Error estimates of residual minimization using neural networks for linear PDEs

Yeonjong Shin, Zhongqiang Zhang, George Em Karniadakis

Published 2020-10-15Version 1

We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates for both continuous and discrete formulations of residual minimization in strong and weak forms. The formulations cover recently developed physics-informed neural networks based on strong and variational formulations.