Solving PDEs by Variational Physics-Informed Neural Networks: an a posteriori error analysis
Numerical Analysis
2022-10-19 v1 Numerical Analysis
Abstract
We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linear functions on a triangulation of the domain. We define an a posteriori error estimator, made of a residual-type term, a loss-function term, and data oscillation terms. We prove that the estimator is both reliable and efficient in controlling the energy norm of the error between the exact and VPINN solutions. Numerical results are in excellent agreement with the theoretical predictions.
Cite
@article{arxiv.2205.00786,
title = {Solving PDEs by Variational Physics-Informed Neural Networks: an a posteriori error analysis},
author = {Stefano Berrone and Claudio Canuto and Moreno Pintore},
journal= {arXiv preprint arXiv:2205.00786},
year = {2022}
}
Comments
14 pages, 3 figures