Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems
- Authors: Patrick Dondl, Johannes Müller, Marius Zeinhofer
- Preprint year: 2021
- First public date: 2021-11-10
- arXiv: 2111.05637
- Status: Published
- Publication type: Journal article
- Publication year: 2022
- Journal: Advances in Continuous and Discrete Models (2022)
- DOI: 10.1186/s13662-022-03722-8
Abstract
We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the $p$-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.