Seminar for Applied Mathematics

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19992022

most citedSolving high-dimensional partial differential equations using deep learning

1.8k citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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Showing 2022 · math.NAShow all

4 papers · 2 filters

math.NA2022

Monte Carlo convergence rates for $k$ th moments in Banach spaces

Kristin Kirchner, Christoph Schwab

We formulate standard and multilevel Monte Carlo methods for the $k$ th moment $M_{ε}^{k} [ξ]$ of a Banach space valued random variable $ξ : Ω \to E$ , interpreted as…

math.NA2022★ 11 cited

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 $h p$ finite element discretizations for the integral fractional diffusion operator of order $2 s \in (0, 2)$ subject to homogene…

math.NA2022★ 4 cited

Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D

Markus Faustmann, Carlo Marcati, Jens Markus Melenk +1

We prove weighted analytic regularity for the solution of the integral fractional Poisson problem on bounded intervals with analytic right-hand side. Based on this regularity resul…

math.NA2022★ 12 cited

De Rham compatible Deep Neural Network FEM

Marcello Longo, Joost A. A. Opschoor, Nico Disch +2

On general regular simplicial partitions $T$ of bounded polytopal domains $Ω \subset R^{d}$ , $d \in {2, 3}$ , we construct \emph{exact neural network (NN) emulations}…

Monte Carlo convergence rates for kth moments in Banach spaces

Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons

Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D

De Rham compatible Deep Neural Network FEM

Monte Carlo convergence rates for $k$ th moments in Banach spaces