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 …

The past decade has seen increasing interest in applying Deep Learning (DL) to
Computational Science and Engineering (CSE). Driven by impressive results in applications …

This work surveys mathematical foundations of Model Order Reduction (MOR for short)
techniques in accelerating computational forward and inverse UQ. Operator equations …

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 …

We study quasi-Monte Carlo (QMC) integration of smooth functions defined over the
multidimensional unit cube. Inspired by a recent work of Pan and Owen, we study a new …

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 …

Algorithms that combat the curse of dimensionality take advantage of nonuniformity
properties of the underlying functions, which may be rotational (eg, grid alignment) or …

We analyze the convergence of compressive sensing based sampling techniques for the
efficient evaluation of functionals of solutions for a class of high-dimensional, affine …

We analyse convergence rates of Smolyak integration for parametric maps u: U→ X taking
values in a Banach space X, defined on the parameter domain U=[− 1, 1] N. For parametric …

We develop a convergence analysis of a multilevel algorithm combining higher order quasi--
Monte Carlo (QMC) quadratures with general Petrov--Galerkin discretizations of countably …