【Wei Cai】AI, BI & SI—Artificial, Biological and Statistical Intelligences

Feynman-Kac Formula and Numerical Methods and Neural Networks for Solving PDEs

In this talk, we will show how the probalistic solution of elliptic and parabolic PDE's via Feynman-Kac formula can be used to design parallel deterministic nunerical methods for BVPs of PDEs and deep learning methods for solving high dimensional PDEs to tackle the issue of curse of dimensionality.

Prof. Cai’s research interest focuses on developing advanced fast machine learning, stochastic, and deterministic numerical methods to understand complex physical phenomena with a special focus on quantum phenomena, electromagnetic processes, and wave scattering in random media.  He has published over 130 refereed articles in top international journals such as SIAM J. on Numerical Analysis, SIAM J. on Scientific computing, and Journal of Computational Physics, IEEE transactions on MTT,  among others,  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 serves on the editorial boards for Communications in Computational Physics, Journal of Computational Mathematics, and Communications in Mathematics & Statistics. His research has been funded by the National Science foundation, Department of Energy, US Army Research Office, the National Institute of Health, and US Air Force Office of Scientific Research.