2 citations · 4 across the 9 of their papers we have counts for
9 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…
Stochastic Transport with Lévy Noise -- Fully Discrete Numerical Approximation
Andrea Barth, Andreas Stein
Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian sett…
Numerical analysis for time-dependent advection-diffusion problems with random discontinuous coefficients
Andrea Barth, Andreas Stein
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To…
A Multilevel Monte Carlo Algorithm for Parabolic Advection-Diffusion Problems with Discontinuous Coefficients
Andrea Barth, Andreas Stein
The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium…
A study of elliptic partial differential equations with jump diffusion coefficients
Andrea Barth, Andreas Stein
As a simplified model for subsurface flows elliptic equations may be utilized. Insufficient measurements or uncertainty in those are commonly modeled by a random coefficient, which…