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 …

In this paper we address the problem of the prohibitively large computational cost of existing
Markov chain Monte Carlo methods for large-scale applications with high-dimensional …

Constructing surrogate models for uncertainty quantification (UQ) on complex partial
differential equations (PDEs) having inherently high-dimensional O (10 n), n≥ 2, stochastic …

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

The Bayesian approach to inverse problems provides a rigorous framework for the
incorporation and quantification of uncertainties in measurements, parameters and models …

General multivariate distributions are notoriously expensive to sample from, particularly the
high-dimensional posterior distributions in PDE-constrained inverse problems. This paper …

This article reviews the application of some advanced Monte Carlo techniques in the context
of multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations …

We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal
control problems subject to parabolic partial differential equation (PDE) constraints under …

Characterising intractable high-dimensional random variables is one of the fundamental
challenges in stochastic computation. The recent surge of transport maps offers a …

For two probability measures ρ and π with analytic densities on the d-dimensional cube [-1,
1] d, we investigate the approximation of the unique triangular monotone Knothe–Rosenblatt …