Zu Chongzhi Center Mathematics Research Seminar
Date and Time (China standard time): Wednesday, April 12, 2:00-3:00 pm
Location: IB 2026
Title: Bayesian inversion for a class of tumor growth models
Speaker: Yu Feng
Bio: Yu Feng obtained his PhD from the University of Wisconsin, Madison. He is currently a postdoc at the Beijing International Center for Mathematical Research (BICMR) at Peking University. His research interests are theoretical applied math and mathematical physics, which include mixing and dissipation enhancement in fluid dynamics, PDEs in mathematical biology (Tumor growth and Neurosciences), inverse problem and narrow exit problem.
Abstract: In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. This family of problems is indexed by a physical parameter $m$, which characterizes the constitutive relation between density and pressure, and these models converge to a Hele-Shaw type problem as $m$ tends to infinity.
For each model (fix a $m$), we provide well-posedness and stability theories for its Bayesian inversion problem and employ an MCMC method to obtain the posterior distribution in practice. It is worth mentioning that these theoretical and numerical methods work uniformly well for the whole family of models. We arrived at such a conclusion; the theoretical part is benefit from some uniform estimate of $m$, while the numerical part is rely on the asymptotically preserving (AP) property of our forward problem solver.
