Wednesday, April 8, 2020 - 4:00pm to 4:30pm
Event Calendar Category
LIDS & Stats Tea
Center for Computational Science & Engineering and AeroAstro
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.
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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