General exam

event Tuesday, October 21, 2025
access_time 1:30pm (CDT)
room PHSC 809
info Ying will be the host.

Abstract: It has been shown that neural networks can be used to approximate any function from $\mathbb{R}^n$ to $\mathbb{R}^m$ with compact support arbitrary well. This motivates the usage of neural networks to approximate the solution to a PDE. Such ideas were introduced in the late 1990's but only today's modern computational ability allows for this approach to be a viable option. In this presentation, I will show how traditional numerical methods can be limited by stepsize and reliance on mesh creation; then I'll introduce physics-informed neural networks (PINNs): a deep-learning framework for solving PDEs. The idea is to utilize the physical properties of a PDE to train a neural network that can approximate the solution to the equation. To this end, I will show the implementation of this scheme for both forward and inverse problems, compute the solutions to test examples, and point out the limitations and recent developments regarding this framework.


For more information on this event, please contact Weinan Wang.