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
Descripción
Sumario: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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