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Hayden Schaeffer, POB 6.304: Learning Governing Equations from Data Using Sparse Optimization and Neural Networks
Thursday, February 13, 2020, 03:30pm - 04:30pm
Given data sampled from some unknown dynamic process, there is significant interest in learning the underlying high-dimensional system that generates the data, with the goal to extract information from the governing system and make meaningful predictions. In this talk I will present various data-driven methods for learning nonlinear dynamical systems with theoretical guarantees. The main techniques will involve sparse optimization or deep neural networks. The sparse optimization problem is written as a linear parameter estimation over a nonlinear dictionary of candidate functions. We provide guarantees on the recovery rate, probability of success, and stability. The neural network approach utilizes the `spirit' of sparse optimization, but takes the form of an optimal control problem for some unknown differential equation. Extensions and applications will be discussed. Bio: Dr. Hayden Schaeffer is an Associate Professor in the Department of Mathematical Sciences and is affiliated with the Center of Nonlinear Analysis at Carnegie Mellon University. He holds a Ph.D. and Master's in Mathematics from UCLA and a B.A. from Cornell. He has received an NSF CAREER award and an AFOSR Young Investigator Award. Previously, he was an NSF Mathematical Sciences Postdoctoral Research Fellow, a von Karman Instructor at Caltech, a UC President's Postdoctoral Fellow at UC Irvine, and a Collegium of University Teaching Fellow at UCLA.
Location: POB 6.304

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