Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations

arXiv:2402.07153v3 Announce Type: replace-cross Abstract: This paper provides rigorous error bounds for physics-informed neural networks approximating the semilinear wave equation. We provide bounds for the generalization and training error in terms of the width of the network's layers and the number of training points for a tanh neural network with two hidden layers. Our main result is a bound of the total error in the $H^1([0,T];L^2(\Omega))$-norm in terms of the training error and the number