Deep Neural Networks and Finite Element Methods


Jihong Wang, Beijing Computational Science Research Center


2019.10.16 12:20-13:50


Room 306, No.5 Science Building


In recent years, although DNN models have achieved great success, why DNNs can work so well is still unclear. In this talk, we review the progress in mathematical analysis of DNNs with finite element method. We focus on the paper “ReLU Deep Neural Networks and Linear Finite Elements” written by Prof. Jinchao Xu’s group. This paper investigated the relationship between DNN with ReLU function as the activation function and continuous piecewise linear (CPWL) functions, especially CPWL functions from the simplicial linear finite element method (FEM). In addition, we review the related works in solving high dimensional PDEs by DNN combined with FEM.