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.
