PINNs error estimates for nonlinear equations in $\mathbb{R}$-smooth Banach spaces
Functional Analysis
2024-06-07 v3 Machine Learning
Numerical Analysis
Numerical Analysis
Abstract
In the paper, we describe in operator form classes of PDEs that admit PINN's error estimation. Also, for spaces, we obtain a Bramble-Hilbert type lemma that is a tool for PINN's residuals bounding.
Cite
@article{arxiv.2305.11915,
title = {PINNs error estimates for nonlinear equations in $\mathbb{R}$-smooth Banach spaces},
author = {Jiexing Gao and Yurii Zakharian},
journal= {arXiv preprint arXiv:2305.11915},
year = {2024}
}
Comments
30 pages, 9 figures