报告题目：Deep Neural Network Algorithms for Oscillatory Flows, Causality Operators, and High Dimensional Fokker-Planck Equations

报告时间：2023-05-30 15:30-16:30

报告人：Prof.Wei Cai  Southern Methodist University

报告地点：理学院东北楼三楼会议室

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.