Widely Applied Mathematics Seminars

Leveraging Nonlinear Latent Dynamics for Data-driven Predictions

Benjamin Peherstorfer, Associate Professor, New York University

Thursday, Feb 15, 2024

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 argue that modern machine learning can help leverage latent dynamics that are out of reach with more traditional computational methods. In the first part, I will introduce Neural Galerkin schemes that overcome the so-called Kolmogorov barrier to rapidly predict latent dynamics of transport-dominated phenomena, which are inaccessible to traditional model reduction methods. The key feature of Neural Galerkin schemes are nonlinear latent representations from machine learning combined with active sampling for efficient training over even high-dimensional spatial domains. In the second part, I will focus on solving downstream tasks such as control, uncertainty quantification, and optimal design and show that latent dynamics that are informed by downstream tasks can be learned efficiently from few data points, even when learning models of the underlying physics phenomena from data is infeasible. Along the way, I will report on collaborations with domain scientists and engineers that showcase how leveraging latent dynamics enables real-world applications, from predicting instabilities in liquid-fueled rocket engines to optimal design under uncertainty of stellarator coils for magnetic fusion energy devices.

Location: Maxwell Dworkin G125 and Zoom

Speaker Bio

Benjamin Peherstorfer is Associate Professor at Courant Institute of Mathematical Sciences. His research is broadly in computational mathematics, with a focus on the intersection of machine learning, numerical analysis, and approximation theory. 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 his Ph.D. degree from the Technical University of Munich (Germany) in 2013. 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.


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