142 citations · 696 across the 46 of their papers we have counts for
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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…
Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in
Christoph Schwab, Jakob Zech
For artificial deep neural networks, we prove expression rates for analytic functions in the norm of where $d\in {\mathbb{N}}\…
Multilevel approximation of Gaussian random fields: Covariance compression, estimation and spatial prediction
Helmut Harbrecht, Lukas Herrmann, Kristin Kirchner +1
Centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds are determined by their covariance…
Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations
Lukas Gonon, Christoph Schwab
Deep neural networks (DNNs) with ReLU activation function are proved to be able to express viscosity solutions of linear partial integrodifferental equations (PIDEs) on state space…
Deep ReLU Network Expression Rates for Option Prices in high-dimensional, exponential Lévy models
Lukas Gonon, Christoph Schwab
We study the expression rates of deep neural networks (DNNs for short) for option prices written on baskets of risky assets, whose log-returns are modelled by a multivariate Lé…