Error estimates of residual minimization using neural networks for linear PDEs
Numerical Analysis
2023-10-04 v3 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2010.08019,
title = {Error estimates of residual minimization using neural networks for linear PDEs},
author = {Yeonjong Shin and Zhongqiang Zhang and George Em Karniadakis},
journal= {arXiv preprint arXiv:2010.08019},
year = {2023}
}