3:30 pm Thursday, February 13, 2020
Oden Seminar: Learning Governing Equations from Data Using Sparse Optimization and Neural Networks by Hayden Schaeffer (Carnegie Mellon) in POB 6.304
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. Submitted by
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