2 citations · 2 across the 4 of their papers we have counts for
4 papers
Exponential Convergence of -ILGFEM for semilinear elliptic boundary value problems with monomial reaction
Yanchen He, Paul Houston, Christoph Schwab +1
We study the fully explicit numerical approximation of a semilinear elliptic boundary value model problem, which features a monomial reaction and analytic forcing, in a bounded pol…
Neural Networks for Singular Perturbations
Joost A. A. Opschoor, Christoph Schwab, Christos Xenophontos
We prove deep neural network (DNN for short) expressivity rate bounds for solution sets of a model class of singularly perturbed, elliptic two-point boundary value problems, in Sob…
Weighted analytic regularity for the integral fractional Laplacian in polyhedra
Markus Faustmann, Carlo Marcati, Jens Markus Melenk +1
On polytopal domains in , we prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian with analytic right-hand s…
Deep Operator Network Approximation Rates for Lipschitz Operators
Christoph Schwab, Andreas Stein, Jakob Zech
We establish universality and expression rate bounds for a class of neural Deep Operator Networks (DON) emulating Lipschitz (or Hölder) continuous maps $\mathcal G:\mathcal X\to\ma…