output
19992022
most citedSolving high-dimensional partial differential equations using deep learning

1.8k citations

researchers with a paper here

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

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Showing 2021Show all

5 papers · 1 filter

math.AP2021★ 16 cited

Weighted analytic regularity for the integral fractional Laplacian in polygons

Markus Faustmann, Carlo Marcati, Jens Markus Melenk +1

We prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian in polygons with analytic right-hand side. We localize the problem…

math.NA2021★ 26 cited

Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations

Carlo Marcati, Christoph Schwab

We construct and analyze approximation rates of deep operator networks (ONets) between infinite-dimensional spaces that emulate with an exponential rate of convergence the coeffici…

math.AP2021★ 5 cited

Spurious Quasi-Resonances in Boundary Integral Equations for the Helmholtz Transmission Problem

Ralf Hiptmair, Andrea Moiola, Euan A. Spence

We consider the Helmholtz transmission problem with piecewise-constant material coefficients, and the standard associated direct boundary integral equations. For certain coefficien…

math.AP2021★ 5 cited

On Bayesian data assimilation for PDEs with ill-posed forward problems

Samuel Lanthaler, Siddhartha Mishra, Franziska Weber

We study Bayesian data assimilation (filtering) for time-evolution PDEs, for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Na…

math.NA2021★ 2 cited

On the approximation of functions by tanh neural networks

Tim De Ryck, Samuel Lanthaler, Siddhartha Mishra

We derive bounds on the error, in high-order Sobolev norms, incurred in the approximation of Sobolev-regular as well as analytic functions by neural networks with the hyperbolic ta…