4 papers
Neural Networks for Singular Perturbations -- Finite Regularity
F. Rohner, Ch. Schwab, C. Xenophontos
We study finite-element and deep feedforward neural network (DNN for short) expressivity rate bounds for solution sets of a model linear, second order singularly perturbed, ellipti…
Neural Shape Operator Surrogates -- Expression Rate Bounds
Helmut Harbrecht, Christoph Schwab
We prove error bounds for operator surrogates of solution operators for partial differential and boundary integral equations on families of domains which are diffeomorphic to one c…
Exponential Convergence of -FEM for the Integral Fractional Laplacian on cuboids
Björn Bahr, Markus Faustmann, Carlo Marcati +2
For the Dirichlet integral fractional Laplacian, we prove root exponential convergence of tensor-product -finite element approximations on , for forcing that is an…
Expression Rates of Neural Operators for Linear Elliptic PDEs in Polytopes
Carlo Marcati, Christoph Schwab
We study the approximation rates of a class of deep neural network approximations of operators which arise as data-to-solution maps of linear elliptic partial differe…