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

Wei Cai (SMU, Dallas, USA)

Abstract: In this talk, we will present results on new types of deep neural network (DNN) in the following areas: (a) a multi-scale DNN method for solving  highly oscillatory Navier-Stokes flows in complex domains (b) a causality DNN learning algorithm for nonlinear 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 in statistical description of biochemical systems, with application to compute the committor functions and reaction rates in transition path sampling theory of complex chemical and biological systems.