Practicum Experience(s)
Pacific Northwest National Laboratory (2024)
Summary of Research
My research broadly focuses on the numerical approximation of deterministic and stochastic partial differential equations. I'm also interested in using information theory and machine learning for physics-based and data-driven modeling. My masters work focused on addressing outstanding limitations of wall-modeled large-eddy simulation for high-speed compressible turbulence modeling. My current research is related to exploring the connection between unresolved subgrid dynamics and stochastic modeling and also the potential stabilizing effect that stochastic models could have on linearized sensitivity of chaotic systems. My ultimate goal is to employ novel approaches for function approximation.
Annual Program Review Abstracts
Publications
Williams, E., and Darmofal, D., "Stochastic generative methods for stable and accurate closure modeling of chaotic dynamical systems," arXiv 2504.09750, April 2025.
Williams, E., Howard, A., Meuris, B., and Stinis, P., "What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications," arXiv 2411.18459, November 2024.
Williams, E., Arranz, G., and Lozano-Duran, A., "Near-Field Wall-Modeled Large-Eddy Simulation of the NASA X-59 Low-Boom Flight Demonstrator," arXiv 2307.02725, July 2023.
Williams, E. and Lozano-Duran, A., "Information-Theoretic Approach for Subgrid-Scale Modeling for High-Speed Compressible Wall Turbulence," AIAA Aviation Forum, June 2022.
Awards
AIAA New England Community Award (MIT), 2023
Vickie Kerrebrock Award (MIT), 2022
AIAA & Aviation Week 20 Twenties (UIUC), 2021
Scott R. White Aerospace Visionary Scholarship (UIUC), 2020
Dale Margerum Memorial Award (UIUC), 2020
Philip Lazzara Memorial Scholarship (UIUC), 2020