26 citations · 100 across the 15 of their papers we have counts for
17 papers
Neural and Spectral Operator Surrogates on Gaussian Spaces
Carlo Marcati, Mario Marić, Christoph Schwab +1
We prove expression rate bounds of finite-parametric, spectral and neural surrogates for holomorphic maps between separable Hilbert spaces. The surrogates have an encoder-approxima…
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…
Sparsity for Infinite-Parametric Holomorphic Functions on Gaussian Spaces
Carlo Marcati, Christoph Schwab, Jakob Zech
We investigate the sparsity of Wiener polynomial chaos expansions of holomorphic maps on Gaussian Hilbert spaces, as arise in the coefficient-to-solution maps of line…
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…
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…
Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons
Markus Faustmann, Carlo Marcati, Jens Markus Melenk +1
We prove exponential convergence in the energy norm of finite element discretizations for the integral fractional diffusion operator of order subject to homogene…