8 citations · 25 across the 13 of their papers we have counts for
4 papers · 1 filter
Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems
Patrick Dondl, Johannes Müller, Marius Zeinhofer
We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the -Laplace equation or…
Notes on Exact Boundary Values in Residual Minimisation
Johannes Müller, Marius Zeinhofer
We analyse the difference in convergence mode using exact versus penalised boundary values for the residual minimisation of PDEs with neural network type ansatz functions, as is co…
Error Estimates for the Deep Ritz Method with Boundary Penalty
Johannes Müller, Marius Zeinhofer
We estimate the error of the Deep Ritz Method for linear elliptic equations. For Dirichlet boundary conditions, we estimate the error when the boundary values are imposed through t…
Deep Ritz revisited
Johannes Müller, Marius Zeinhofer
Recently, progress has been made in the application of neural networks to the numerical analysis of partial differential equations (PDEs). In the latter the variational formulation…