Work

Error Estimates of Residual Minimization Using Neural Networks for Linear Pdes

Year: 2023

Type: article

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 physicsinformed neural networks based on strong and variational formulations.

Source: Journal of Machine Learning for Modeling and Computing

DOI: 10.1615/jmachlearnmodelcomput.2023050411

Authors: Yeonjong Shin, Zhongqiang Zhang, George Em Karniadakis

Institutions: North Carolina State University, Worcester Polytechnic Institute, Brown University

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: bronze