In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …

This text provides a framework in which the main objectives of the field of uncertainty
quantification (UQ) are defined and an overview of the range of mathematical methods by …

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 …

Monte Carlo methods are a very general and useful approach for the estimation of
expectations arising from stochastic simulation. However, they can be computationally …

This work presents an optimal model management strategy that exploits multifidelity
surrogate models to accelerate the estimation of statistics of outputs of computationally …

In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …

It is important to design robust and reliable systems by accounting for uncertainty and
variability in the design process. However, performing optimization in this setting can be …

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 …

We propose and analyze a novel multi-index Monte Carlo (MIMC) method for weak
approximation of stochastic models that are described in terms of differential equations …

Recent advances in sensor technologies, field methodologies, numerical modeling, and
inversion approaches have contributed to unprecedented imaging of hydrogeological …