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 …

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 …

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

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 …

A probabilistic approach to phase-field brittle and ductile fracture with random material and
geometric properties is proposed within this work. In the macroscopic failure mechanics …

Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients∗
Page 1 ESAIM: M2AN 51 (2017) 341–363 ESAIM: Mathematical Modelling and Numerical …

We are interested in computing the expectation of a functional of a PDE solution under a
Bayesian posterior distribution. Using Bayes's rule, we reduce the problem to estimating the …

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 …

We propose a parallel version of the cross interpolation algorithm and apply it to calculate
high-dimensional integrals motivated by Ising model in quantum physics. In contrast to …

We propose a multifidelity dimension reduction method to identify a low-dimensional
structure present in many engineering models. The structure of interest arises when …