Gaussian (normal) distribution is a basic continuous probability distribution in statistics, it
plays a substantial role in scientific and engineering problems that related to stochastic …

This paper is a contemporary review of QMC ('quasi-Monte Carlo') methods, that is, equal-
weight rules for the approximate evaluation of high-dimensional integrals over the unit cube …

These lecture notes highlight the mathematical and computational structure relating to the
formulation of, and development of algorithms for, the Bayesian approach to inverse …

Many large scale problems in computational fluid dynamics such as uncertainty
quantification, Bayesian inversion, data assimilation and PDE constrained optimization are …

Parametrized families of PDEs arise in various contexts such as inverse problems, control
and optimization, risk assessment, and uncertainty quantification. In most of these …

In this paper quasi-Monte Carlo (QMC) methods are applied to a class of elliptic partial
differential equations (PDEs) with random coefficients, where the random coefficient is …

This article provides a survey of recent research efforts on the application of quasi-Monte
Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion …

Lattice rules are particular instances of quasi-Monte Carlo rules for numerical integration of
functions over the 𝑑-dimensional unit cube [0, 1] 𝑑, where the emphasis lies on high …

We study an optimal control problem under uncertainty, where the target function is the
solution of an elliptic partial differential equation with random coefficients, steered by a …

In this paper we present a rigorous cost and error analysis of a multilevel estimator based on
randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems …