hyperbolic systems, on which classical approaches (e.g., Stochastic Galerkin) often fail to yield adequate results.
Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Sandia National Laboratories Internship location: Albuquerque, NM Mentors:
Internship Coordinator:


Yes  USDAAMATYA1*  11/23/2020  1606107600000  USDA Forest Service, Center for Forest Watershed Research  Asheville, NC  Analysis, Applied Mathematics, Operations Research, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:The discipline of hydroclimatology relies heavily on meaningful information retrieved from the data associated with it. Hydroclimatological data includes temporal (time series) and spatial (landscape) information. Spatiotemporal data helps in assessing the various levels of impacts of frequently occurring disastrous extreme events. Extreme events, including coastal flooding on the Southeastern Atlantic and Gulf Coastal Plain and forest fires on the west coast, have adversely affected economic resources and losses of enormous property and human lives. To improve the preparedness plan and reduce such losses, the protection and mitigation planning agencies want information before the natural disaster hits the ground. A mitigation plan can potentially be put in place with the velocity and volume of necessary information the hydroclimatological data is producing. This study aims to use the longterm climate data and information from USDA Forest Service Santee Experimental Forest (SEF) and assess the changes in climate over space and time at the study site. The observations would, then, be related to natural physical processes, including soil moisture and temperature and evapotranspiration for woodland fire risk assessment. 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 students will also learn about field experimental studies, forest hydrologic processes and tidal flow dynamics represented by mathematical equations, realtime monitoring technology, and managing and analyzing the Big Data sets using statistics at the host SEF study site.
Disciplines: Analysis, Applied Mathematics, Operations Research, and Probability and Statistics Hosting Site:USDA Forest Service, Center for Forest Watershed Research Internship location: Asheville, NC Mentors:
Internship Coordinator:


No  USDAAMATYA2  11/23/2020  1606107600000  USDA Forest Service, Center for Forest Watershed Research  Asheville, NC  Analysis, Applied Mathematics, Geometry, Operations Research, Probability and Statistics 
Project Description:Climate extremes, such as hurricanes and tropical storminduced rainfall, cause severe floods, which is expected to happen more frequently in the future due to climate change. Coastal communities and infrastructure systems, including water, energy, and communications, are particularly vulnerable to flooding caused by combined rainfall, sea level rise, and high tide. Communities are investigating and implementing flood risk mitigation and adaptation strategies, such as early warning systems and flood control structures, to reduce the flooding risk and damages. This research aims to enhance the response time and accuracy of flood detection, early warning and monitoring systems, by integrating the rapid growth in visual sensing technologies into flood data acquisition and modeling. This will be achieved by developing a visual sensing tool which measures the river depth and discharge using groundbased cameras and compare them with data from a watershed at USDA Forest Service Santee Experimental Forest (SEF). The objectives are a) collecting visual information from cameras and observed hydrologic data for the study site and b) extracting numerical information from semantic segmented images using a trained convolutional neural network (CNN). The tasks to achieve the goal are to i) develop program to extract onsite visual data to train CNNs, ii) conduct hydrologic analysis and develop stream network bathymetry, iii) to run trained CNNs and numerically integrate the information with the bathymetry to extract the water depth and computed discharge at different locations. Finally, the collected data will be used as inputs to a flood model developed for SEF to simulate and predict the streamflow discharge and flood properties. The students will learn about field experimental studies, hydrologic processes and flood flow dynamics represented by mathematical equations, realtime monitoring technology, and analyzing the Visual and Big Data using statistics at the SEF study site. Disciplines: Analysis, Applied Mathematics, Geometry, Operations Research, and Probability and Statistics Hosting Site:USDA Forest Service, Center for Forest Watershed Research Internship location: Asheville, NC Mentors:
Internship Coordinator:


No  USDAAMATYA3  11/23/2020  1606107600000  USDA Forest Service, Center for Forest Watershed Research  Asheville, NC  Analysis, Operations Research, Probability and Statistics, Topology 
Project Description:Increased peakflow magnitudes resulting from growing extreme precipitation events might have adverse effects on existing road drainage and culverts, resulting in their failures, increased flooding, soil erosion, economic losses, and disruption of stream connectivity critical for aquatic organisms. Engineers and hydrologists often use precipitation intensitydurationfrequency (PIDF) curves for design of such infrastructure. The goal of this study is to develop an online spatial hydrologic tool (Realtime Dashboards on Cloud) to generate a vulnerability assessment map for road culverts using longterm data from a lowgradient watershed at USDA Forest Service Santee Experimental Forest. The objectives are a) to identify erosion hazards and vulnerability risks to these structures using the PIDFbased design rainfall intensities and other geospatial data for the study site and b) to quantify the design discharge using widely used empirical methods. The proposed tasks are to i) develop a program to extract onsite longterm precipitation data to derive the PIDF distribution, ii) to conduct watershed hydrologic analysis using ArcHydro Tools to develop stream network and determine the potential culvert locations, iii) to use USDAARS RUSLE model and also develop a Stream Bank Erosion Vulnerability Analysis (SBEVA) model, both in ArcGIS ModelBuilder, to identify low, moderate, and high erosion vulnerable locations for determining the scalebased vulnerable culverts by combining results from both the models, and iv) link both the models in ArcGIS Pro (on Cloud) with design discharge estimating equations to assess capacities of culverts and develop a realtime Dashboard online culvert vulnerability assessment software. The students will also learn about field experimental studies, hydrologic processes and tidal flow dynamics represented by mathematical equations, realtime monitoring technology, and managing and analyzing the Big Data sets using statistics at the host site.
Disciplines: Analysis, Operations Research, Probability and Statistics, and Topology Hosting Site:USDA Forest Service, Center for Forest Watershed Research Internship location: Asheville, NC Mentors:
Internship Coordinator:


No  SNLTENCER1  11/23/2020  1606107600000  Sandia National Laboratories  Albuquerque, NM  Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:Projectionbased reducedorder models are a class of physicsinformed surrogate models suitable for largescale nonlinear dynamical systems. Traditionally, projectionbased reducedorder models have involved projection of the system dynamics onto a lowdimensional linear space. Unfortunately, for a certain class of physical systems, a suitable lowdimensional linear space does not exist. For these systems, a lowdimensional nonlinear manifold is more appropriate. In this work, we will examine various manifold learning techniques and their suitability for use with projectionbased reducedorder models. Of particular interest are algorithmic and architectural improvements for reducing offline and online computational costs associated with graph convolutional auto encoders. Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Sandia National Laboratories Internship location: Albuquerque, NM Mentors:
Internship Coordinator:


No  SNLTENCER2  11/23/2020  1606107600000  Sandia National Laboratories  Albuquerque, NM  Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:Are you in interested in learning cuttingedge computational methods and algorithms for largescale dynamical systems? This might be the right project for you! This project focuses on advancing algorithms and computational methods for projectionbased reduced order models (ROMs) of largescale dynamical systems. Stateoftheart ROM formulations pivot around expressing the state as a rank1 tensor (i.e. a vector) leading to computational kernels that are memory bandwidth bound and, therefore, illsuited for scalable performance on modern manycore and hybrid computing nodes. We aim at exploring alternative formulations, e.g., rank2, batched kernels and/or hierarchical parallel approaches, to overcome the memory bandwidth bottleneck and solve these problems efficiently. This would substantially impact the scalability and efficiency for solving manyquery problems, e.g., those stemming from uncertainty quantification studies. Desired skills and experience: experience in applied mathematics and physical simulations, good knowledge of linear algebra, and basic knowledge of tensor algebra. Good knowledge of Python (possibly objectoriented) and basic knowledge of C++. Knowledge of GPU computing is a plus. Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Sandia National Laboratories Internship location: Albuquerque, NM Mentors:
Internship Coordinator:


Yes  USACEMUSTY1*  11/23/2020  1606107600000  U.S. Army Corps of Engineers, Engineer Research and Development Center  Vicksburg, MS  Mathematics (General), Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:The intern will support the “Reading The Ground” project through the development of classification algorithms and detailed performance comparisons. The activity will require some knowledge of multiclass classification techniques as well as some knowledge of the relevant performance metrics. The primary focus of the activity will be a detailed algorithm comparison and documentation. The intern will join a cooperative group and will participate in laboratory meetings and showcase results. Disciplines: Mathematics (General), and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center Internship location: Vicksburg, MS Mentor:
Internship Coordinator:


Yes  USACEMUSTY2*  11/23/2020  1606107600000  U.S. Army Corps of Engineers, Engineer Research and Development Center  Vicksburg, MS  Analysis, Mathematics (General) 
U.S. Citizenship is a requirement for this internship Project Description:The intern will support the Modernizing Environmental Signature Physics for Target Detection project through the development of processes for the efficient analysis of large and disparate datasets. The activity will require the integration of image files for EO and IR cameras. LIDAR data, soil sensor data, and meteorological data in order to perform data analysis. The intern will need a familiarity with multivariate and spatial data analysis and the development of MATLAB or R scripts to facilitate the data analysis or data retrieval in order to perform the analysis. The project involves assessing the soil and meteorological conditions that hamper improvised buried object detection yielding inconsistent probability of detections and high false alarm rates. The intern will join a growing cooperative group and will assist many group members, participate in laboratory meetings, and showcase results. The intern should have experience with algorithm development, coding, script development, machine learning, MATLAB, R, multivariate statistical analysis, and stochastic modeling as well as an interest in physics, mathematics. Disciplines: Analysis, and Mathematics (General) Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center Internship location: Vicksburg, MS Mentors:
Internship Coordinator:


No  LLNLCHEN1  11/23/2020  1606107600000  Lawrence Livermore National Laboratory  Livermore, CA  Applied Mathematics, Probability and Statistics 
Project Description:This project studies corrosion inhibitor molecules in the form of coordination complexes with a datadriven approach that utilizes graph neural networks (GNNs) for a natural, intuitive featurization and embedding of molecular structures. Based on properties computed from highfidelity atomistic simulation (e.g., densityfunctional theory), we will train molecular GNNs to predict properties of complexes that are relevant to corrosion inhibition (e.g., binding energy). Additionally, due to the combinatorically and virtually infinite space of ligandmetal coordination configurations, we will develop a combined molecular GNN with Gaussian process to form a “monolith” machine learning model that can be conveniently trained endtoend. The uncertainty estimates from such model can help inform us to efficiently sample the space of the coordination configurations using sampling policies similar to that in Bayesian optimization techniques. Finally, this project has practical application in the area of highthroughput screening of molecules for ideal properties with respect to corrosion inhibition. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Lawrence Livermore National Laboratory Internship location: Livermore, CA Mentors:


No  LLNLCHEN2  11/23/2020  1606107600000  Lawrence Livermore National Laboratory  Livermore, CA  Applied Mathematics, Probability and Statistics 
Project Description:In this project, we will develop a novel datadriven, chanceconstrained and riskaware decision making under uncertainty framework. The framework will be demonstrated on power system planning, operation, and control, for which we will strive to make the decisionmaking procedure applicable for different practical situations. This project will address the challenges related to the (1) computational efficiency of the algorithm, (2) the estimation accuracy in the uncertainty quantification, (3) the scalability of the proposed algorithm to a nonlinear system model, (4) the complexity in highdimensional uncertainty modeling, and (5) the adaptivity in the decisionmaking. Through this studied decisionmaking under uncertainty procedure, the efficiency, security, economy and the risks of power system cascading failures can be properly managed to enhance the robustness and the riskawareness in the operation. Specially, the tasks include (1) using traditional lineartransformationbased approach to explore the latent space for the surrogates, (2) using the proposed manifoldlearningbased approach to explore the latent space for the surrogates, and (3) Comparing the performance of the manifoldlearningbased approach with other dimensionreduction methods. To sum up, we will develop the surrogatebased decisionmaking under uncertainty framework in this project. The framework will not be limited to the applications in the power systems but providing great benefits in the control and design procedure of many engineering fields, such as the circuit design, air craft design and control, robot control, vehicle and train control. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Lawrence Livermore National Laboratory Internship location: Livermore, CA Mentors:


No  ORNLHAUCK1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics 
Project Description:The goal of this project is to design and implement an optimization algorithm for model calibration. The algorithm seeks to identify model parameters whose values are not known and must be determined from indirect measurement via an inverse problem. The optimization problem to be solved uses a metric based on the earth mover's distance from optimal transport, which has been shown to be insensitive to noise in the data. Thus it may provide a better alternative to other approaches based on standard norms. Students will learn about regularization for inverse problems, tools from optimization, and topics from optimal transport. Disciplines: Applied Mathematics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLHAUCK3  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics 
Project Description:The goal of this project is to explore transportbased algorithms for improving the stability and training efficiency of neural networks. The project involves the approximation of neural networks as continuum equations, implicit discretizations of those equations, and iterative methods for solving them using tools borrowed from kinetic transport equations. Students will learn about neural networks, iterative methods for nonlinear systems, numerical tools for solving transport equations, and hyperbolic relaxation. Disciplines: Applied Mathematics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


Yes  ORNLHATHHORN1*  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Logic or Foundations of Mathematics, Mathematics (General) 
U.S. Citizenship is a requirement for this internship Project Description:Programmable logic controllers (PLCs) are used for industrial automation in many safety and securitycritical contexts. The IEC 611313 standard informally describes five languages intended for programming PLCs. Three of these are graphical  ladder diagrams (LD), function block diagrams (FBD), and sequential function charts (SFC)  while two are textual  structured text (ST) and instruction lists (IL). And often, PLCs are programmed using a combination of these languages. As the scale and complexity of industrial automation grows, so do the scale and complexity of these programs. When these programs are deployed in a critical role, we would like mathematicallyrigorous confidence in their correctness. This project will explore techniques for highassurance PLC programming in the IEC 611313 languages: formal verification of PLC programs or an IEC 611313 language implementation, model checking, abstract interpretation, or other static or dynamic analyses of IEC 611313 programs. Past MSGI projects have successfully published papers to top computer science and security conferences. Likewise, we plan to publish a paper on these findings in one of the highranking computer science (programming languages, formal methods) or cyber security conferences with the student as the lead author. Disciplines: Applied Mathematics, Logic or Foundations of Mathematics, and Mathematics (General) Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentors:
Internship Coordinator:


Yes  ORNLHATHHORN2*  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Mathematics (General), Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Modern critical infrastructure (e.g. power grids, water and gas utilities, factories, etc.) face attacks by nationstates and advanced adversaries on a regular basis, yet few techniques exist to detect *cyber*specific faults (i.e. problems) on the critical infrastructure devices. Given ORNL's existing platforms for building resilient cyberphysical systems and digital twin platforms for SCADA devices, this project seeks to classify relevant SCADA communications as corresponding to faults as opposed to normal operational behavior, like turning on or off power flow on purpose, rather than done by a malicious entity. The project will take advantage of modern data science, machine learning, and natural language processing techniques, or any technique of interest to the participant that could classify SCADA communications as corresponding to a true fault. 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 platform which will be deployed to utilities and live power grids in 2021. A successful student has prior experience with data science techniques and the basics of machine learning, but is not expected to have deep experience with programming. Notably, prior projects at ORNL by MSGI participants by this team have led to papers published at major computer science conferences. Based on the findings here, we will also seek to publish a paper in a major computer security venue with the participant as the lead author. Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  LANLLI1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics 
Project Description:The discovery of exoplanets (Nobel Prize 2019) and observations of protoplanetary disks (where exoplanets were born) have yielded rich information on the formation and evolution of planets and their systems. The primary building blocks of planets are gas and dust (Earth is made of mostly dust). As these components move around their protoSun, their dynamics can be modeled using advanced hydrodynamic simulations. But dust and gas move at different speed and their interactions can promote dust clumping, leading to condensation and eventual planet formation. These processes create "footprints" that are being observed by the most powerful telescopes in the world, giving us hints and hope to understand such complicated yet fundamental processes. The objective is to help interns learn and use the stateoftheart numerical methods and tools in modeling such multicomponent systems. The interns will collaborate with scientists on exploring new numerical methods that can speed up the simulations of dustgas evolution in protoplanetary disks. A fair amount of simulations on supercomputers will be involved as well. The interns will also interact with other students, postdocs and scientists in a group environment that emphasize discussions, learning and collaboration. Regular activities such as hiking and cookout are included as well. Disciplines: Applied Mathematics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  ORNLLIM1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Probability and Statistics 
Project Description:This project will investigate the algorithmic scalability of neural network model training. Scalable training of neural network models allows researchers and practitioners to efficiently explore the effectiveness of larger models, larger data sets, and longer training epochs. Such a study is especially important for emerging model families in deep learning to understand their tradeoffs between their algorithmic scalability and their expressiveness power. As an example, a graph neural network is an expressive and flexible neural network model family that can understand either the properties of the whole graph structure or the properties of individual constituents in graphs. Graph neural network models are actively investigated in DOEmission relevant areas due to the state of the art accuracy in calculating energy levels in chemical, biological, and materials systems, with radically lower computational costs than Density Functional Theorybased approaches. However, similar to other emerging model families in deep learning, the tradeoff between its algorithmic scalability and expressiveness power is still an open question. Including graph neural networks, such a gap creates challenges to use emerging neural network models in scientific areas. Students will learn pythonbased deep learning platforms in high performance computing environments, with the empirical studies on public graph datasets. Student will also gain knowledge in discrete optimization, graph algorithms, and stochastic optimizations. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  LANLLIN1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Probability and Statistics 
Project Description:We propose to develop methods that extract and construct reducedorder dynamics from the output of highfidelity (HiFi) simulation of dynamical systems in a principled way. Given the dimensionality of the reduced configurational space, our aim to develop algorithms to identify a reducedorder dynamical model that optimally approximates the HiFi dynamics. We will leverage the mathematical structures developed in the Koopman von Neumann (KvN) formalism, in which fittingtodata is always a linear regression and convex problem, but with the disadvantage that the operating space is an infinitedimensional Hilbert space. We will address the problem of infinitedimensionality by operating in the Mori–Zwanzig (MZ) projection operator formalism which provides mathematically accurate reducedorder dynamics and associated error, and we will use algorithms, including but not limited to machinelearning methods, to minimize the error. Initial applications will focus on reduced models of atomistic simulations of molecules and materials. The intern will participate in a highly interdisciplinary research project which involves applied functional analysis (Koopman von Neumann and Mori–Zwanzig formalism), dynamical systems, optimization methods, and datadriven and machinelearning methods. The mentors will collaborate with the intern to formulate a subcomponent of the project. Examples of subcomponents include: (1) developing loss function(al) for optimizing the reducedorder model, (2) imposing the mathematical structure of KvN and MZ to offtheshelf machinelearning architectures, such as recurrent neural networks, and (3) demonstrating the approaches on data produced by largescale atomistic simulations. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  LANLLIN2  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Probability and Statistics 
Project Description:Probabilistic modeling has unique advantages in solving complex problems. On the one hand, the sampling procedures in probabilistic computing, e.g., various Monte Carlo techniques, bypass the curse of dimensionality and deliver key statistical quantities of the highdimensional systems of interests without solving the full system. On the other hand, a probabilistic reasoning and learning framework has the capability to allow noisy, uncertain, heterogeneous, or even sparsely collected data streams, and is favored in causal inference, uncertainty quantification, and data fusion. As increasing amounts of heterogeneous data are collected, it is critical to develop datadriven methods to calibrate and construct large probabilistic models. Such an approach is currently challenging due to the absence of a scalable algorithm to extract the essential sensitivity information—the derivatives of the error measure with respect to each of the model parameters—which is required in gradientbased optimization and uncertainty quantification procedures for efficiently improving the performance of the models. In this research project, we will explore two approaches to fill the void: (1) to develop importance sampling procedures for approximately solving the adjoint states which contain the sensitivity information, and (2) to leverage and generalize the "reparametrization trick" which is recently proposed in the field of probabilistic machine learning. We expect the developed algorithms will enable datadriven methods of parametrizing and constructing largescale probabilistic models and will analogously play the pivotal role of the automatic differentiation which enabled deterministic deep learning practices. The recruited intern will collaborate with the mentors to define a smallerscale yet selfcontained project which may lead to a successful scientific publication. Disciplines: Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  NRELMARTIN1  11/23/2020  1606107600000  National Renewable Energy Laboratory  Golden, CO  Applied Mathematics, Mathematics (General) 
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 highefficiency energy systems that enable carbon separation, utilization, and storage (CCUS), liquid sodium for energy storage, biomass for energy applications, and lowtemperature helium for energyefficient 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 highfidelity opensource 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. This is a relatively open field with significant opportunities for future activities and publication. Disciplines: Applied Mathematics, and Mathematics (General) Hosting Site:National Renewable Energy Laboratory Internship location: Golden, CO Mentor:
Internship Coordinator:


No  LBNLMINION1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics 
Project Description:The focus of this proposal is to consider two approaches for solving PDE problems with constraints: one based on Machine Learning (ML) using deep neural nets (DNNs) and the second based on a PDE constrained optimization approach using adjoint equations. From a mathematical perspective, a complicating feature of DNNs is A recent approach to interpretability is to cast DNNs in the context of dynamical Disciplines: Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentors:
Internship Coordinator:


No  LBNLMINION2  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics 
Project Description:This project concerns the analysis and numerical evaluation of methods to extend spatial multigrid based methods for the implicit treatment of nonlinear diffusion terms in massively parallel PDE simulations. Our approach combines highlyoptimized secondorder multigrid methods in the AMReX code framework with an iterative spacetime deferred correction iteration to produce higherorder solvers designed for combustion applications. The focus of this summer project will be investigating combining these solvers with the timeparallel library LibPFASST to expose further concurrency and reduce run times. Disciplines: Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentors:
Internship Coordinator:


No  LANLMOORE1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Probability and Statistics, Topology 
Project Description:Modern deep learning models have proven to be highly effective at performing a wide range of discriminative tasks on complex data types, such as speaker detection in audio, object detection in images, and action detection in video. However, deep neural networks tend to be poorly calibrated (i.e. they do not estimate their own uncertainty well) [1], and they are vulnerable to a wide range of adversarial attacks [2]. These findings indicate that the methods are not effective at characterizing the true distribution of complex data types, such as natural images. Generative neural models, such as variational autoencoders and normalizing flows, show some promise in estimating complex data manifolds, but recent research has shown that they are ineffective at detecting outofdistribution data [3]. This weakness in outofdistribution detection is especially apparent when performing tasks such as misinformation detection, where we rely on subtle differences between synthetic, altered content and real content. In this project, we aim to characterize the difference in distribution of syntheticallygenerated images and audio from natural images and audio, and plan to develop robust methods for detecting fake data detection with unsupervised models. As an intern in this project, you will collaborate with a team of experts in machine learning and neuromorphic computing. The intern should have strong coding skills in Python, should be skilled in developing machine learning models, and should have a strong background in probability and statistics.
Disciplines: Probability and Statistics, and Topology Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  ORNLMORIANO1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Probability and Statistics 
Project Description:The Internet is notoriously vulnerable to attack by means of the Border Gateway Protocol (BGP). BGP attacks are escalating in frequency, severity, and sophistication, creating an urgent demand for the deployment of the next generation of realtime BGP anomaly detection technologies. This project aims to provide a basic understanding of how BGP works as well as its existing threats. The ultimately goal is to design and implement AI/ML based anomaly detection algorithms for better detecting incidents such as route leaking/hijacking and traffic interception attacks. The project includes theoretical and applied components that requires to write high level code to demonstrate its application is a practical setting. Learning objectives of the applicant include: (1) develop a basic understanding of time series base anomaly detection methods and its application to BGP anomaly detection; (2) acquire a set of analytical and computing skills for implementing the algorithms; (3) apply acquired skills for detecting BGP anomalies on realtime fashion. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  LANLMORREALE1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Analysis, Probability and Statistics 
Project Description:The Electron Ion Collider (EIC) will be a future particle accelerator that will collide electrons with protons and nuclei to study the internal structure of particles. The electron beam will scan the arrangement of the quarks and gluons that make up the protons and neutrons of nuclei. The force that holds quarks together, carried by the gluons, is the strongest force in Nature. The EIC will allow us to study this "strong nuclear force" and the role of gluons in the matter within and all around us.[1] The project encompasses the evaluation of beam backgrounds that may muddle up the physics signatures we are looking for. It is an essential task to study the impact these backgrounds will have to the detector and any measurement at the EIC. Background studies will facilitate current experimental efforts to actively ensure that the machine design will not be adverse to physics in terms of background load. In this project we will focus on two major sources of background: 1. background due to protons in the beam interacting with residual gas in the beam pipe (beamgas) and 2: photons arising from synchrotron radiation due to the electron beam. The internship will focus on synchrotron calculations, running and/or improving existing simulations and presenting the results in group[2] and collaboration meetings. The goal will be to interpret the results and provide an initial estimate of the background expected at regions about +1m or more from the beam interaction region. C++ or a similar computing expertise will facilitate the integration in the internship. An initial bibliographical task will be given at the beginning of the internship to familiarize the student with the physics of interest. Finally, our group has a number of experts committed to the project. The intern will work/telework with the mentor on a daily basis. [1]https://www.bnl.gov/eic/ Disciplines: Analysis, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  LBNLMUELLER4  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Probability and Statistics 
Project Description:Deep Learning (DL) models are nowadays used in many scientific applications, e.g., for making predictions when mechanistic models are not available or too hard to use. However, blindly applying DL models to a dataset has its dangers, especially when critical decisions are based on predictions whose uncertainties are not properly quantified. Uncertainties in DL models can arise from a variety of sources and may influence what the best DL model type and architecture should be. In this project, your research will be to develop numerical optimization methods for identifying the best DL model architectures while taking into account the prediction uncertainties in order to obtain robust and reliable DL models. You will make use of a variety of tools including derivative free optimization and uncertainty quantification methods. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LBNLMUELLER2  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Probability and Statistics 
Project Description:In many scientific applications, computer simulations are used to approximate complex physical phenomena. These simulations often contain parameters that must be tuned in order to optimize an objective (e.g., maximize a performance measure, minimize an error metric). For these types of simulation optimization problems, we generally do not have an analytic description of the objective function or its derivatives (blackbox) and evaluating the simulation is computationally expensive. In addition, if the simulation contains stochastic dynamics (evaluating the simulation for the same parameters gives different results), the simulation must be evaluated multiple times for the same parameters in order to obtain a statistically significant estimate of the response. Due to these challenges (computational expense, blackbox functions, stochasticity), new derivativefree sampling algorithms that minimize the number of queries to the simulation must be developed in order to find optimal solutions efficiently. In this project, your research will focus on the development of efficient and effective algorithms for solving these computationally expensive stochastic blackbox optimization problems. This research requires the development of new sampling strategies that adaptively determine where in the parameter space the next simulation evaluation will be done and how many replicates of the simulation evaluation should be done. You will develop a suite of test problems to assess the performance of your developed algorithm and finally apply it to a realworld science problem. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LBNLMUELLER3  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Probability and Statistics 
Project Description:In many scientific applications, computer simulations are used to approximate complex physical phenomena. These simulations usually have parameters that must be adjusted in order to obtain the most accurate simulations. Accuracy is assessed by comparing the simulation output to observation data. However, these data are often noisy, and therefore parameter inference is needed to determine those simulation parameters that most likely explain the observations. Simulations are often computationally expensive and may require several minutes or hours per run. Thus, during inference, we cannot query the simulation model thousands of times in order to find the desired parameter posterior distributions. Moreover, simulations are often provided as black boxes, i.e., there is no analytic description available and inference methods that are based on adaptive exploration of the sample space are needed. Previously, methods have been developed that exploit Gaussian process models as surrogates of the expensive simulation in Bayesian inference. However, these methods do not scale well with an increasing number of sample points and parameters. In this project, your research will focus on the development of scalable inference algorithms that are efficient and effective for computationally expensive models. In order to achieve this, your will iproject nvolve the development of new sampling strategies that adaptively explore the potentially largedimensional parameter space; the use of dimension reduction and sample space reduction methods; the use of Gaussian process models (or other types of surrogate models); and Bayesian inference methods. You will develop a suite of fasttocompute test problems to assess the performance of your developed algorithm and finally apply it to a realworld science problem. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  LANLNEGRE1  11/23/2020  1606107600000  Los Alamos National Laboratory  Applied Mathematics 
Project Description:Solving flow and transport through complex geometries such as porous media involves an extreme computational cost. Simplifications such as pore networks, where the pores are represented by nodes and the pore throats by edges connecting pores, have been proposed. These models have the ability to preserve the connectivity of the medium. However, they have difficulties capturing preferential paths (high velocity) and stagnation zones (low velocity), as they do not consider the specific relations between nodes. Network theory approaches, where the complex network is conceptualized like a graph, can help to simplify and better understand fluid dynamics and transport in porous media. To address this issue, we propose a method based on eigenvector centrality. It has been corrected to overcome the centralization problem and modified to introduce a bias in the centrality distribution along a particular direction which allows considering the flow and transport anisotropy in porous media. The model predictions are compared with millifluidic transport experiments, showing that this technique is computationally efficient and has potential for predicting preferential paths and stagnation zones for flow and transport in porous media. Entropy computed from the eigenvector centrality probability distribution is proposed as an indicator of the “mixing capacity” of the system. We propose to generalize this tool to three dimensions and produce a MATLAB based library for open source release. We are also envisioning interfacing LANL’s Basic Matrix Library (BML) with MATLAB for access to exascale HPC architectures. The Student will be exposed to the state of art of the HPC techniques, and cutting edge advances in microfluidics. Moreover, the student will be in contact with scientists from both LANL and ETH, two world leading scientific institutions. Disciplines: Applied Mathematics Hosting Site:Los Alamos National Laboratory Mentors:
Internship Coordinator:


No  LBNLNIGMETOV1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics 
Project Description:Broadly speaking, the goal of the project is to use descriptors developed in Topological Data Analysis (persistence diagrams and merge trees) in machine learning. There are two possibilities: either one uses these descriptors as an input to machine learning algorithms or one uses these topological tools to regularize the ML models trained on a traditional input (e.g., a set of vectors from a Euclidean space of some fixed dimension). A concrete direction that the project can take is regularization of neural networks using persistencesensitive simplification. Here a student can investigate how different choices of topological simplification algorithms affect the performance of the regularized model. Ideally, by the end of the project the student will have handson experience with topological descriptors and training of machine learning models. The project will involve a fair amount of coding and some experience in programming, in particular, in Python is desirable; knowledge of C++ will be beneficial, too, because the key topological algorithms are usually implemented in this language. Prior knowledge of (simplicial) homology and persistent homology will be helpful, but not required. The project will probably begin with a reading phase, when a student will get some highlevel understanding of all theoretical aspects (persistent homology, persistence diagrams, topological simplification, etc.). After that the student will implement different variants of simplification and perform experiments. Disciplines: Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  ORNLNUTARO1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics 
Project Description:There is a growing interest in large scale power system simulations that generate detailed, cycle accurate voltage and current signals within the transmission and distribution systems during large electromechanical transient events. These models are computationally intensive and could be significantly improved with new numerical methods targeted specifically at this problem. The proposed research would seek to discover new, efficient numerical methods for simulating alternating current circuits with sources that have time varying frequency and phase, and analysis of the generator and circuit interface model to identify modeling techniques that promote numerical stability. Experimental development of the new methods will be facilitated with benchmark models that are part of a new power system simulator being developed at Oak Ridge National Laboratory.
Disciplines: Applied Mathematics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


Yes  USACEOBER1*  11/23/2020  1606107600000  U.S. Army Corps of Engineers, Geospatial Research Laboratory  Alexandria, VA  Analysis, Applied Mathematics, Geometry, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:The Kinematically Linked Model Framework (KLMF) uses the same mathematics found in 3D gaming (temporally linked quaternion based 6D transformations and ray tracing) to track multiple sensor components (e.g. bearings, encoders, readheads, GPS, IMU, lenses, mirrors, and 2D/3D detectors) associated with optically based imaging systems (e.g. Lidar & Electrical Optical). KLMF provides the structure to design, develop, and link mechanical and optical models for rigorous propagation of optical field aberrations and lower level optical and mechanical misalignments to final 2D/3D products – revolutionizing the study of complex systematic biases and parameterization of calibration models in order to remove systematic 2D/3D image distortions. KLMF also enables scientists to visualize distortion propagation in 3D movies providing additional insights and study into the positioning of new sensors to automatically detect and remove systematic biases within the error propagation chain. Students will learn how to study the calibration of imaging sensors using the following steps:
Disciplines: Analysis, Applied Mathematics, Geometry, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Geospatial Research Laboratory Internship location: Alexandria, VA Mentor:
Internship Coordinator:


No  USDAOBRIEN1  11/23/2020  1606107600000  USDA Forest Service Southern Research Station, Athens Forestry Laboratory  Athens, GA  Applied Mathematics, Biometrics and Biostatistics, Probability and Statistics 
Project Description:The intern would have an opportunity to collaborate with a large multidisciplinary team investigating wildland fire effects on plant tissue and subsequent whole plant mortality. The project includes both laboratory and field studies of energy dose dependent tissue damage to be able to both understand the mechanisms behind fire driven damage and mortality and be able to connect this knowledge to coupled fireatmosphere models such as FireTEC and QUICFire. Opportunities would include helping develop energy dosedamage relationships, novel ways of modeling 3D heat transfer, and fluid dynamics of heat flow through a tree canopy. Other opportunities would be available depending on the applicants areas of interest and expertise. Ideally the intern would participate at the USFS fire laboratory in Athens, Georgia. Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Probability and Statistics Hosting Site:USDA Forest Service Southern Research Station, Athens Forestry Laboratory Internship location: Athens, GA Mentor:
Internship Coordinator:


No  FNLPERDUE1  11/23/2020  1606107600000  Fermi National Laboratory  Batavia, IL  Applied Mathematics, Probability and Statistics 
Project Description:We seek to mitigate the effects of quantum errors in quantum simulation on gatebased universal quantum computers using machine learning. In particular, we want to mitigate errors in the time evolution of a neutrino scattering simulation (no knowledge of scattering physics is expected or required). Precise simulation of the quantum computer will soon be impractical, but even in the cases where we may simulate the device, building realistic noise models is extremely challenging. Therefore, we will study the applicability of machine learning as a heuristic algorithm, with the special advantage that we may train our error correction scheme on hardware directly and remove the need to build an accurate noise model. Students will develop knowledge in using a quantum programming package (e.g. IBM’s Qiskit or Rigetti’s PyQuil) and develop a family of neural network algorithms (using either TensorFlow or PyTorch) to mitigate error in the simulation. Next we will study algorithm performance on real quantum computing devices. This project will be conducted in a team setting under the primary direction of researchers at Fermilab, but with opportunities to interact with team members at the University of Washington. 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, and Probability and Statistics Hosting Site:Fermi National Laboratory Internship location: Batavia, IL Mentors:
Internship Coordinator:


Yes  USACEPILKIEWICZ1*  11/23/2020  1606107600000  U.S. Army Corps of Engineers, Engineer Research and Development Center  Vicksburg, MS  Applied Mathematics, Biometrics and Biostatistics, Probability and Statistics 
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 agentbased models of obstacle navigation, simulating those models computationally, and devising/testing various statistical metrics drawn principally from information theory to quantify interagent communication as obstacles are encountered and circumnavigated. These metrics will eventually be applied to trajectory data from experiments using both dermestid beetles and simple, noninteracting 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 Internship location: Vicksburg, MS Mentors:
Internship Coordinator:


No  ORNLRESTREPO1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Biometrics and Biostatistics, Probability and Statistics 
Project Description:Using models, COVID19 data as well as socioeconomic models that represent the key drivers for social contacts, we will develop a probabilistic assessment of public health policies aimed at improving socioeconomic resiliency of a community faced with the prospects of an epidemic. The novel aspect of this project is that we are going to apply ideas nonequilibrium statistical mechanics to formulate a scheme that evaluates health policies which are usually captured by models with many adjustable parameters. The product would be a metric that assesses the effectiveness (resilience) of a particular or a group of policies. A second part of this project will look for ways to combine time dependent Bayesian estimation, the models and the data, along with learning networks, with the aim of formulating a linear response theory that can discover policy practices and characteristics (parameters) that lead to desired metric goals and report the cost of achieving these. Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  LANLLEDUC1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Probability and Statistics 
Project Description:Rapid and large amplitude ground deformation such as induced by large magnitude earthquakes are now routinely imaged by Interferometric Synthetic Aperture Radar (InSAR). However, measuring smaller amplitude signals remains challenging due to atmospheric propagation delays which may exceed the signature of deformation in InSAR time series. Although atmospheric correction methods improve our ability to observe slow and small (i.e. mm/yr) deformations, expert interpretation and a priori knowledge of deforming systems is always required to highlight deformation signals. In our initial research, we developed a deep learning architecture tailored to remove atmospheric delays due to turbulence and layering of the atmosphere, as well as to identify and extract transient episodes of ground deformation. In this project, you will be exploring probabilistic deep learning architectures and methods that can push InSAR data analysis towards reliable automation at a global scale. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  LANLSCHWENK1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Mathematics (General) 
Project Description:Satellites have been observing the Earth for decades, with new satellites coming online at a rapid pace. These massive archives provide new opportunities to understand the distribution and dynamics of surface water across the planet, but this is only achievable through tools that can automatically and accurately extract waterbodies. Using a large training dataset collected over Arctic Rivers, we found a deep convolutional neural network (CNN) model showed great promise toward this goal, with higher accuracies and better boundary delineations than standard machine learning pixelbased classification approaches. We are aiming to build from this initial success by expanding the domain of the model (from Arctic to other regions), expand its application from Landsatonly to other satellite sensors, and improve boundary detection through super resolution techniques. A candidate for this research would have interest applying deep machine learning to remotely sensed data. Our current codebase relies on the Python package Tensor flow, and we can provide training in using this package if you have no previous experience. Some Python programming experience is recommended. Specific project goals can be customized around your interest and, in addition to the problems mentioned above, can include applications of the CNN model to analyze surface water dynamics in Arctic regions (such as lake expansion and shrinkage, river migration, and/or delta channel morphodynamics) or more general problems such as reservoir monitoring. We would also like to build a model for highresolution imagery such as Planet Labs that may contain only RGB bands. Disciplines: Applied Mathematics, and Mathematics (General) Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  LBNLSMIDT1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Geometry, Mathematics (General), Topology 
Project Description:Topological properties of physical systems that are those that are preserved under continuous deformations. Such properties which may manifest in vector fields and other tensor fields in Euclidean space responsible for many exotic properties of physical systems (e.g. KTtransition). Preserving (i.e. encoding) the topology of such systems is important for building learnable models that generalize well across various physical systems. In this project, we will construct modular neural network operations that preserve the topology of inputs and are able to transform inputs to outputs of different representations (e.g. vector field to a higherrank tensor field) while preserving topological features. We will use test cases inspired by physical systems, e.g. spin waves on periodic lattices and vortices in 2D vector fields. Recommended prerequisites (by start of internship): Knowledge of group theory and representation theory and how to articulate the tools of these theories in code. Familiarity with python, PyTorch, and the mathematical underpinnings of basic neural network operations (forward and backward propagation). Some familiarity with concepts in equivariant neural networks will be helpful (see e3nn.org for an example). Disciplines: Applied Mathematics, Geometry, Mathematics (General), and Topology Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentors:
Internship Coordinator:


No  LBNLSMIDT2  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Geometry, Mathematics (General) 
Project Description:Point geometry, especially the point geometry of atomic structures, can be hierarchical in nature and composed of geometric motifs that can reoccur in any location or orientation in a given example. It is an open question how to sample conditional probabilities of pointwise geometries in a way that preserves the underlying symmetry of 3D space. In this project, we will construct methods for sampling pointwise geometries using Euclidean Neural Networks which are equivariant to elements of Euclidean symmetry (rotations, translations, and inversion). We will build upon the research in this reference: https://arxiv.org/abs/2007.02005 and determine the form of networks output needed for the sampling of degenerate outputs. Recommended prerequisite (by start of internship): Familiarity with degeneracy as it manifests in quantum mechanical systems and concepts such as density matrices. Familiarity with python, PyTorch, and the mathematical underpinnings of basic neural network operations (forward and backward propagation). Some familiarity with concepts in equivariant neural networks will be helpful (see e3nn.org for an example). Disciplines: Applied Mathematics, Geometry, and Mathematics (General) Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentors:
Internship Coordinator:


No  ORNLSMITH1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Probability and Statistics 
Project Description:The Metalog distribution (http://www.metalogdistributions.com/) is a flexible family of continuous probability distributions. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  LANLSORNBERGER1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Probability and Statistics 
Project Description:In this project, we will explore 'spiking' algorithms for machine learning. These algorithms will be implemented on a neuromorphic computing system. Neuromorphic systems are designed to compute in a similar way to how the brain computes. That is, they are based on units that are meant to act like neurons in the brain and the neurons are connected in a massively parallel way. Implementing spiking algorithms is challenging and similar to the construction of a logical circuit. That is, neuromorphic computing is at the stage where we are identifying circuit mechanisms that we can use to make use of the parallelism available. These mechanisms consist of a library of useful concepts for performing important operations. Our Laboratory (Sornborger) has been working on such a 'programming' framework and we have a set of mechanisms that we use to implement algorithms. In this project, we will use these mechanisms (and possibly invent new mechanisms) to implement a spiking machine learning algorithm. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  LANLSWEENEY1  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Geometry, Mathematics (General), Probability and Statistics, Topology 
Project Description:The Computational Earth Science (EES16) group at Los Alamos National Laboratory is looking for a highly motivated student with a strong background in applied mathematics and scientific programming to join us in the ongoing development and application of our discrete fracture network (DFN) software dfnWorks (2017 R&D 100 Winner – dfnworks.lanl.gov). DFN models sit at the junction of highperformance computing (HPC), numerical analysis, graph theory, and computational geometry. The student will collaborate directly with Los Alamos National Laboratory scientists to take part in the development of new capabilities in the software and using the new capabilities to probe critical questions at the frontier of our understanding of flow and transport through fractures. The project will include a variety of aspects of DFN modeling, such as machine learning, graph theory, computational geometry and meshing algorithms, as well as scientific applications of DFN models in the earth and environmental sciences. Specific objectives will be defined in collaboration with the selected student to fit their interests and background and there will be opportunities to collaborate and interact with other students, postdocs, and scientists in the group through weekly seminars and a research symposium. Last year, the successful candidate developed a new meshing algorithm for DFNs, that is now part of the production version of dfnWorks, and which is also forming the basis of a manuscript and part of their thesis research. For more information please contact Dr. Matthew Sweeney (msweeney2796@lanl.gov).
Disciplines: Applied Mathematics, Geometry, Mathematics (General), Probability and Statistics, and Topology Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  LBNLTANG1  11/23/2020  1606107600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics 
Project Description:Machine learning (ML) and artificial intelligence (AI) are transforming scientific research both within the Department of Energy and across academia at large. In particular, machine learning models based on tensor factorization have gained significant traction and seen widespread adoption thanks to their strong generalizability and interpretability. The proposed research concerns the acceleration of computing approximate tensor factorizations of high order data. To this end, we will investigate algorithmic primitives for tensor factorization that are scalable and friendly for massively parallel heterogeneous supercomputers, in particular those that are accelerated with generalpurpose graphics processing units (GPUs). Learning objectives & activities:
Disciplines: Applied Mathematics Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  NRELTHOMAS1  11/23/2020  1606107600000  National Renewable Energy Laboratory  Golden, CO  Applied Mathematics, Mathematics (General) 
Project Description:Recent advances in sparse linear algebra solvers suggest that the next step in scalable solver performance may be adaptive parameter estimation together with feedback and control approaches to optimize solver convergence rates. This approach would reduce the time to solution and overall model compute time. Because of the importance of sparse linear solvers to computational fluid dynamics (CFD) codes such as the NaluWind code under development at NREL, these improvements would enable improved simulations of critical problems in renewable energy such as control of wind turbine wakes. Recent research in optimal control theory applied to the generalized minimal residual (GMRES) iterative Krylov solver shows these methods can lead to possible acceleration of linear and nonlinear solvers in CFD codes. Nonlinear solvers are typically embedded within a Picard iteration that can be accelerated with extrapolation schemes such as the Andersson algorithm. These solvers can also be accelerated using similar approaches and in combination with socalled Krylov recycling and optimal initial solution guesses. AI/ML can also be employed to learn the optimal solver parameters based on the flow physics of simulations. We propose to have a graduate student explore both aspects with a view towards improving the speed of HPACF science applications with a specific focus on wind energy technologies and the NaluWind and AMRWind software packages. Disciplines: Applied Mathematics, and Mathematics (General) Hosting Site:National Renewable Energy Laboratory Internship location: Golden, CO Mentors:
Internship Coordinator:


No  ORNLTOMBS1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Algebra or Number Theory, Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:The GeoAI group at ORNL is hosting students in mathematics this summer to collaborate on a project that is developing novel private lowshot learning methods. Current areas of research include metric learning and metal learning for few shot; developing and incorporating privacy preserving methods into lowshot models to mitigate against membership inference and model inversion attacks; broadening the definition of membership inference attacks on various imagery domains; quantifying privacy loss due to membership inference or model inversion attacks; and understanding potential information loss in lowshot models. A participant on this project will, together with their mentor, have wide discretion in selecting a problem of interest from a variety of topics in lowshot learning, private machine learning, mathematics and statistics. Disciplines: Algebra or Number Theory, Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLTOMBS2  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Algebra or Number Theory, Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:The GeoAI group at ORNL is hosting students in mathematics this summer to collaborate on a project that is developing novel private lowshot learning methods. Current areas of research include metric learning and metal learning for few shot; developing and incorporating privacy preserving methods into lowshot models to mitigate against membership inference and model inversion attacks; broadening the definition of membership inference attacks on various imagery domains; quantifying privacy loss due to membership inference or model inversion attacks; and understanding potential information loss in lowshot models. A participant on this project will, together with their mentor, have wide discretion in selecting a problem of interest from a variety of topics in lowshot learning, private machine learning, mathematics and statistics. Disciplines: Algebra or Number Theory, Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  BNLURBAN1  11/23/2020  1606107600000  Brookhaven National Laboratory  Upton, NY  Applied Mathematics, Biometrics and Biostatistics, Probability and Statistics 
Project Description:Engineering and applicationoriented mission science aims to alter system behavior to achieve specific objectives, or to make optimal decisions/predictions regarding system behavior. Many realworld 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. Machine learning (ML) has made datadriven models, such as deep neural networks, widely popular for learning such surrogates. 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. This project aims to develop Scientific ML techniques that enable objectivedriven uncertainty quantification (UQ) for datadriven models. We will focus on developing theories and algorithms that can ultimately lead to an automated learning procedure of effective surrogates for complex systems that can be used for making optimal decisions robust to system uncertainties and surrogate approximation errors. These goals will be attained based on a Bayesian ML paradigm, in which we integrate scientific prior knowledge on the system and the available data to obtain a prior directly characterizing the scientific uncertainty in the physical system, quantify the uncertainty relative to the objective, develop optimal operators robust to the uncertainty, and design strategies that can optimally reduce the uncertainty and thereby directly contribute to the attainment of the objective. Potential applications of this methodology will be discussed with the student, but may focus on biological and biomedical discovery science. Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Probability and Statistics Hosting Site:Brookhaven National Laboratory Internship location: Upton, NY Mentors:
Internship Coordinator:


No  BNLURBAN2  11/23/2020  1606107600000  Brookhaven National Laboratory  Upton, NY  Applied Mathematics 
Project Description:Deep neural networks have proven to be powerful tools for regression and function approximation, with wellknown applications to image, video, speech, and natural language processing. More recently, researchers have begun to explore the application of deep learning methods to the solution of differential equations, with aims to produce more generalpurpose numerical solvers or, potentially, to arrive at (possibly more approximate) solutions with greater speed. The applicability of these methods to geophysical fluid dynamics problems in weather and climate science is still poorly understood. This project will investigate the accuracy and efficiency of physics informed machine learning (PIML) algorithms on partial differential equation (PDE) test problems of interest to atmospheric and ocean dynamics, such as the quasigeostrophic or shallow water equations. Of particular interest could be the recent meshfree neural operator approaches that learn datadriven approximations to infinitedimensional maps from PDE input spaces (boundary conditions or parameters) to output (solution) spaces directly, rather than by first passing through a fixed spatial discretization. The particular PIML methods to be used in the project will be determined in discussion with the student. Disciplines: Applied Mathematics Hosting Site:Brookhaven National Laboratory Internship location: Upton, NY Mentors:
Internship Coordinator:


No  NISTIYER1  11/23/2020  1606107600000  National Institute of Standards and Technology  Gaithersburg, MD  Applied Mathematics, Biometrics and Biostatistics, Probability and Statistics 
Project Description:The concept of “measurement”, once restricted to onedimensional features such as height, weight, density, voltage, lifetime, etc., has, over time, expanded to accommodate modernday problems such as use of brainscans to detect tumor, use of mass spectra and other types of spectra to identify drugs and other chemicals, use of fingerprints or footwear impressions to identify a pool of individuals who may have been present at the scene of a crime, use of DNA sequences to infer presence or absence of an abnormal gene, use of the chemical structure of a candidate therapeutic drug to infer efficacy in treating a patient, and so on. These modern problems have risen because of our ability to “sense” (or measure) more complex attributes of objects or entities than ever before. As a result, the fields of statistics, mathematics, and computer science are being challenged to keep pace and invent/discover more powerful approaches to measure, describe, and analyze complex, highdimensional data. Richard Royall (“Statistical Evidence: A Likelihood Paradigm”, 1997, Chapman & Hall/CRC) argues that, the degree of support provided by data in favor of a proposition A versus another proposition B is appropriately quantified by the ratio of the likelihoods for A and B, given the data. Accepting this point of view, interest turns to assessing likelihoods in any particular situation where evidential value is of interest. When the data are complex and highdimensional (images, acoustic data, spectral data, shape data, etc.) assessment of likelihoods is extremely challenging partly due to the fact that modeling highdimensional measurements requires a large amount of training data. In this project we will explore several currently available methods, including neural networks and deep learning, and transfer learning, for modeling highdimensional data, especially in the context of data in the form of fingerprint images, footwear impression images, and spectral data. Disciplines: Applied Mathematics, Biometrics and Biostatistics, and Probability and Statistics Hosting Site:National Institute of Standards and Technology Internship location: Gaithersburg, MD Mentors:
Internship Coordinator:


No  ANLCHANG1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Analysis, Applied Mathematics, Geometry, Operations Research, Probability and Statistics 
Project Description:The Delaunay interpolant is a piecewise linear interpolant for finite datasets, which has been shown to have optimal accuracy in a sense with respect to other piecewise linear interpolants. Similarly, when taken to zero training error, a feedforward neural network regressor with fully connected layers and ReLU activation functions is also a piecewise linear interpolant. The purpose of this project is to study the connection between Delaunay interpolation accuracy and neural network accuracy, potentially leveraging this connection to verify the accuracy of neural network regressors and detect inputs for which the neural networks may be subject to lowaccuracy. Research activities may consist of mathematical analyses and experimental verification. This project is made feasible by the HPC resources available at Argonne and recent advances in Delaunay interpolation software, which allow for Delaunay interpolation in hundreds of input dimensions. Disciplines: Analysis, Applied Mathematics, Geometry, Operations Research, and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


Yes  USACEFISCHELL1  12/3/2020  1606971600000  U.S. Army Corps of Engineers, Engineer Research and Development Center  Vicksburg, MS  Analysis, Applied Mathematics, Logic or Foundations of Mathematics, Operations Research, Probability and Statistics 
U.S. Citizenship is a requirement for this internship Project Description:Background: Lidar systems use the reflections of beams of light to determine the distance between the system and an object. One known issue with lidar systems is penetration through foliage. The human eye can often pass through foliage to discern what is on the other side, but even sparsely placed objects between the system and another object may interfere with lidar systems. Objectives: The objective is to quantify the relationship between the density of “foliagelike” occlusion and the ability of a lidar system to discern what is beyond the “foliage.” This experiment will be used for the verification and validation of lidar system models in ERDC Modeling and Simulation (M&S) software. Responsibilities and Learning Objectives: The student will fulfill all responsibilities for the completion of this project under the guidance of the researchers. The responsibilities of the students include but are not limited to: creating and improving experimental design, (reliably) implementing experimental set up, completing detailed and scientifically thorough testing and analysis, collecting and analyzing results, finding places to publish the research and conferences to present at, and writing publications. As such, learning objective include: design of experiments (DOE), statistical analysis, M&S/V&V exposure, publication and public speaking experience. The researchers will provide funding, publication support (such as editing), coordination, and fill other supervisory roles. Disciplines: Analysis, Applied Mathematics, Logic or Foundations of Mathematics, Operations Research, and Probability and Statistics Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center Internship location: Vicksburg, MS Mentors:
Internship Coordinator:


No  ORNLLUNGA2  12/3/2020  1606971600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Logic or Foundations of Mathematics, Probability and Statistics 
Project Description:This project seeks to develop a variational autoencoder inspired domain separation network framework to learn probabilistic multidomain shared features. In many applications where intrinsic domain biases exist between source and target domain pairs, existing works have shown that the domain adversarial similarity loss is superior to extract shared features. However, when there are subtle differences between domains, as is the case in many remote sensing and medical imaging applications, the extraction of shared features via the adversarial domain classifier may be prohibitive. The goal of the project will be to develop a probability distribution inspired and distancebased similarity measure to learn a shared latent feature space. Variational autoencoders offer one way to establish a probabilistic latent variable model with rich information of the approximate posterior distribution. Our assumptions are that shared feature similarities can be computed between latent variables while taking into account the shape of the posterior distribution. This probabilistic modification of existing domain separation networks approach can benefit from current work being performed in our related projects. The reserach includes variational methods for uncertainty quantification, as well as scaling the methods to prototype on the Summit supercomputing environment. As an outcome we would like to enable the transfer of knowledge across object detection tasks to related domains for which shared embeddings must be compared per distributional features. Disciplines: Applied Mathematics, Logic or Foundations of Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLLUNGA1  12/3/2020  1606971600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Operations Research, Probability and Statistics 
Project Description:Methods for multitask learning that take advantage of natural groupings of related tasks are emerging across machine learning, computer vision and natural language processing communities. However the accompanying optimization techniques have so far demonstrated limitations when intertask interactions are expected. In this project our interests are twofold: (1) designing new generic serial and parallel neural network architectures to enable multitask models for Earth science challenges, (2) designing efficient optimization techniques to enable multidomain learning with limited training data. We define tasks groups to represent supervised information at the intertask level that can be encoded into the model. For application we seek to efficiently learn different feature spaces at the levels of individual tasks, task groups, as well as the universe of all tasks while exploring the limitations of, (1) parallel architectures that encode each input simultaneously into feature spaces at different levels; and (2) serial architectures that encode each input successively into feature spaces at different levels in the task hierarchy. We have a globally distributed buildings dataset gathered from Terabytes of remote sensing images. The data is representative and diverse enough to explore hundreds of tasks in this project. Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  NISTIYER2  12/3/2020  1606971600000  National Institute of Standards and Technology  Gaithersburg, MD 
Project Description:The success of convolutional neural networks (CNN) and deep learning methods in solving a wide variety of difficult problems is well known. In classification or discrimination tasks involving 2D images the ability of CNNs to extract appropriate features from the training set of images has been well established. The realization that low level features extracted during the early layers of CNNs may be generalizable to image classes not part of the training set has led to ideas such as transfer learning. Notwithstanding such successes one might ask how efficient deep networks are in extracting the ‘correct set of features’ for a given task, say classification. The phrase ‘correct set of features’ can be given a definite meaning using ideas from classical statistics – ideas such as minimal sufficient statistics, complete sufficient statistics, etc. There are families of distributions for which a minimal set of features for discriminating between two or more distributions can be analytically derived. This minimal set is the absolute best data reduction possible without sacrificing discrimination power and is unique to within a onetoone transformation. It is possible to produce realizations from these distributions in the form of images of arbitrary size (M x N pixels). Given two classes of images arising from two different parent distributions, some questions of considerable interest are: (1) What is the relationship between features extracted by a network and the theoretically optimal features? How does this relationship evolve as the number of training samples or network complexity increases? (2) To what extent does the discrimination efficiency (compared to theoretical optimum) depend on the type of architecture used for the network? (3) Can generative adversarial networks (GANs) be used in any way to gain efficiency? (4) Does classical statistics provide any insights regarding these questions? (5) Rather than pitting one classifier against another and comparing their performances, can we use challenging data sets where the best possible discrimination power is theoretically known, and any algorithm can assess its efficiency relative to this best case? A number of experiments will be conducted to answer these questions. Step 1: Identify classes of distributions that are capable of producing realizations in the form of images and for which the set of minimal sufficient statistics (minimal feature set) is analytically available. We have identified a few such classes for starters (multivariate Gaussian, multivariate Bernoulli, Ising Models) and we plan to consider other potentially interesting (but less well known) distribution families as well. Step 2: Identify a small number of candidate deep network architectures for use in the experiments. Step 3: Write software scripts for generating arbitrary (as many as needed) number of examples to form training sets (as many examples as the network needs for training it). Step 4: Train each candidate network using the training sets. Examine the features generated at various layers of the network, assess the degree of equivalence of the extracted features to the theoretically optimal feature set, and compute the discrimination power loss of the trained network pitted against the theoretical best feature set. Step 5: Study the ‘discrimination power loss’ as a function of number of training examples used and number of trainable parameters of the network. The proposed set of activities will provide answers to the questions posed at the outset and provide insights into the strengths, and more interestingly, limitations, of plugandplay deep learning approaches. Testing deep learning approaches in situations where groundtruth optimal performance is known is an excellent way of understanding its performance characteristics. We view our efforts as the first step in creating certified image data collections with optimal features. This approach will shift the current culture of pitting one algorithm against another with respect to relative classification performance to a paradigm where each classification algorithm will be able to assess its efficiency by comparing itself to the theoretical limit of discrimination power. Hosting Site:National Institute of Standards and Technology Internship location: Gaithersburg, MD Mentors:
Internship Coordinator:


No  LANLYOUZOULIN1  12/3/2020  1606971600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics 
Project Description:Time series signals are quite common in various physical systems. Particularly in this project, we will explore the acoustic time series collected from Acoustic Resonance Spectroscopy and Resonant Ultrasound Spectroscopy measurements. Contained in both the spectral information and the timeseries signals are signatures relating to material property, boundary condition, and/or dimensional/shape changes. The mechanical vibrations from these experiments, and the signatures therein are used for nondestructive evaluation, material characterization and component sorting for inspection purposes of missionrelevant materials and components. Effective extraction of the useful signatures and events from acoustic time series can be challenging in that they are limited in time duration, varied by signal amplitude, and corrupted by all sorts of environmental noise, as well as natural variations arising from the processing. Simultaneously, it is necessary to limit the number of “false detections” to a small fraction of the true detections. The student will collaborate with both experimental acousticians and computational scientists to develop machinelearning algorithms to extract useful features and infer the events of interests. In order to gain the most out of our research project, we would expect students to have the following: [2]. Yue Wu, Youzuo Lin, Zheng Zhou, David Chas Bolton, Ji Liu, Paul Johnson, "DeepDetect: A Cascaded Regionbased Densely Connected Network for Seismic Event Detection," in IEEE Transactions on Geoscience and Remote Sensing, 57(1), 6275, 2019. Disciplines: Applied Mathematics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentors:
Internship Coordinator:


No  LANLHLAVACEK1  12/3/2020  1606971600000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Probability and Statistics 
Project Description:Recently, we showed how a large number of *qualitative* observations of system behavior (e.g., +/ scoring of mutant viability) can be used in an automated fashion to parameterize a mathematical model for a cellular network [Mitra ED, Dias R, Posner RG, Hlavacek WS (2018) Using both qualitative and quantitative data to improve parameter identification for systems biology models. Nat Common 9: 3901]. The methods used in this study, and other related methods, are implemented in the PyBioNetFit software package [Mitra ED, Suderman R, Colvin J, Ionkov A, Hu A, Sauro HM, Posner RG, Hlavacek WS (2019) PyBioNetFit and the Biological Property Specification Language. iScience 19: 10121036]. Qualitative observations have tremendous (but not widely appreciated) utility for model parameterization, as these observations define a feasible region in the parameter space of a model. Modelers routinely ignore qualitative data but 1) numerous qualitative datasets consisting of diverse data types are available, 2) qualitative distinctions often represent the type of data that we have the most confidence in, and 3) qualitative data can usually be more readily generated than quantitative data. Indeed, there exists potential to generate qualitative data at scale in support of modeling efforts via highthroughput screeningtype measurement techniques. In this project, we will further explore the potential of qualitative data to aid in biological model development. We will develop a model for a cell signaling system, parameterize it on the basis of qualitative and quantitative data available in the literature or provided by experimental collaborators, and then quantify uncertainty in parameter estimates and model predictions. We study cell signaling systems that play a role in cancer and immunity. The student joining this project will have an opportunity to apply rulebased/ODE/stochastic modeling, optimization, MCMC, and Bayesian parameter estimation and uncertainty quantification.Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  LBNLKRISHNAPRIYAN1  12/3/2020  1606971600000  Lawrence Berkeley National Laboratory  Berkeley, CA  Applied Mathematics, Geometry, Topology 
Project Description:Machine learning for scientific applications, ranging from physics and materials science to biology, has emerged as a promising alternative to more timeconsuming experiments and simulations. The challenge with this approach is the selection of features that enable universal and interpretable system representations across multiple prediction tasks, and harnessing this understanding into designing new technologies. In this project, we will develop tools from computational topology and geometry to study scientific systems, such as materials and molecular systems. We will combine these tools with machine learning to encode representations of these systems to aid in designing new systems to maximize desirable properties (such as those related to energy sustainability). Recommended prerequisites (by start of internship): Knowledge of areas of topological data analysis and some of the code implementations related to this. Familiarity with python and PyTorch. Disciplines: Applied Mathematics, Geometry, and Topology Hosting Site:Lawrence Berkeley National Laboratory Internship location: Berkeley, CA Mentor:
Internship Coordinator:


No  ANLMADIREDDY1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics, Operations Research, Probability and Statistics, Topology 
Project Description:Some unique challenges in scientific data that need to be considered while building datadriven models are: (1) Noise and uncertainty (2) Data scarcity, in addition to the large feature spaces. Probabilistic models are a natural choice to address many of these challenges and provides a systematic approach to reason about the prediction uncertainty. Historically, the adoption of probabilistic modeling approaches has been limited by the scalability of the inference approaches. With the recent advances in Bayesian deep learning, especially in approximate inference approaches such as variational inference, we are able to efficiently handle flexible models (with millions of parameters) efficiently on modest hardware and obtain stateoftheart predictive accuracy. The project would involve developing novel deep probabilistic machine learning approaches tailored to the unique needs of scientific data. The participant will learn to develop deep generative models (that are at the intersection of Bayesian probabilistic modeling and deep learning) in the context unsupervised representation learning and supervised learning, for both Euclidean and nonEuclidean feature spaces as well as training them on leadershipclass systems. Of particular interest would be to design efficient neural architectures and learning mechanisms through exploration of model hierarchy, topology preservation, contrastive learning, normalizing flows and careful neural architecture search for variational autoencoder and information bottleneck models. The participant will be part of a multidisciplinary team and will work on problems from different domains such as material science, highenergy physics and fusion energy sciences. Disciplines: Applied Mathematics, Operations Research, Probability and Statistics, and Topology Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLBESSAC1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Probability and Statistics 
Project Description:Wind conditions influence many human and natural systems (renewable energies, shipping, aviation, erosion, …) and extreme events of winds can have dramatic impacts on these systems. Wind speeds are typically measured as averages over a given time window. However, timeaveraged wind speed misrepresents potential wind gusts (stronger winds usually recorded as a maximum over a timewindow) happening during a given temporal window. Therefore, extreme wind events are not adequately captured by this data. We propose to address the discrepancy between available measurements of timeaveraged wind speed and wind gusts. We aim to develop hybrid techniques blending modern machine learning with classical statistics. The first facet of the project will consist of estimating and modeling features of the dependence between wind gusts and average wind speed with artificial neural networks (ANN) and deep learning (DL). ANN and DL have proven to reproduce complex nonlinear behaviors but have rarely been used in the context of extremes. This project connects the two emerging research areas, extreme event modeling and DL. In the second part, we propose to hybridize statistical models, that embed uncertainty associated with these phenomena, with predictions from ANNs. Disciplines: Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentor:
Internship Coordinator:


No  ANLLEYFFER2  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics, Operations Research, Probability and Statistics 
Project Description:We are interested in the development of optimal control models and algorithms for the simulation of quantum dynamics. We will investigate different sampling techniques and their impact on the performance of the optimal control techniques. We will also investigate the use of secondorder information in the algorithms. This project requires familiarity with one or more of the following topics: optimal control, quantum computing, automatic differentiation, optimization methods. Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLLEYFFER1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics, Operations Research, Probability and Statistics 
Project Description:We are interested in the development of optimization techniques that can make use of machinelearning (ML) surrogates trained on scientific applications within an outer loop design optimization and optimal control applications. This project will develop new optimization models and algorithms that enable design and control decisions over ML surrogates. Possible applications include the use of ML surrogates as regularization terms in inverse problems arising at Argonne's advanced photon source. Familiarity with one or more of the following areas is a plus: optimization methods, ML tools, and inverse problems. Disciplines: Applied Mathematics, Operations Research, and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentor:
Internship Coordinator:


No  ANLRUDI2  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:Many interesting physical phenomena happen at scales finer than the discretization of numerical solvers can resolve; hence, the phenomena tend to be misrepresented in numerical solutions. We consider multiscale problems based on partial differential equations (PDEs), where the presence of small localized features is challenging for numerical methods. At the same time, however, these finescale phenomena are critical to better represent the entire system. The numerical solution can be improved through several ways including: (i) adaptive mesh refinement and (ii) deterministic or stochastic subgridscale models. These approaches increase the computational or modeling efforts, respectively. Therefore, it is crucial to accurately identify the regions of the domain that require higher resolutions or adequate subgridscale models. In this project, our goal is to develop new machine learning techniques, based on deep neural networks, to locate smallscale features of physical processes based on observable physical properties. This research will introduce the student to concepts from PDEs, statistics, numerical analysis, and deep learning, and we will explore ways of using techniques from these areas in creative and interdisciplinary ways. Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLRUDI1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics, Biometrics and Biostatistics, Mathematics (General), Probability and Statistics 
Project Description:Spiking neurons in the brain and spinal cord are typically modeled by systems of nonlinear ordinary differential equations (ODEs). For instance, one popular model, called HodgkinHuxley, is a nonlinear system of four ODEs. These ODE equations represent how spikes (electrical voltages) are generated in a neuron cell for a given current or sensor stimuli. The output of one such ODE takes the form of a spiking voltage timeseries (similar to an electrocardiogram). These systems of ODEs contain numerous uncertain parameters that control the opening and closing of ionchannels on a cell membrane. Their exact values are not known in a prior, but rather their ranges are available from experiments. Therefore, the goal of this project is to numerically estimate the parameters' value such that the simulation output of the ODE fits spike recordings from laboratory experiments. This amounts to solving a socalled inverse problem. This can be done deterministically by solving an optimization problem; or in a statistical framework by estimating a posterior distribution for the parameters. Disciplines: Applied Mathematics, Biometrics and Biostatistics, Mathematics (General), and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLLENZI1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Probability and Statistics 
Project Description:Highly flexible statistical models have the advantage of capturing intrinsic data characteristics such as spatial dependency or smoothness at various levels of extremes. However, some models are notoriously tricky to fit, even with relatively small data sets. On the other hand, machine learning techniques have proved successful in predicting complex systems or feature detection but are usually difficult to interpret and provide little uncertainty quantification. In this work, we propose to use machine learning techniques to estimate parameters and features of statistical models that are challenging to infer in the classical setups. The idea is that statistical models' interpretability still holds, and the machine learning tools become a standin for fitting purposes. Artificial neural networks will be trained using the statistical parameters or distribution features as output and the process's realizations as input data. Ideally, these parameters will have a distribution to characterize the uncertainty from the network output using a more statistical framework. Finally, we will explore the construction of distributions to characterize the uncertainty associated with the network outputs. Disciplines: Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLFADIKAR1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics, Probability and Statistics 
Project Description:We are developing strategies for multivariate statistical modelling, in the context of model calibration and optimization, where the model response can be of arbitrary dimension or type. The project will entail (a) building surrogates for multioutput computer simulations, (b) discovering and modelling correlations among multioutput observational data, and (c) performing uncertainty quantification. Students will use multivariate modelling (parametric/nonparametric) apparatuses to achieve (a) and (b), and basic knowledge about model calibration is desired. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLMARIN1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:Special functions may be defined as nonalgebraic functions, including anything from simple trigonometric functions to Bessel functions. The accurate evaluation of such functions has always been problematic, the more common functions such as sines or exponentials may have compiler support, while functions like Bessel/Hankel require tailored libraries. Even so the evaluations may at times be inaccurate or inefficient. Deep learning models have the ability to provide very efficient evaluations on graphical processing units, as well as provide more accurate values given the independence of the training set once the model has been developed. The end scope of this project is to develop the basis of a library for special functions in the language Julia, that outperforms traditional libraries and provides models portable to any other programming language. The work involves both theoretical analysis for determining optimal choices for model training, as well as programming for assuring the models are robust and portable. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentor:
Internship Coordinator:


No  ANLZHANG2  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:Adjointbased error estimation methods have been popular for estimating the global error in PDEs and ODEs. The basic idea is to use adjoint solutions to compute the inner product between a random vector and the global error at the final time. To estimate the pointwise global error at the final step, one would have to solve an adjoint system many times for each given vector. Existing methods allow us to evaluate the l2 error norm with a few random vectors. However, l2norm is often not sufficient for studying the spatial distribution of error and providing systematic insights in error control. In this project, we will take a novel approach to recover the global error. We will identify the problem as a compressive sensing problem and exploit efficient strategies to reduce the number of random vectors needed. An alternative direction is to develop adjointbased error estimation in multirate time integration methods. The participant does not need to develop adjoint models from scratch, the research will make use of the adjoint ODE solvers available in PETSc. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLZHANG1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:Sparse linear systems are a foundational component in modeling and simulation. As the workhorse of these applications, solution of sparse linear systems has been continuously driving the development of efficient iterative algorithms and their highperformance implementation. Because of the overwhelming choices of algorithms, data structures, and hardware architectures, selecting the optimal solution to a given system is difficult for application developers and researchers and may require deep skills and expertise in numerical analysis, HPC, and domain knowledge. In this project, we aim to automate the process and ease the reliance on numerical analysis and hardware knowledge by using graph neural networks (GNNs) for fast selection and tuning of preconditioners and sparse linear solvers adaptive to matrix properties and hardware architectures. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentor:
Internship Coordinator:


No  ANLMALLICK1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Analysis 
Project Description:In many scientific domains, the data stems from different sources. Fusing the data from these sources is critical for many machine learning tasks. In this project, we will focus on data fusion methods for spatial temporal graph neural networks. Specifically, we will develop representation learning methods using encoderdecoder neural networks to model and learn the joint distribution of the modalities. We will use the trained generative model to sample data from the modality where the data is limited. We will evaluate the efficacy of the developed method on large scale traffic forecasting problems. Disciplines: Analysis Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLMAULIK1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:The quantum Fourier transform (QFT) promises an exponential speedup over its classical counterpart. In this project, the QFT will be assessed for utilization in pseudospectral methods for numerically solving partial differential equations (PDE). Currently, pseudospectral methods require several forward and inverse classical Fourier transforms for the computation of the nonlinear terms in a PDE. In this project, the QFT will be used to assess potential improvements in the scaling of these techniques. This will be through an analysis of the computational cost of the QFT in a PDE solver setting, as well as studies of practical deployments on quantum hardware. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentor:
Internship Coordinator:


No  ANLRAGHAVAN1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:Dataset imbalance refers to the issue when certain classes are represented by significantly more number of data points relative to others. It is a prevalent issue in machine learning especially classification problems in many scientific applications. This issue materializes itself when the final performance of a model is biased towards the class with a larger number of sample points. One way to correct this bias is to equalize the imbalance and intelligent sampling strategies play a critical role in this procedure. However, due to a lack of efficient approaches, a common way to address the issue involves trial and error driven uniform oversampling of the underrepresented class or undersampling of the overrepresented class. In this project, we will formulate the problem of imbalance in a data batch as an optimization problem and derive conditions which must be satisfied for sampling a balanced data batch. We then integrate the condition into the neural network learning problem. We will develop a game theoretic approach to resolve the tradeoff between the performance of the neural network and the variance in the data. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLBALAPRAKASH2  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:Developing a new optimization solver for a particular class of optimization problems is an expertdriven, iterative, and timeconsuming process. While the process requires the knowledge and experience of the optimization expert, a major bottleneck stems from the trialanderror approaches involved in trying out different initial ideas and algorithmic components, computationally expensive hyperparameter tuning, and extensive testing and validation across problem instances. In this project, we will develop learning to optimize approach, an emerging approach that adopts machine learning methods to help automate the design and development of optimization solvers and methods. Specifically, we will focus on designing mixed precision stochastic solvers using reinforcement learning methods and evaluate its efficacy to optimize neural network training. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLMCINNES1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Mathematics (General) 
Project Description:The project will focus on developing a universal mathematical and computational framework for handling largescale hyperbolic net and network problems. The basic computational methodology will be the discontinuous Galerkin method, with novel design of numerical fluxes in handling coupling conditions at network junctions that preserve mass conservation/balance of forces, continuity of solutions, as well as physical invariances such as positivity and wellbalance properties of numerical solutions. In addition, the project will explore the development EulerianLagrangian solvers for 1D and 2D shallow water systems with positivity preserving and wellbalance preserving properties. Such solvers will be potentially integrated into the hyperbolic net/network to handle junction conditions going beyond the simple 1D algebraic coupling of solutions at different branches. The project will also address the challenge of the multiscale nature of the modelling levels and computational mesh levels. The mathematical development will be implemented in the highperformance PETSc/DMNetwork libraries (https://www.mcs.anl.gov/petsc) for applications such as shallow water canal flows, blood flows, and the deformation of elastic nets for medical devices such as stents. The outcomes of this project will benefit the scientific community at large. Disciplines: Mathematics (General) Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLMANNS1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Applied Mathematics 
Project Description:Mixedinteger optimal control problems are a mathematical modeling tool with many applications ranging from the design of electromagnetics cloaks over energy management of buildings to image reconstruction. Solving mixedinteger optimal control problems on the other hand is a difficult task because the problems often combine both the challenges from PDEconstrained optimization and discrete optimization. Therefore, efficient approximation techniques have gained interest in recent years and we have contributed to this research area by developing approximation algorithms that guarantee certain degrees of performance. In the proposed project, the student will be working on novel approximation algorithms for mixedinteger optimal control problems. The tasks include the development, analysis, implementation and testing of the algorithms on academic and realworld problem instances. Disciplines: Applied Mathematics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  ANLKRISHNAMOORTHY1  12/3/2020  1606971600000  Argonne National Laboratory  Lemont, IL  Analysis, Operations Research, Probability and Statistics 
Project Description:Simulations of complex physical phenomena is prevalent in many applications important to the Department of Energy, including climate sciences, high energy physics, and combustion research. These simulations usually contain parameters that determine how well the simulation represents reality. Optimizing these parameters is a computationally expensive task as it may take several minutes to hours to run the simulations with a given parameter set. Efficient optimization algorithms that do not rely on derivative information of the simulation objective function are needed. Surrogate model algorithms are commonly used to tackle these types of blackbox expensive optimization problems. To obtain the surrogate models, analysis is required to extract features such as the parameter dimensions that are variant to the simulations and to determine the degrees of freedom in the surrogate model so that it can fit the simulation data with high accuracy. Additionally, different physical aspects of the simulation may live in parameter subspaces of different dimensions. Hence, this project will focus on the use machine learning and statistical techniques to determine problem and simulation features that can be exploited in the optimization problem that fits the surrogate model to simulation data. Disciplines: Analysis, Operations Research, and Probability and Statistics Hosting Site:Argonne National Laboratory Internship location: Lemont, IL Mentors:
Internship Coordinator:


No  SNLD'ELIA2  11/23/2020  1606107600000  Sandia National Laboratories  Albuquerque, NM  Applied Mathematics, Mathematics (General) 
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 nontrivial and illposed 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 datadriven 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 newmodel discovery. Disciplines: Applied Mathematics, and Mathematics (General) Hosting Site:Sandia National Laboratories Internship location: Albuquerque, NM Mentor:
Internship Coordinator:


Yes  USACELYONS1*  12/21/2020  1608526800000  U.S. Army Corps of Engineers, Engineer Research and Development Center  Vicksburg, MS  Applied Mathematics 
U.S. Citizenship is a requirement for this internship Project Description:Accurate measurement of shock wave fields with traditional pressure sensors is impossible under certain conditions, due to submicrosecond shock rise times. Wave fields with known radial symmmetry can be reconstructed with higher accuracy from the optical phase difference induced in a MachZehnder interferometer probe beam through an Abel transform relation. However, when the acoustic field departs from constrained spherical or cylindrical symmetry, additional unknown geometrical and physical parameters are introduced which confound the inversion. To overcome this limitation, we propose to develop approximate methods for local pressure field inversion from multiple, spatiallydisplaced interferometer probe beams. Physical and mathematical properties of the acoustic pressure perturbation can be used to develop displacementdependent relations for optical phase. Based on these relations, the student intern will develop analytical and numerical methods for pressure inversion by exploiting the acoustic field similarity. In addition, the student intern will examine the sensitivity of the reconstruction to the diameter, profile, and positions of the interferometer probe beams. 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 the Abel and related integral transforms, analytical properties of acoustic wave fields, and principles of MachZehnder interferometry. The student intern should have introductory coursework in numerical methods and Fourier analysis, and be proficient in a higherlevel programming language, such as Python, for implementing numerical methods. Disciplines: Applied Mathematics Hosting Site:U.S. Army Corps of Engineers, Engineer Research and Development Center Internship location: Vicksburg, MS Mentors:
Internship Coordinator:


No  ORNLTRAN1  12/21/2020  1608526800000  Oak Ridge National Laboratory  Oak Ridge, TN  Analysis, Applied Mathematics 
Project Description:The goal of this project is to design and implement a deep neural network framework to infer the dynamics of physical systems from data, which also identifies and respects fundamental properties such as conservation and invariance. We will explore a particular class of neural networks, known as Hamiltonian neural networks (HNN), which discover conserved quantities via parameterizing the Hamiltonian of the system with neural networks and then learning it directly from data. We will examine properties of Hamilton’s equations as well as the class of symplectic numerical schemes to adapt and inform HNN designs. In this project, the student will learn about neural networks, Hamilton mechanics and how to apply them to extract the physical laws from scientific data, in particular, from fluid simulations and particle systems. Disciplines: Analysis, and Applied Mathematics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  NISTLU1  12/21/2020  1608526800000  National Institute of Standards and Technology  Gaithersburg, MD  Probability and Statistics 
Project Description:Motivated by an ongoing project to help NIST engineers to design a cooktop fire warning system based on some preselected sensors to collect cooktop gas signals that may help predict potential fire based on a number of experiments that have already been completed, in this project student will explore the general issue of classification in the context of timevarying time series and how dynamic classification may be achieved using standard statistical discriminant analysis techniques such as logistic regression or recursive treebased methods (using R) based on some multivariate features. Performance of these results may be compared with other machine learning methods such as neural networks that have already been tried but are known to have their own limitations such as unrealistic experimental data size requirements. Disciplines: Probability and Statistics Hosting Site:National Institute of Standards and Technology Internship location: Gaithersburg, MD Mentor:
Internship Coordinator:


No  LANLHLAVACEK2  12/21/2020  1608526800000  Los Alamos National Laboratory  Los Alamos, NM  Applied Mathematics, Probability and Statistics 
Project Description:In recent work, we used compartmental epidemiological modeling and Markov chain Monte Carlo (MCMC) sampling to make daily Bayesian inferences to improve situational awareness of COVID19 transmission in the 15 largest US metropolitan areas [Lin YT, Neumann J, Miller EF, Posner RG, Mallela A, Safta C, Ray J, Thakur G, Chinthavali S, Hlavacek WS (accepted) Daily forecasting of new cases for regional epidemics of Coronavirus Disease 2019 with Bayesian Uncertainty Quantification. Emerging Infectious Diseases]. Prediction of future new case detection with rigorous quantification of uncertainty was extremely computationally challenging, which has motivated an interest in developing software tools that facilitate efficient and scalable Bayesian inference that would be useful in future modeling studies. The student working on this project will become engaged in design, software implementation, and evaluation of MCMC algorithms. The goal is to implement one or more, potentially novel algorithms that are as efficient as possible and also scalable, meaning that computational cost does not grow explosively as the number of input/training data points or number of adjustable model parameters grows. The new methods will be incorporated into PyBioNetFit [Mitra ED, Suderman R, Colvin J, Ionkov A, Hu A, Sauro HM, Posner RG, Hlavacek WS (2019) PyBioNetFit and the Biological Property Specification Language. iScience 19: 10121036], which is an opensource Python software package designed to aid modelers in leveraging parallel computing resources to solve hard statistical inference problems. It is hoped that the student joining this project will apply the tools that they help to develop in a modeling study of a complex system of interest to them. The Hlavacek research team develops software for modeling of cell signaling systems and collaborates with quantitative experimentalists to study cell signaling systems involved in cancer and immunity. Our research is supported by grants from NIGMS and NCI. The student working on this project will learn about ODE modeling of nonlinear dynamics, parallel computing, Bayesian inference, and uncertainty quantification. Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  USDALOUDERMILK1  11/23/2020  1606107600000  USDA Forest Service Southern Research Station, Athens Forestry Laboratory  Athens, GA  Analysis, Applied Mathematics, Mathematics (General) 
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 fireatmosphere dynamics. Mathematical relationships between multidimensional 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 inperson 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 Mentor:
Internship Coordinator:


Yes  LANLMONROE1*  11/23/2020  1606107600000  Los Alamos National Laboratory  Los Alamos, NM  Algebra or Number Theory, Applied Mathematics, Mathematics (General) 
U.S. Citizenship is a requirement for this internship Project Description:Inexact computing is any kind of computing where one does not get the exact numerical result. This can include approximate and probabilistic computation. This will be applicable to a wide range of postMoore’s era architectures, because of reliability issues, potential power savings, increased resilience to faults and architectural changes. Some combination of general processors, general inexact processors and specialized inexact processors will have to be developed, as well as efficient ways to use them. LANL has an ongoing exploration of inexact computing techniques, with projects in a range of areas of inexact computing. We are exploring reduced precision, machine learning approaches, advanced error detection and correction methods and other techniques, and applying these to problems in computational mathematics, basic mathematics and computer science. The specific project we address with an NSFMSGI intern will depend on intern interests and background. Our current projects include:
>We encourage publication of results. LANL has a wide range of compute systems, and students will have access to cuttingedge devices of interest. If onsite activity is possible at the time of the internship, the intern will sit in the Ultrascale Systems Research Center, which supports a wide range of research in computer science. We are happy to discuss the project in more detail upon request. For further information, please contact: Dr. Laura Monroe (lmonroe@lanl.gov). Disciplines: Algebra or Number Theory, Applied Mathematics, and Mathematics (General) Hosting Site:Los Alamos National Laboratory Internship location: Los Alamos, NM Mentor:
Internship Coordinator:


No  ORNLKOTEVSKA1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:The number of intelligent systems around us is growing rapidly. These Internet of Things (IoT) devices include smart home devices, health monitors, autonomous vehicles, and the smart grid, collecting data about our home activities, our health, where we visit, and our electricity usage, respectively. These technical means are constantly growing in power and sophistication and will likely see even more rapid development with the widespread deployment of 5G wireless networks, which will provide high speed data transfer and more precise location information. However, as these systems scale up, privacy is being left behind. We currently lack the ability to ensure meaningful data privacy guarantees to citizens, institutions, and infrastructure. And, we ask the question of how data privacy should be protected in a world where data is gathered and shared with increasing speed and ingenuity? Differential privacy (DP) is a new model of cybersecurity that proponents claim can protect sensitive data far better than traditional methods. Until recently differential privacy had been a topic of theoretical research without much application to realworld scenarios. So, there is a huge gap between theoretical bounds and practical implementation which opens the possibility for experiments. The aim is to create mathematically provable guarantee of data privacy protection and validate on realworld dataset related to smart grid to address the potential privacy consequences in those systems.
Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLKOTEVSKA2  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Analysis, Applied Mathematics, Probability and Statistics 
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 realworld data and evaluation.
Disciplines: Analysis, Applied Mathematics, and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  ORNLCHOI1  11/23/2020  1606107600000  Oak Ridge National Laboratory  Oak Ridge, TN  Applied Mathematics, Mathematics (General), Probability and Statistics 
Project Description:As scientific experiments and HighPerformance Computing (HPC) infrastructure evolve, data capture rates continue to exceed the available storage, network, and compute infrastructure for subsequent postprocessing. The scientific data challenge is similar but distinct to many of the “Big Data” challenges we see in the commercial space. The trend from the newest diagnostics and exascale computations clearly shows that advanced machine learning techniques are necessary to manage, reduce, refactor, and extract information. The project will focus on applying various machine learning and deep learning techniques for analyzing scientific data. The main research goals are i) how to analyze scientific data and apply machine learning algorithms for performance improvement, ii) researching advanced machine learning techniques for faster and more accurate models, and iii) how to automate science machine learning and deep learning workflows. The project will provide the following learning opportunities; i) develop a basic understanding of scientific data processing workflows, ii) acquire skills in applying machine learning algorithms, and iii) gain experience in managing largescale scientific data. Disciplines: Applied Mathematics, Mathematics (General), and Probability and Statistics Hosting Site:Oak Ridge National Laboratory Internship location: Oak Ridge, TN Mentor:
Internship Coordinator:


No  LLNLCHEN3  11/23/2020  1606107600000  Lawrence Livermore National Laboratory  Livermore, CA  Applied Mathematics, Probability and Statistics 
Project Description:The overall objective of this framework is to enable complex interactions between physicsbased and datadriven systems to be accounted for in realtime decision making while retaining credibility in mitigating rare events. This project will develop a datadriven surrogate model assisted deep reinforcement learning (DRL) framework to achieve fast and uncertainty aware decision makings. It has the following tasks: Task 1: Datadriven surrogate modeling and chance constraints reformulation: We will develop sparse Gaussian process (SGP)based surrogate model to describe the relationships between uncertainty resources and the chance constraints. In particular, the SGP surrogate will be decomposed into two stages: the statisticalmomentbased, 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 moments information. Note that no priori distribution assumption is needed for uncertain variables. Task 2: Integrated SGP surrogate model and DRL algorithm for fast decision making: to enable a good performance, nonlinear SGP is usually required, yielding nonconvex chance constrained OPF. This significantly increases the difficulty for nonlinear programming methods in getting good solutions and achieving fast decision makings. We will develop new safe DRL algorithms, i.e., safe actorcritic network that can continuously interact with SGP surrogate model and train an agent to learn the optimal control strategies. The 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 is able to make fast control decision with new input variables, i.e., forecasted DERs and loads.
Disciplines: Applied Mathematics, and Probability and Statistics Hosting Site:Lawrence Livermore National Laboratory Internship location: Livermore, CA Mentors:


No  NISTSCHNEIDER1  11/23/2020  1606107600000  National Institute of Standards and Technology  Gaithersburg, MD  Applied Mathematics 
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 Internship location: Gaithersburg, MD Mentor:
Internship Coordinator:


Yes  NISTSCHNEIDER2*  11/23/2020  1606107600000  National Institute of Standards and Technology  Gaithersburg, MD  Applied Mathematics 
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 Internship location: Gaithersburg, MD Mentor:
Internship Coordinator:

The name and contact information of the hosting site internship coordinator is provided for further assistance with questions regarding the hosting site; local housing availability, cost, or roommates; local transportation; security clearance requirements; internship start and end dates; and other administrative issues specific to that research facility. If you contact the internship coordinator, identify yourself as an applicant to the NSF Mathematical Sciences Graduate Internship (MSGI) Program.
Interns will not enter into an employee/employer relationship with the Hosting Site, ORAU/ORISE, NSF or DOE. No commitment with regard to later employment is implied or should be inferred.