This seminar will take place online, via Zoom. Please contact the APAM Department ahead of time to request the Zoom link.

Speaker: Jack Xin, UC Irvine

Title: DeepParticle: deep-learning invariant measure by minimizing Wasserstein distance on data generated from an interacting particle method 

Abstract: High dimensional partial differential equations (PDE) are challenging to compute by traditional mesh based methods especially when their solutions have large gradients or concentrations at  unknown locations. Mesh free methods are more appealing, however they remain slow and  expensive when a long time and resolved computation is necessary.  

We present DeepParticle, an integrated deep learning (DL), optimal transport (OT), and interacting particle (IP) approach through a case study of Fisher-Kolmogorov-Petrovsky-Piskunov front speeds in incompressible flows. PDE analysis reduces the problem to a computation of principal eigenvalue of an advection-diffusion operator. Stochastic representation via Feynman-Kac formula makes possible a genetic interacting particle algorithm that evolves particle distribution to a large time invariant measure from which the front speed is extracted. The invariant measure is parameterized by a physical parameter (the Peclet number). We learn this family of invariant measures by training a physically parameterized deep neural network on affordable data from IP computation at moderate Peclet numbers, then predict at a larger Peclet number when IP computation is expensive. The network is trained by minimizing a discrete Wasserstein distance from OT theory. The DL prediction serves as a warm start to accelerate IP computation especially for a 3-dimensional time dependent Kolmogorov flow with chaotic streamlines. Our methodology extends to a more general context of deep-learning  stochastic particle dynamics. This is joint work with Zhongjian Wang (University of Chicago) and Zhiwen Zhang (University of Hong Kong).

Biography: Jack Xin is the Chancellor's Professor of Mathematics at UC Irvine. He received his Ph.D in applied mathematics from the Courant Institute at New York University in 1990. He was a postdoctoral fellow at Berkeley and Princeton in 1991 and 1992. He was an assistant and associate  professor of mathematics at the University of Arizona (1991-1999). He was a professor of mathematics at the University of Texas at Austin (1999-2005). His research interests include applied analysis, computational methods and their applications in multi-scale problems and data science. He has authored over one hundred eighty journal/conference papers, and two Springer books. He is a fellow of the Guggenheim Foundation, the American Mathematical Society, the American Association for the Advancement of Science, and the Society for Industrial and Applied Mathematics. He is a recipient of Qualcomm Faculty Award (2019-2021).