Christoph Schwab

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math.NA2026

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…

math.NA2026

Exponential Convergence of $h p$ -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 $h p$ -finite element approximations on $(0, 1)^{3}$ , for forcing $f$ that is an…

math.NA2024

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 $S$ of linear elliptic partial differe…

Neural Networks for Singular Perturbations -- Finite Regularity

Exponential Convergence of hp-FEM for the Integral Fractional Laplacian on cuboids

Expression Rates of Neural Operators for Linear Elliptic PDEs in Polytopes

Exponential Convergence of $h p$ -FEM for the Integral Fractional Laplacian on cuboids