Speaker: Wei Cai, Southern Methodist University

Time: 10:30-11:30 a.m., June 6, 2023, GMT+8

Venue: Room 1114, Sciences Building No.1

Abstract:

In this talk, we will present recent results on new types of deep neural networks (DNNs) in the following areas: (a) to overcome the spectral bias of DNNs in learning PDE solutions of wide frequency range , a multi-scale DNN method is proposed and used for solving  highly oscillatory Navier-Stokes flows in complex domains, and mathematical analysis will also be given explaining the improved performance of the multi-scale DNN; (b) a causality DNN learning algorithm for operators in highly oscillatory function spaces encountered in  seismic wave responses and other evolution PDEs systems with causalities; (c) a DNN based on forward and backward stochastic differential equations (FBSDEs) for high dimensional PDEs such as Fokker-Planck equations arising from statistical descriptions of biochemical systems.

Biography:

Prof. Wei Cai is the Clements Chair Professor at the Department of Mathematics at Southern Methodist University,  and he obtained his B.S. and M.S. in Mathematics from the University of Science and Technology of China (USTC) in 1982 and 1985, respectively, and his Ph.D. in Applied Mathematics at Brown University in 1989. Before he joins SMU in the fall of 2017, he was an assistant and then associate professor at the University of California at Santa Barbara during 1995-96, and a full Professor at the University of North Carolina after 1999.  He has also conducted collaborative research in USTC, Peking University, Fudan University, and Shanghai Jiao tong University.  His research interest focuses on the development of deterministic and stochastic and machine learning numerical methods for studying electromagnetic, fluid,  and quantum phenomena with applications in CFD,  meta-materials, nano-photonics, nano-electronics, biological systems, and quantum systems.  He has published over 130 refereed research articles and is the author of the book "Computational Methods for Electromagnetic Phenomena: electrostatics in solvation,  scattering, and electron transport" published by Cambridge University Press, 2013.  He was awarded the Feng Kang prize in scientific computing in 2005.

Source: School of Mathematical Sciences