报告题目 (Title)：Two novel deep neural networks methods for high dimensional partial differential equations

报告人 (Speaker)： 邹青松教授（中山大学）

报告时间 (Time)：2022年12月8日(周四) 15:30

报告地点 (Place)：腾讯会议（会议号：206-148-943)

邀请人(Inviter)：刘东杰

主办部门：理学院数学系

报告摘要：

In this talk, we report two novel deep NN methods for high dimensional PDEs. Our first method is the so-called deep temporal difference methods(DTD). With this method, we first transform the deterministic parabolic PDE to a system of forward backward stochastic differential equation. Then by regarding this FBSDE as a Markov rewarding process, we use the Temporal Difference method in the reinforcement learning to train a neural network. Comparing to the deep stochastic method such as deep BSDE in the literature, our method can improve the accuracy and computational speed. Our second method is the so-called deep finite volume method (DFVM). By this method, the loss function is designed according to local conservation laws. Comparing to the well-known PINN, our method involves no calculation of the second order derivative of a function and thus converges faster. Moreover, it could be used to solve some singular problems that the PINN could not well solve. The advantages of our methods are also justified by some numerical examples.