no code implementations • 24 May 2024 • Felix Dangel, Johannes Müller, Marius Zeinhofer
Physics-informed neural networks (PINNs) are infamous for being hard to train.
1 code implementation • 25 Feb 2023 • Johannes Müller, Marius Zeinhofer
We propose energy natural gradient descent, a natural gradient method with respect to a Hessian-induced Riemannian metric as an optimization algorithm for physics-informed neural networks (PINNs) and the deep Ritz method.
no code implementations • 5 Jul 2022 • Alex Kaltenbach, Marius Zeinhofer
We establish error estimates for the approximation of parametric $p$-Dirichlet problems deploying the Deep Ritz Method.
no code implementations • 14 Oct 2021 • Patrick Dondl, Marius Zeinhofer
We propose a simple model for scaffold aided bone regeneration.
no code implementations • 1 Mar 2021 • Johannes Müller, Marius Zeinhofer
Our results apply to arbitrary sets of ansatz functions and estimate the error in dependence of the optimization accuracy, the approximation capabilities of the ansatz class and -- in the case of Dirichlet boundary values -- the penalization strength $\lambda$.
no code implementations • ICLR Workshop DeepDiffEq 2019 • Johannes Müller, Marius Zeinhofer
In this notes we use the notion of $\Gamma$-convergence to show that ReLU networks of growing architecture that are trained with respect to suitably regularised Dirichlet energies converge to the true solution of the Poisson problem.