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

Uncertainty quantification (UQ) includes the characterization, integration, and propagation of
uncertainties that result from stochastic variations and a lack of knowledge or data in the …

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

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that
accelerates the estimation of statistics of computationally expensive simulation models using …

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 …

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

The computational cost of high-fidelity numerical models makes outer-loop analysis, which
requires repeated interrogation of the model such as uncertainty quantification …

The accurate but fast calculation of molecular excited states is still a very challenging topic.
For many applications, detailed knowledge of the energy funnel in larger molecular …

In this paper, we present an adaptive algorithm to construct response surface
approximations of high‐fidelity models using a hierarchy of lower fidelity models. Our …

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for
computing statistics of the solution of a PDE with random data. MISC is a combination …