Computing Entropy Production Rates and Chemotaxis Dynamics in High Dimensions by Stochastic Interacting Particle Methods
Jack Xin, UC Irvine

Abstract: We study stochastic interacting particle methods with and without field coupling for high dimensional  concentration and singularity formation phenomena. In the first case study of entropy production of  reverse-time diffusion processes (a problem dated back to Kolmogorov 1937), the method computes  concentrated invariant measures mesh-free up to  dimension 16 at a linear complexity rate based on solving a principal eigenvalue problem of  a non-self-adjoint advection-diffusion operator.   In the second case study of fully parabolic chemotaxis nonlinear dynamics in 3 space dimensions,  our method captures critical mass for finite time singularity formation and blowup time at low costs  through a smoother field without relying on self-similarity. The method generalizes to a  haptotaxis advection-diffusion system modeling cancer cell invasion.

Bio: Jack Xin received Ph.D. degree in mathematics from New York University’s Courant  Institute of Mathematical Sciences in 1990. He was a faculty member at the University of Arizona,  from 1991 to 1999, and the University of Texas at Austin, from 1999 to 2005.  He is currently a Chancellor’s Professor of Mathematics at UC Irvine.  His research interests include applied analysis and computational methods, and their applications  in multi-scale problems and data science. He is a fellow of Guggenheim Foundation,  American Mathematical Society, American Association for the Advancement of Science,  the Society for Industrial and Applied Mathematics (SIAM) and  Asia-Pacific Artificial Intelligence Association. He was editor-in-chief (2014-2019) of  Multiscale Modeling and Simulation, a SIAM Interdisciplinary Journal. He was a recipient of Qualcomm Faculty and Gift Awards.