2 citations · 4 across the 9 of their papers we have counts for
5 papers · 1 filter
Deep Operator Network Approximation Rates for Lipschitz Operators
Christoph Schwab, Andreas Stein, Jakob Zech
We establish universality and expression rate bounds for a class of neural Deep Operator Networks (DON) emulating Lipschitz (or Hölder) continuous maps $\mathcal G:\mathcal X\to\ma…
An Antithetic Multilevel Monte Carlo-Milstein Scheme for Stochastic Partial Differential Equations with non-commutative noise
Abdul-Lateef Haji-Ali, Andreas Stein
We present a novel multilevel Monte Carlo approach for estimating quantities of interest for stochastic partial differential equations (SPDEs). Drawing inspiration from [Giles and…
Multilevel Markov Chain Monte Carlo for Bayesian Elliptic Inverse Problems with Besov Random Tree Priors
Andreas Stein, Viet Ha Hoang
We propose a multilevel Monte Carlo-FEM algorithm to solve elliptic Bayesian inverse problems with "Besov random tree prior". These priors are given by a wavelet series with stocha…
Multilevel Monte Carlo FEM for Elliptic PDEs with Besov Random Tree Priors
Christoph Schwab, Andreas Stein
We develop a multilevel Monte Carlo (MLMC)-FEM algorithm for linear, elliptic diffusion problems in polytopal domain , with Besov-tree random coeffic…
A-posteriori QMC-FEM error estimation for Bayesian inversion and optimal control with entropic risk measure
Marcello Longo, Christoph Schwab, Andreas Stein
We propose a novel a-posteriori error estimation technique where the target quantities of interest are ratios of high-dimensional integrals, as occur e.g. in PDE constrained Bayesi…