Available Projects

Project Description:

Attributed graphs, having side information from nodes and edges, are widely used in many fields within the DOE applications, such as neuroscience, biological discovery, power grid, and distributed computing facilities. Learning the similarities of graphs, also known as graph matching, is one of the fundamental problems in machine learning tasks with structured data. Even though the graph-matching problem has been studied in the last decades, the research on learning the similarities between attributed graphs still remains open. Moreover, methods inspired by optimal transport, such as Gromov-Hausdorff and (Fused) Gromov-Wasserstein distances, have shown promising results to compare not only on structures but also in attributed graphs.

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

Disciplines: Applied Mathematics, Combinatorics, Geometry, and Topology

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL or Virtual

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA

Project Description:

Disciplines: Analysis, and Applied Mathematics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL

Project Description:

Disciplines: Analysis, and Applied Mathematics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL

U.S. Citizenship is a requirement for this internship

Project Description:

Student will utilize spectrogram images/digital data to identify patterns that indicate the passage of watercraft.  An extensive suite of vessel wake data is available to develop robust training algorithms as well as sample data to verify and develop a vessel wake detection algorithm.  Student should possess working knowledge of ML concepts and be able to work independently in MATLAB and/or Python environment.  Experience with data analysis, including digital filtering, wavelet analysis and higher level ML tools/applications is highly desirable. Work will mostly be in an office setting but some possibility for field work during vessel wake collections for interested students.

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

Hosting Site:

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

Internship location: Vicksburg, MS

Project Description:

In this project, novel deep learning algorithms will be constructed to learn solutions to the Fokker-Planck equations for stochastic dynamical systems. The key challenges to overcome include the possibility of non-locality, i.e., when such systems are driven by Levy noise; high-dimensionality, and non-Markovian characteristics. Potential data-driven solutions to such systems include the use of normalizing flows, generative adversarial networks, and neural stochastic differential equations. Some preliminary work in this area has been done by our team (across ANL, IIT-Chicago, Johns Hopkins University) here: https://arxiv.org/pdf/2107.13735.pdf

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL

Project Description:

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

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

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

In this work, we will develop and implement scalable HPO algorithms for GCNNs. We will use the RayTune library for hyperparameter tuning and we will integrate the RayTune functionalities into an existing implementation of GCNNs. The performance of the HPO procedure will be assessed in terms of: (1) scalability attained by distributing the hyperparameter search over hundreds of compute nodes on supercomputers at the Oak Ridge Leadership Computing Facility (OLCF) and (2) validation accuracy of the trained GCNN model on ab-initio density functional theory (DFT) data generated by material scientists at Oak Ridge National Laboratory (ORNL) that describe the functional behavior of solid solution alloys at atomic scale.

The expected outcome is a scalable HPO framework integrated with the existing implementation of the GCNN model that attains linear scaling up to 100 compute nodes on the OLCF supercomputer Summit, with an improved accuracy by a factor of 10x with respect to existing GCNN models trained on the DFT data.

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

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

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

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

This summer experience revolves around algorithm creation and analysis for design problems for which goals are only available through observations of complex systems. Such settings commonly arise in the fields of derivative-free (zeroth-order) optimization. Our objectives include some combination of modeling specific problems, implementing novel algorithms, and analyzing (non)asymptotic performance.

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

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA or Virtual

Project Description:

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

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

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

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

Disciplines: Applied Mathematics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

Our group has developed methods for mapping the evaluation of certain mathematical functions to modern processors, for example by exploiting the associativity of operators to allow dynamic scheduling and accumulation of results. This allows us to compute these functions faster and using less energy.
In this project, you would help us develop the theory and software to perform these computations even faster, more reliably, or on different hardware platforms including GPUs or other accelerators. If successful, this work can improve the building blocks that are used by developers of scientific computing, engineering, and machine learning applications.

Disciplines: Applied Mathematics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

U.S. Citizenship is a requirement for this internship

Project Description:

We'll be assisting with perspectives and interpretations applying differential geometry and competitive linear and non-linear model-based dimension reductions to explore applications ranging from computer vision to materials science and next generation communications technology. Example applications include: statistics of material microstructures, general image classification, and high-dimensional bi-criteria optimization for next generation wireless spectrum sharing. The position requires a candidate curious to explore some or all of the following topics in applied mathematics: (i) novel low-dimensional visualization and approximation methods, (ii) abstractions of computational differential geometry over matrix manifolds, (iii) linear and non-linear model-parameter dimension reduction, and (iv) infinite dimensional extensions of spaces of discrete shapes.

Disciplines: Applied Mathematics, Geometry, Probability and Statistics, and Topology

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Boulder, CO

Project Description:

Wildland fire is a natural process that has become problematic in society because of the expansion of human developments, increased fuel loads due to past fire suppression activities, climate change, and a myriad of other factors. Solutions for this problem require a more advanced understanding of the fundamental physical processes of these fires and how they propagate from the very small scale (fuel particles) to landscapes. Large efforts are currently underway to integrate highly instrumented field experiments, machine learning, artificial intelligence, and computational fluid dynamics models to advance our decision making in the future.

The applicant, with the guidance of several mentors, will have the opportunity to design an experience that focuses on their analytical strengths to help us to disentangle and understand complex relationships of fire spread and behavior. The applicant will examine a set (n=30) of recent fire field experiments with data including multi-temporal 3-D laser scanning (LiDAR), infrared and color video, 3-D wind fields, temperature profiles, and radiative fluxes. The primary objectives of the experience are: 1) Expand the applicant’s understanding of datasets of different spatial and temporal resolutions, 2) develop an approach to decompose and relate these data streams, and 3) to present the techniques and results in a way that is understandable to scientists from other disciplines and land managers.

This internship will be based at the Forestry Sciences Laboratory in Morgantown, WV in collaboration with Scientists from the USDA Forest Service, Rochester Institute of Technology, West Virginia University, and other institutions. The applicant will have the opportunity to collect data (in a learning setting) with the same instruments used in the fire experiments to understand their intricacies and limitations. Depending on Covid restrictions, the applicant may have the opportunity to visit several field sites, interact with other scientists and fire managers, and observe a prescribed burn.

Disciplines: Applied Mathematics, Probability and Statistics, and Topology

Hosting Site:

USDA Forest Service, Northern Research Station

Internship location: Morgantown, WV

U.S. Citizenship is a requirement for this internship

Project Description:

Disciplines: Analysis, and Probability and Statistics

Hosting Site:

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

Internship location: Fairbanks, AK

Project Description:

To enable practically useful quantum computing, this project aims to improve the error rate of logical gates on superconducting quantum devices by augmenting the quantum dynamical model with a data-driven approach to identify and incorporate latent dynamics. Quantum dynamics are often modeled by Schrödinger’s and Liouville-von Neumann’s equations, that evolve the quantum state and density matrix according to a Hamiltonian model. The Universal Differential Equations approach augments this model by a neural network that is trained from device data to account for unknown dynamics, such as drift in system parameters, control line losses, cross talk, and environmental interactions. The trained augmented model will provide a more accurate simulation of the quantum dynamics in superconducting quantum devices, that will then be used within our optimal control software stack to design control strategies that achieve higher fidelity of quantum gates on noisy quantum hardware. The trained neural network will further be analyzed using symbolic regression to provide a mathematical description and understanding of the latent quantum dynamics.

Disciplines: Applied Mathematics

Hosting Site:

Lawrence Livermore National Laboratory (LLNL)

Internship location: Livermore, CA

Project Description:

The goal of this project is to develop tools for image and data analysis, by leveraging scientific computing and machine learning algorithms. Various research opportunities exist in the following topics:
- Image segmentation, region and geometry detection in 2d/3d images,
- Analysis and statistics of geometries and shapes,
- Finite element modeling and meshing of evolving surfaces,
- Shape and topology optimization,
- Image-based meshing,
with applications in material science, biology and forensics. These projects involve knowledge of different mathematical areas, such as variational models, energy minimization, free boundary problems, meshing, mesh adaptivity and smoothing, continuous and discrete optimization, dynamic programming, and machine learning.

Disciplines: Applied Mathematics, Geometry, and Probability and Statistics

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Gaithersburg, MD

Project Description:

Large language models (LLMs) such as ChatGPT and LLaMA have had transformative impact on natural language processing, with significant scientific knowledge processing. Better understanding of LLMs may be necessary for further advances in this high interdisciplinary field. This project will involve learning about the LLMs and their applications, mathematical foundations, and explore further possibilities in applying LLMs for physics and other natural sciences, including processing the scientific knowledge information.

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

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Over the past three centuries, significant attention has been dedicated to the study of how mechanical instabilities such as wrinkling, buckling, and blistering cause patterns to emerge in inanimate materials. Can these principles be applied to the analysis of living systems? From the fractal-like edges of a kale leaf to the undulating crinkles of the human brain, many of the striking morphologies emblematic of living entities do not arise exclusively from gene expression programs but rather from the presence of mechanical forces. Elucidating this relationship between applied stresses and geometric forms will help guide scientific innovations ranging from the creation of bioinspired materials to the establishment of metrological standards. Students will gain experience with topics in applied and computational mathematics, particularly the calculus of variations, differential geometry, and nonlinear partial differential equations.

Disciplines: Applied Mathematics, and Computational Mathematics, Mathematical Biology Analysis

Hosting Site:

National Institute of Standards and Technology (NIST)

Internship location: Gaithersburg, MD or virtual

Project Description:

The purpose of this project is to study large language models (LLMs) that are founded on explicit probabilistic models, rather than on transformer-type architectures. The objective is to obtain predictive models for discrete sequence data such as natural language, DNA sequences, chemical formulae, etc. that are transparent in their operation and amenable to furnishing characterizations of predictive uncertainty.

The MSGI Intern will participate in theoretical development and exploration of models, and in exploration of corpuses of sequential data to determine model structures appropriate to each type of data. As this is a computational statistics project, the intern should expect to write code implementations of models, and also to code data exploration methods.  Equally important is the expectation that the intern will prepare a report that should function as an outline or first draft of a paper on the methods developed in the project.

The intern will learn techniques for probabilistic modeling of discrete sequences, and for characterizing the statistical behavior of this type of data. A model in current development uses Gaussian process (GP)-type methods, so the intern should expect to learn the theory and practice of GPs. Model training is likely to require use of Argonne's high-performance computing (HPC) facilities, and the intern should also expect to learn to utilize such facilities.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL

Project Description:

Expensive-to-evaluate stochastic oracles appear throughout the quantum information sciences research field. Unfortunately, optimizing such oracles is considerably more difficult than optimizing deterministic oracles. This is because of the varying output observed for repeated calls to the oracle, even with a fixed set of input variables. This project seeks to develop, analyze, and implement numerical methods for optimizing oracles that are stochastic in nature and that are relatively expensive to evaluate. Application problems include stochastic oracles that appear across the quantum information sciences. We are especially interested in using (polynomial and Bayesian) model-based methods to identify high-quality local optima for such problems.  

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

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL

Project Description:

In this project, the student will learn to work on generalizable deep causality representation learning for scientific data. Causality Learning is a challenging task for many scientific domains due to the high dimension and availability of limited ground truth. Learning causality structure between multiple variables from low-fidelity simulations can aid in modeling and understanding high-fidelity data. This project will provide an opportunity to explore the state-of-the-art deep learning-based causality techniques, especially transformers and graph neural networks on large-scale, high-dimensional scientific data, e.g., neuroscience, climate, etc.

Disciplines: Analysis, and Applied Mathematics

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

Dataset imbalance refers to the issue when certain classes are represented by significantly more number of data points relative to others. It is a prevalent issue in machine learning especially classification problems in many scientific applications. This issue materializes itself when the final performance of a model is biased towards the class with a larger number of sample points. One way to correct this bias is to equalize the imbalance and intelligent sampling strategies play a critical role in this procedure. However, due to a lack of efficient approaches, a common way to address the issue involves trial and error driven uniform oversampling of the underrepresented class or undersampling of the over-represented class.

In this project, we will formulate the problem of imbalance in a data batch as an optimization problem and derive conditions which must be satisfied for sampling a balanced data batch. We then integrate the condition into the neural network learning problem. We will develop a game theoretic approach to resolve the tradeoff between the performance of the neural network and the variance in the data.

Disciplines: Applied Mathematics

Hosting Site:

Argonne National Laboratory

Internship location: Lemont, IL

Project Description:

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

Hosting Site:

USDA Forest Service, Southern Research Station

Project Description:

Adversarial robustness is a pressing concern in multimodal frameworks, especially in large language models (LLMs) that solve a spectrum of problems like text-to-image, image-to-text, and text-to-text translations. Multimodel LLM such as ChatGPT, despite their powerful capabilities, are vulnerable to adversarial attacks. These attacks subtly manipulate input modalities, compromising model responses, and can even be insidiously embedded within training datasets, affecting model embeddings and overall performance. Building upon our previous work, where we utilized the AdversarialTensors framework to effectively mitigate adversarial noises in an unsupervised manner for standard CNNs, we aim to extend this ability to enhance the robustness of multimodal frameworks. Our goal is to purify input modalities from adversarial contaminations before they are processed by LLMs and to fortify model robustness by integrating tensorial defense strategies alongside LORA—a widely adopted, low-complexity fine-tuning model. Moreover, by integrating knowledge graphs, we can harness the structured and interlinked knowledge between input and corresponding embeddings to identify and counteract inconsistencies or adversarial perturbations, thereby enhancing the model's ability to reason and improve its resilience against malicious attacks.

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

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM or virtual

Project Description:

This project aims to develop spatial mechanistic models of respiratory virus infection (such as SARS-CoV-2, influenza) and the immune responses to understand how stochasticity and immune regulation impact on viral infection and pathogenesis. Respiratory viruses (such as SARS-CoV-2 and influenza) cause a high mortality and morbidity every year. Their infections usually result in a wide range of clinical outcomes, from asymptomatic to lethal. There is an urgent need to quantitatively define the specific factors that govern infection outcomes to develop better therapeutic and intervention strategies. Therefore, the work will be critical for rational design of vaccines to prepare for the current or next pandemic caused by respiratory viruses.

Disciplines: Computational Mathematics, and Mathematical Biology

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Matrix-free high-order finite element method (MF-FEM) is a cutting-edge method to perform fast, robust, and accurate simulations of advection-diffusion partial differential equations (PDEs) that are ubiquitous in computational physics. However, currently the application of MF-FEM is limited to algorithms that are explicit in time. The presence of diffusion or stiff source terms calls for implicit or implicit-explicit timestepping methods, which negatively impacts the efficiency of MF-FEM. To overcome this performance issue, we propose to couple fast multigrid (MG) methods for the discrete diffusion operators with MF-FEM for advection operators.

Geometric multigrid (GMG) methods are one of the fastest classes of linear and nonlinear solvers for implicit equations arising in numerical methods for PDEs. GMG methods typically rely on a hierarchy of nested structured meshes, and the physical equations are solved on ""coarse"" meshes to provide corrections to the solution on the original ""fine"" mesh. For unstructured meshes that are moving or adapting in time, it is not obvious how to construct a mesh hierarchy, and algebraic multigrid (AMG) methods provide a less intrusive multigrid option that are often used instead. However, AMG methods require assembling a full matrix for the discretization, and, although efficient, do not compete with GMG in terms of computational efficiency, particularly on GPUs. Some previous work has considered semi-geometric MG (sGMG) methods, where an initial simplicial (triangular) mesh is coarsened to construct a nested grid hierarchy on which to apply GMG. We are, however, interested in coupling implicit solvers to Arbitrary Lagrangian-Eulerian simulations of hydrodynamics, where quadrilateral and hexahedral (non-simplicial) meshes offer significantly higher physics fidelity.

The goals of the proposed project are: (1) the development of novel sGMG solvers for the advection-diffusion PDEs on quadrilateral and hexahedral meshes and (2) efficient implementation in LANL’s open source GPU-based code Fierro (https://lanl.github.io/Fierro).

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

Many complex systems are usually represented by networks (e.g., communication networks, power grids, social networks, etc.). Communities or clusters are key to understand the structure and function of these complex systems because communities represent important functional modules in networked systems. Therefore, there is an increasing interest in understanding the limits of the robustness of the community structure. This is because maintaining the functionality of networked systems is heavily dependent on preserving their community structure.

Given ORNL's expertise on modeling and simulation of complex systems using leadership computing facilities, this project will take advance of modern data science, machine learning, and network science techniques, or any technique of interest to the participant that could help on better understand the limits of the robustness of the community structure in interconnected systems. We are highly interested in exploring data clustering techniques that use graph embeddings for clustering both synthetic and empirical real-world networks. We will seek to understand the limitations of current graph embedding methods for clustering tasks and propose ways to alleviate these limitations.

This project will allow the participant to actively drive an exciting facet of an ongoing research project at ORNL, and have their contributions directly integrated into the Computer Science and Mathematics Division research priorities. A successful student has prior experience with data science techniques, machine learning, and network science, but is not expected to have deep experience with programming.

Notably, prior projects at ORNL by interns in this team have led to published papers at top interdisciplinary/applied math journals. Examples include:

• PLOS ONE: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0284077
• IEEE IoTJ: https://ieeexplore.ieee.org/abstract/document/10213280
• PRE: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.054302

Based on the findings here, we will also seek to publish a paper in a major data science/applied math venue with the participant as the lead author.

Feel free to reach out if questions.

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

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN or virtual

Project Description:

The promise of ubiquitous connectivity brought by emerging technologies (i.e., 5G/6G) will enable interconnected systems (e.g., Internet of things (IoT), smart cities, science facilities, among others) to work faster and more efficiently. However, ubiquitous connectivity comes at the expense of augmenting the attack surface and the risk of suffering from advanced cyber attacks. Detection and adaptation to such threats requires collecting, filtering, and analyzing event data of heterogeneous scale, speed, and modality. The design and deployment of trustworthy methods and algorithms that can accommodate volume, velocity, and variety is key for near real-time detection, continuous adaptation, and quick attack recovery is challenging and requires innovation. Thus, to address the emerging challenges of next generation of cyber threats, the goal of this project is to design and implement a suite of algorithms that allow near real-time detection of adaptive cyber attacks in interconnected systems.

Given ORNL's expertise in acquisition and processing of data for enterprise and cyber physical domains using leadership computing facilities along with leading researchers in applied mathematics, computer science, statistics, and cybersecurity, this project will take advance of modern data science, machine learning, or any technique of interest to the participant (including but not limited to multivariate time series analysis, clustering, graph mining, etc.) that could help to design and implement algorithms that will enable quick detection, adaptation, and recovery from sophisticated and evolving cyberattacks targeting modern interconnected systems. Learning objectives for the applicant include: (1) develop a basic understanding of novel cyberattacks affecting modern interconnected systems; (2) design and development of data-driven models for detecting advanced cyberattacks; (3) validate the efficacy of developed algorithms using empirical data and compare its performance against state-of-the-art classical approaches.

This project will allow the participant to actively drive an exciting facet of an ongoing research project at ORNL, and have their contributions directly integrated into the Computer Science and Mathematics Division research priorities. A successful participant has prior experience with data science techniques and machine learning but is not expected to have deep experience with programming.

Notably, prior projects at ORNL by interns in this team have led to papers published at top interdisciplinary/applied mathematics journals. Examples include:

• PLOS ONE: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0284077
• IEEE IoTJ: https://ieeexplore.ieee.org/abstract/document/10213280
• PRE: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.054302

Based on the findings here, we will also seek to publish a paper in a major data science/applied math venue with the participant as the lead author.

Feel free to reach out if questions.

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

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN or virtual

Project Description:

Kleene algebra with tests (KAT) is an algebraic technique for mathematical reasoning about the behavior of computer programs. In this project we will explore the semantic foundations of KAT as applied to the task of program verification.

Potential projects include:

• generalizing KAT's theory to discharge realistic program verification conditions;
• developing algorithms for converting between traditional verification input and a KAT representation;
• a prototype implementation of a KAT-based program verifier;
• a mechanization of KAT in a mathematical proof assistant such as Lean, Coq, Agda, etc;
• exploring the connections between first-order satisfiability modulo theories (SMT) logic and KAT logic;
• or others, depending on student interest.

Disciplines: Computational Mathematics, and Foundations

Hosting Site:

Lawrence Livermore National Laboratory (LLNL)

Internship location: Livermore, CA or virtual

Project Description:

Graph Neural Networks (GNNs) have gained significant attention owing to their ability to handle graph-structured data and the improvement in practical applications. However, many of these models prioritize high utility performance, such as accuracy, with a lack of privacy consideration, a significant concern in modern society where privacy attacks are rampant. In this project, we want to focus on privacy-preservation techniques. With guidance from a mentor, the student will help developing new defense mechanisms and design comparison study with the state of the art methods. The student will learn about privacy-preservation algorithms, graph neural networks numerical analysis, and writing/presentation skills.

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

Hosting Site:

Oak Ridge National Laboratory (ORNL)

Internship location: Oak Ridge, TN

Project Description:

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

U.S. Citizenship is a requirement for this internship

Project Description:

The Army maintains stringent requirements for equipment in the Arctic operational environment and expresses concerns of risk to mission failure for sustaining the forces at temperatures down to -65^oF, wind speeds greater than 100 mph, and 25 lb/ft² snow load. However, these conditions may only be encountered on rare occasions, and in certain subregions of the Arctic.

In this new start ESTCP project, we explore refining the Arctic climatic zones characterization relative to these design thresholds. This includes identifying the circumpolar north climate breaks for environmental parameters to narrow the contingency, logistics and resources needed, and develop site-focused requirements for the Services to operate across the region. To accomplish this, we intend to include three climate characteristics (air temperature extremes, snow depth and wind speed limits) to the currently defined climate zones and conduct analysis against materiel and equipment exposure thresholds. This will provide mission critical data and information for operations managers to make better risk-informed decisions and to operate equipment, materiel, and force projection in the circumpolar region.

Disciplines: Applied Mathematics, and Probability and Statistics

Hosting Site:

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

Internship location: Hanover, NH or virtual

Project Description:

We are exploring new optimization methodologies to optimize with digital twins. Optimization methodologies are a critical component to make digital twins a reality. They are needed in the optimal design of experiments that integrate data acquisition with simulation, the optimal steering of processes or devices modeled as digital twins, and the connection to neighboring digital twins. In this project, we will explore the use of distributed optimization techniques to control a swarm of vehicles used to optimally acquire environmental data along different paths. The project combines the solution of PDEs with the design of experiments and optimal control. Our goal is to build a prototype model and computational simulation using python and Fenics.

Disciplines: Computational Mathematics, and Probability and Statistics

Hosting Site:

Argonne National Laboratory (ANL)

Internship location: Lemont, IL, or virtual

Project Description:

Viruses with segmented genomes such as Crimean Congo hemorrhagic fever virus (CCHFV), hantaviruses, and influenza can form chimeric viruses when an individual host becomes co-infected by distinct variants of a given virus. This reassortment of genomic segments is postulated to be an important aspect in the emergence and re-emergences of both old and new infectious diseases. The ultimate goal of this project is to answer a scientific question: can we determine if a virus experienced a genomic reassortment event in the past that increased its fitness by looking at contemporary genomic samples of that virus? The challenge is that there are no robust off-the-shelf methods that can infer the presence of genomic reassortment (see https://doi.org/10.1101/2023.09.20.558687 for our preprint on this issue). Further, while there are interesting candidate methods that might allow for robust maximum likelihood inference of genomic reassortment from phylogenetic trees, it is unlikely that those methods will have reasonable computational efficiency. This project seeks to address that issue by 1) building a mechanistic model to simulate both the transmission dynamics and the viral evolution of a segmented virus in an idealized population, 2) build a Deep Neural Network mapping the simulated phylogenetic trees to the model parameters such as increased contagiousness of the reassorted virus, and 3) infer the presence of relevant genomic reassortment using real genetic sequence data from CCHFV. Participants will gain hands-on experience in epidemiological research, enhance their mathematical modeling, statistical analysis, and machine learning skills, and prepare for future careers in academia, research, or related industries. This opportunity contributes to vital scientific discoveries and equips students with highly sought-after skills in computational biology and public health research.

Disciplines: Applied Mathematics, Computational Mathematics, and Mathematical Biology

Hosting Site:

Los Alamos National Laboratory (LANL)

Internship location: Los Alamos, NM

Project Description:

This project will build models based on observed discrepancies between theory computer simulations and data at the Large Hadron Collider that fill in the physics behind these gaps.

The models will be developed using artificial intelligence (AI) with two distinguishing and novel features:  we will learn (1) corrections to an existing physics model to describe data using reweighting and (2) symbolic relationships between theory features to construct better physics models.  A mature version of the developed tools will, for example, significantly reduce the measurement uncertainties on the top quark mass and possibly aid in the discovery of a new, weakly-interacting particle.

We propose to complete the early stages of this project with following goals:

(1)        Using techniques such as weakly supervised machine learning to automatically identify collider data in the Rivet analysis library that is poorly described by theory predictions and has no obvious physics explanation

(2)        Developing an AI-based regression model to describe the gap between theory and data using the Pythia event generator

(3)        Constructing metamodels, using Simulation-based inference (SBI) for example, to determine correlations between the gap and the latent variables of the generator. These metamodels will be used to supplement the standard generator predictions and provide candidate physical explanations and descriptions of the data.

Disciplines: Applied Mathematics, and Computational Mathematics

Hosting Site:

Fermi National Accelerator Laboratory (FNAL)

Internship location: Batavia, IL or virtual

Project Description:

Monte Carlo-based event generators are essential tools for analyzing and interpreting data from particle collision experiments. Currently, the physical evolution of a particle collision, and hence the computing algorithms used to make predictions, are serial. On the other hand, many of our computations in the future will be done on chips with GPUs. This project aims to explore how the physics algorithms could be restructured to exploit acceleration. As a first case, we would explore the parton shower algorithm.

Disciplines: Computational Mathematics

Hosting Site:

Fermi National Accelerator Laboratory (FNAL)

Internship location: Batavia, IL or virtual

Project Description:

Randomized algorithms, such as sketching, sparsification, and streaming, are powerful dimensionality reduction tools for analyzing large. The applications for DOE include computational linear algebra (such as solvers, preconditioners, and low-rank approximation) and graph analysis (e.g., graph partitioning, clustering, and graph learning). Many impressive advances in the theory of randomized algorithms have not been translated into practical demonstrations. This project aims to bridge this gap between theory and practice, and to produce high-quality software running on modern HPC hardware with demonstrations in application codes.

Disciplines: Computational Mathematics, and Probability and Statistics

Hosting Site:

Lawrence Berkeley National Laboratory (LBNL)

Internship location: Berkeley, CA or Virtual