ERROR ESTIMATES OF RESIDUAL MINIMIZATION USING NEURAL NETWORKS FOR LINEAR PDES
Yeonjong Shin, Zhongqiang Zhang, George Em Karniadakis
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.
Topics & Concepts
ResidualMinificationArtificial neural networkCover (algebra)Convergence (economics)MathematicsApplied mathematicsNorm (philosophy)Compact spaceMathematical optimizationMinimisation (clinical trials)Computer scienceAlgorithmArtificial intelligenceMathematical analysisStatisticsEngineeringEconomic growthLawEconomicsMechanical engineeringPolitical scienceModel Reduction and Neural NetworksAdvanced Numerical Methods in Computational MathematicsAdvanced Numerical Analysis Techniques