Distinguished Seminar in Computational Science and Engineering

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Distinguished Seminar in Computational Science and Engineering

December 5, 2024, 12-1PM

45-432 in Building 45 and Zoom Webinar

Leveraging nonlinear latent dynamics of high-dimensional systems for data-driven predictions

Benjamin Peherstorfer
Associate Professor
Courant Institute of Mathematical Sciences | New York University

Abstract: 

Many high-dimensional and seemingly intractable problems in science and engineering have well-behaved latent dynamics that offer a path towards their solution. In this talk, I will demonstrate that nonlinear approximations can help leverage latent dynamics that are out of reach of more traditional computational methods. First, I will present Neural Galerkin schemes that overcome the Kolmogorov barrier through nonlinear latent representations and active sampling, enabling rapid predictions of transport-dominated phenomena that are inaccessible to traditional model reduction methods. Second, I will present a variational approach for learning reduced models of systems that feature stochastic and mean-field effects. The approach infers parameter- and time-dependent gradient fields to efficiently generate sample trajectories that approximate the system’s population dynamics over varying physics parameters. Along the way, I will report numerical experiments that showcase how leveraging latent dynamics enables science and engineering applications, from modeling rotating detonation waves that are of interest in space propulsion to predicting Vlasov-Poisson instabilities to forecasting high-dimensional chaotic systems.

Bio:

Benjamin Peherstorfer is Associate Professor at Courant Institute of Mathematical Sciences. Until 2016, he was a Postdoctoral Associate in the Aerospace Computational Design Laboratory (ACDL) at the Massachusetts Institute of Technology (MIT), working with Professor Karen Willcox. He received B.S., M.S., and Ph.D. degrees from the Technical University of Munich (Germany) in 2008, 2010, and 2013, respectively. His Ph.D. thesis was recognized with the Heinz-Schwaertzel prize, which is jointly awarded by three German universities to an outstanding Ph.D. thesis in computer science. Benjamin was selected for a Department of Energy (DoE) Early Career Award in the Applied Mathematics Program in 2018 and for an Air Force Young Investigator Program (YIP) award in Computational Mathematics in 2020. In 2021, Benjamin received a National Science Foundation (NSF) CAREER award in Computational Mathematics. His research focuses on computational methods for data- and compute-intensive science and engineering applications, including scientific machine learning, mathematics of data science, model reduction, and computational statistics.

Leveraging nonlinear latent dynamics of high-dimensional systems for data-driven predictions
Benjamin Peherstorfer
New York University