Uniform convergence guarantees for the deep Ritz method for nonlinear problems.
Patrick W DondlJohannes MüllerMarius ZeinhoferPublished in: Advances in continuous and discrete models (2022)
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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