Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification

TL;DR

This paper reviews recent advances in higher order Quasi-Monte Carlo methods that achieve dimension-robust convergence rates for uncertainty quantification in infinite-dimensional parametric operator equations.

Contribution

It provides a comprehensive review of recent results on higher order convergence rates of Quasi-Monte Carlo Petrov-Galerkin methods in uncertainty quantification.

Findings

Dimension-robust higher order convergence rates established.

Applicability to infinite-dimensional parametric operator equations.

Enhanced efficiency in computational uncertainty quantification.

Abstract

We review recent results on dimension-robust higher order convergence rates of Quasi-Monte Carlo Petrov-Galerkin approximations for response functionals of infinite-dimensional, parametric operator equations which arise in computational uncertainty quantification.