20 citations · 40 across the 5 of their papers we have counts for
5 papers
First Order System Least Squares Neural Networks
Joost A. A. Opschoor, Philipp C. Petersen, Christoph Schwab
We introduce a conceptual framework for numerically solving linear elliptic, parabolic, and hyperbolic PDEs on bounded, polytopal domains in euclidean spaces by deep neural network…
Exponential Expressivity of ReLU Neural Networks on Gevrey Classes with Point Singularities
Joost A. A. Opschoor, Christoph Schwab
We analyze deep Neural Network emulation rates of smooth functions with point singularities in bounded, polytopal domains , . We prove expon…
Deep ReLU networks and high-order finite element methods II: Chebyshev emulation
Joost A. A. Opschoor, Christoph Schwab
We show expression rates and stability in Sobolev norms of deep feedforward ReLU neural networks (NNs) in terms of the number of parameters defining the NN for continuous, piecewis…
De Rham compatible Deep Neural Network FEM
Marcello Longo, Joost A. A. Opschoor, Nico Disch +2
On general regular simplicial partitions of bounded polytopal domains , , we construct \emph{exact neural network (NN) emulations}…
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities
Carlo Marcati, Joost A. A. Opschoor, Philipp C. Petersen +1
We prove exponential expressivity with stable ReLU Neural Networks (ReLU NNs) in for weighted analytic function classes in certain polytopal domains , in space dimensio…