Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems
Numerical Analysis
2021-11-11 v1 Numerical Analysis
Abstract
We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the -Laplace equation or the Modica-Mortola energy with essential or natural boundary conditions. Under additional assumptions, we show that the convergence is uniform across % bounded families of right-hand sides.
Keywords
Cite
@article{arxiv.2111.05637,
title = {Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems},
author = {Patrick Dondl and Johannes Müller and Marius Zeinhofer},
journal= {arXiv preprint arXiv:2111.05637},
year = {2021}
}
Comments
13 pages, 2 figures. arXiv admin note: text overlap with arXiv:2103.01007