Global sensitivity analysis (SA) aims at quantifying the respective effects of input random
variables (or combinations thereof) onto the variance of the response of a physical or …

The quantification of uncertainty in computational fluid dynamics (CFD) predictions is both a
significant challenge and an important goal. Probabilistic uncertainty quantification (UQ) …

The basic random variables on which random uncertainties can in a given model depend
can be viewed as defining a measure space with respect to which the solution to the …

This paper gives an overview of the use of polynomial chaos (PC) expansions to represent
stochastic processes in numerical simulations. Several methods are presented for …

We present a reformulation of the Bayesian approach to inverse problems, that seeks to
accelerate Bayesian inference by using polynomial chaos (PC) expansions to represent …

We consider a Bayesian approach to nonlinear inverse problems in which the unknown
quantity is a spatial or temporal field, endowed with a hierarchical Gaussian process prior …

An uncertainty quantification scheme is constructed based on generalized Polynomial
Chaos (PC) representations. Two such representations are considered, based on the …

A multi-resolution analysis (MRA) is applied to an uncertainty propagation scheme based on
a generalized polynomial chaos (PC) representation. The MRA relies on an orthogonal …

Many researchers have worked to develop methods to analyze and characterize capacity
fade in lithium-ion batteries. As a complement to approaches to mathematically model …

Uncertainty quantification in CFD computations is receiving increased interest, due in large
part to the increasing complexity of physical models, and the inherent introduction of random …