Abstract:
Physics-based simulations play a vital role in many scientific, engineering, and national security domains, including energy infrastructure, atmospheric sciences, and molecular dynamics. They are frequently critical for assessing risk and exploring “what if” scenarios, which require running models many times. Emulators (also known as surrogate models) are models trained to mimic numerical simulations at a much lower computational cost, particularly for parameters or inputs that have not been simulated. In this talk, I will describe new insights and methodologies for two classes of emulators. First, we will examine data-driven emulators, which learn to mimic a black-box simulator or PDE solver using training samples. Existing methods in this space struggle to emulate chaotic systems in which small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, emulators trained to minimize squared error losses, while capable of accurate short-term forecasts, often fail to reproduce statistical or structural properties of the dynamics over longer time horizons and can yield degenerate results. I will describe an alternative framework based on contrastive learning designed to preserve invariant measures of chaotic attractors that characterize the time-invariant statistical properties of the dynamics. Second, we will explore physics-informed neural networks used to solve known differential equations (without using training data) in the context of numerical simulation of a time-evolving Schrödinger equation inspired by generative models. I will describe an approach that adapts to the latent low-dimensional structure of the problem, highlighting how physics-informed neural networks can yield substantial computational speedups. This is joint work with Ruoxi Jiang, Elena Orlova, Aleksei Ustimenko, and Peter Y. Lu.
Bio:
Rebecca Willett is a Professor of Statistics and Computer Science and the Director of AI in the Data Science Institute at the University of Chicago, and she holds a courtesy appointment at the Toyota Technological Institute at Chicago. Her research is focused on machine learning foundations, scientific machine learning, and signal processing. She is the Deputy Director for Research at the NSF-Simons Foundation National Institute for Theory and Mathematics in Biology and a member of the NSF Institute for the Foundations of Data Science Executive Committee. She is the Faculty Director of the Eric and Wendy Schmidt AI in Science Postdoctoral Fellowship and helps direct the Air Force Research Lab University Center of Excellence on Machine Learning. Willett received the inaugural SIAM Activity Group on Data Science Career Prize in 2024, the National Science Foundation CAREER Award in 2007, was a member of the DARPA Computer Science Study Group, received an Air Force Office of Scientific Research Young Investigator Program award in 2010, was named a Fellow of the Society of Industrial and Applied Mathematics in 2021, and was named a Fellow of the IEEE in 2022.
https://willett.psd.uchicago.edu/
