Via Zoom: A Koopman Framework for Sampling in Stochastic Differential Equations

Wednesday, April 8, 2020 - 4:00pm to 4:30pm

Event Calendar Category

LIDS & Stats Tea

Speaker Name

Benjamin Zhang

Affiliation

Center for Computational Science & Engineering and AeroAstro

Abstract

We propose a general framework to construct efficient sampling methods for stochastic differential equations (SDEs) using eigenfunctions of the system’s Koopman operator. Importance sampling for SDEs is typically done by adding a control term in the drift so that the resulting estimator has a lower variance. The optimal choice for the control term is given by the Doob transform, in which the resulting estimator has zero variance. The Koopman operator is a tool from the dynamical systems community that has recently gained much interest in data-driven analysis of dynamical systems. We show how eigenfunctions of an SDE’s Koopman operator can be used to construct approximations of the Doob transform. 

Biography

Ben Zhang is a Ph.D. candidate in computational science and engineering advised by Professor Youssef Marzouk. His research interests lie at the intersection of computational statistics and computational dynamics. He focuses on developing novel sampling methods for dynamical systems. He received his Master’s degree in Aeronautics & Astronautics from MIT in 2017 and Bachelor’s degrees in engineering physics and applied math from UC Berkeley.

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Meeting ID: 778 532 804

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