1.8k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- ETH ZurichCH99 papers
- University of MünsterDE18 papers
- University of PaviaIT9 papers
- University of ViennaAT9 papers
- University of Duisburg-EssenDE7 papers
- Chinese University of Hong Kong, ShenzhenCN6 papers
- Shenzhen Research Institute of Big DataCN6 papers
- University of Maryland, College ParkUS6 papers
- Princeton UniversityUS5 papers
- TU WienAT5 papers
- Austrian Academy of SciencesAT4 papers
- Chalmers University of TechnologySE4 papers
101 papers
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…
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…
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…
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…
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…
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}…
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…
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…
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…
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…
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…
Exponential Convergence of FEM for Spectral Fractional Diffusion in Polygons
Lehel Banjai, Jens M. Melenk, Christoph Schwab
For the spectral fractional diffusion operator of order in bounded, curvilinear polygonal domains we prove exponential convergence of two classes of discreti…
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities
Carlo Marcati, Joost A. A. Opschoor, Philipp C. Petersen +1
We prove exponential expressivity with stable ReLU Neural Networks (ReLU NNs) in for weighted analytic function classes in certain polytopal domains , in space dimensio…
Weighted analyticity of Hartree-Fock eigenfunctions
Yvon Maday, Carlo Marcati
We prove analytic-type estimates in weighted Sobolev spaces on the eigenfunctions of a class of elliptic and nonlinear eigenvalue problems with singular potentials, which includes…
Phase retrieval from sampled Gabor transform magnitudes: Counterexamples
Rima Alaifari, Matthias Wellershoff
We consider the recovery of square-integrable signals from discrete, equidistant samples of their Gabor transform magnitude and show that, in general, signals can not be recovered…
Physics Informed Neural Networks for Simulating Radiative Transfer
Siddhartha Mishra, Roberto Molinaro
We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing…
Phase retrieval of bandlimited functions for the wavelet transform
Rima Alaifari, Francesca Bartolucci, Matthias Wellershoff
We study the recovery of square-integrable signals from the absolute values of their wavelet transforms, also called wavelet phase retrieval. We present a new uniqueness result for…
Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks
Kjetil O. Lye, Siddhartha Mishra, Deep Ray +1
We present a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained optimizat…
The higher order fractional Calderón problem for linear local operators: uniqueness
Giovanni Covi, Keijo Mönkkönen, Jesse Railo +1
We study an inverse problem for the fractional Schrödinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the order…
Change Point Detection in Time Series Data using Autoencoders with a Time-Invariant Representation
Tim De Ryck, Maarten De Vos, Alexander Bertrand
Change point detection (CPD) aims to locate abrupt property changes in time series data. Recent CPD methods demonstrated the potential of using deep learning techniques, but often…
Second-order accurate TVD numerical methods for nonlocal nonlinear conservation laws
Ulrik Skre Fjordholm, Adrian Montgomery Ruf
We present a second-order accurate numerical method for a class of nonlocal nonlinear conservation laws called the "nonlocal pair-interaction model" which was recently introduced b…
Well-balanced finite volume schemes for nearly steady adiabatic flows
Luc Grosheintz-Laval, Roger Käppeli
We present well-balanced finite volume schemes designed to approximate the Euler equations with gravitation. They are based on a novel local steady state reconstruction. The scheme…
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations
Sebastian Becker, Ramon Braunwarth, Martin Hutzenthaler +2
One of the most challenging issues in applied mathematics is to develop and analyze algorithms which are able to approximately compute solutions of high-dimensional nonlinear parti…
Div-Curl Problems and -regular Stream Functions in 3D Lipschitz Domains
Matthias Kirchhart, Erick Schulz
We consider the problem of recovering the divergence-free velocity field of a given vorticity on a bounded…