output
20202022
most citedExponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations

26 citations

15 papers

math.NA2022

Monte Carlo convergence rates for th moments in Banach spaces

Kristin Kirchner, Christoph Schwab

We formulate standard and multilevel Monte Carlo methods for the th moment of a Banach space valued random variable , 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 finite element discretizations for the integral fractional diffusion operator of order subject to homogene…

eess.IV2022★ 5 cited

Localized adversarial artifacts for compressed sensing MRI

Rima Alaifari, Giovanni S. Alberti, Tandri Gauksson

As interest in deep neural networks (DNNs) for image reconstruction tasks grows, their reliability has been called into question (Antun et al., 2020; Gottschling et al., 2020). How…

math.FA2022★ 3 cited

On the connection between uniqueness from samples and stability in Gabor phase retrieval

Rima Alaifari, Francesca Bartolucci, Stefan Steinerberger +1

Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvabilit…

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 of bounded polytopal domains , , we construct \emph{exact neural network (NN) emulations}…