Uniform convergence guarantees for the deep Ritz method for nonlinear problems

We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover nonlinear 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 con...

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Detalles Bibliográficos
Autores principales: Dondl, Patrick, Müller, Johannes, Zeinhofer, Marius
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9287260/
https://www.ncbi.nlm.nih.gov/pubmed/35855462
http://dx.doi.org/10.1186/s13662-022-03722-8
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author Dondl, Patrick
Müller, Johannes
Zeinhofer, Marius
author_facet Dondl, Patrick
Müller, Johannes
Zeinhofer, Marius
author_sort Dondl, Patrick
collection PubMed
description We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover nonlinear 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.
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spelling pubmed-92872602022-07-17 Uniform convergence guarantees for the deep Ritz method for nonlinear problems Dondl, Patrick Müller, Johannes Zeinhofer, Marius Adv Contin Discret Model Research We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover nonlinear 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. Springer International Publishing 2022-07-15 2022 /pmc/articles/PMC9287260/ /pubmed/35855462 http://dx.doi.org/10.1186/s13662-022-03722-8 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Research
Dondl, Patrick
Müller, Johannes
Zeinhofer, Marius
Uniform convergence guarantees for the deep Ritz method for nonlinear problems
title Uniform convergence guarantees for the deep Ritz method for nonlinear problems
title_full Uniform convergence guarantees for the deep Ritz method for nonlinear problems
title_fullStr Uniform convergence guarantees for the deep Ritz method for nonlinear problems
title_full_unstemmed Uniform convergence guarantees for the deep Ritz method for nonlinear problems
title_short Uniform convergence guarantees for the deep Ritz method for nonlinear problems
title_sort uniform convergence guarantees for the deep ritz method for nonlinear problems
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9287260/
https://www.ncbi.nlm.nih.gov/pubmed/35855462
http://dx.doi.org/10.1186/s13662-022-03722-8
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