Neural network and finite element functions

School of Mathematics Colloquium
Thursday, March 18, 2021 - 11:00am for 1 hour (actually 50 minutes)
Jinchao Xu – Pennsylvania State University – xu@math.psu.edu
Anton Bernshteyn

Piecewise polynomials with certain global smoothness can be given by traditional finite element methods and also by neural networks with some power of ReLU as activation function. In this talk, I will present some recent results on the connections between finite element and neural network functions and comparative studies of their approximation properties and applications to numerical solution of partial differential equations of high order and/or in high dimensions.