Convergence Analysis of PINNs with Over-Parameterization

Abstract

Recently, physics-informed neural networks (PINNs) have been shown to be a simple and efficient method for solving PDEs empirically. However, the numerical analysis of PINNs is still incomplete, especially why over-parameterized PINNs work remains unknown. This paper presents the first convergence analysis of the over-parameterized PINNs for the Laplace equations with Dirichlet boundary conditions. We demonstrate that the convergence rate can be controlled by the weight norm, regardless of the number of parameters in the network.