Error Estimation for Physics-Informed Neural Networks Approximating Semilinear Wave Equations
MCML Authors
Gitta Kutyniok
Prof. Dr.
Principal Investigator
Abstract
Gitta Kutyniok
Prof. Dr.
Principal Investigator
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 H1([0,T];L2(Ω))-norm in terms of the training error and the number of training points, which can be made arbitrarily small under some assumptions. We illustrate our theoretical bounds with numerical experiments.
misc
Preprint
Mar. 2024Authors
B. Lorenz • A. Bacho • G. KutyniokLinks
Research Area
BibTeXKey: LBK24a