Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems

2021/11/10 by Dondl, Patrick, Müller, Johannes, Zeinhofer, Marius · 1 citation
#65M12 #65N30 #68T07 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2111.05637

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.

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• Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method

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