PINNs and GaLS: A Priori Error Estimates for Shallow Physics Informed Neural Networks Applied to Elliptic Problems
Numerical Analysis
2022-07-26 v4 Numerical Analysis
Abstract
Physics Informed Neural Networks (PINNs) have recently gained popularity for solving partial differential equations, given the fact they escape the curse of dimensionality. In this paper, we present Physics Informed Neural Networks as an underdetermined point matching collocation method then expose the connection between Galerkin Least Square (GALS) and PINNs, to develop an a priori error estimate, in the context of elliptic problems. In particular, techniques that belong to the realm of least square finite elements and Rademacher complexity analysis are used to obtain the error estimate.
Keywords
Cite
@article{arxiv.2202.01059,
title = {PINNs and GaLS: A Priori Error Estimates for Shallow Physics Informed Neural Networks Applied to Elliptic Problems},
author = {Umberto Zerbinati},
journal= {arXiv preprint arXiv:2202.01059},
year = {2022}
}
Comments
This work has been accepted at MathMOD and will appear on IFAC Conference Papers