Purpose This paper aims to provide a comprehensive review of uncertainty quantification
methods supported by evidence-based comparison studies. Uncertainties are widely …

In recent years, there has been a growing interest in analyzing and quantifying the effects of
random inputs in the solution of ordinary/partial differential equations. To this end, the …

The quantification of probabilistic uncertainties in the outputs of physical, biological, and
social systems governed by partial differential equations with random inputs require, in …

This work proposes and analyzes a stochastic collocation method for solving elliptic partial
differential equations with random coefficients and forcing terms. These input data are …

Mathematical models are widely used in many science disciplines, such as physics, biology
and meteorology. They are aimed at better understanding and explaining real-world …

Generalized polynomial chaos (gPC) has non-uniform convergence and tends to break
down for long-time integration. The reason is that the probability density distribution (PDF) of …

We combine multi-element polynomial chaos with analysis of variance (ANOVA) functional
decomposition to enhance the convergence rate of polynomial chaos in high dimensions …

This paper presents an adaptive-sparse polynomial chaos expansion (adaptive-sparse
PCE) method for performing engineering reliability analysis and design. The proposed …

We develop an efficient, Bayesian Uncertainty Quantification framework using a novel treed
Gaussian process model. The tree is adaptively constructed using information conveyed by …

The idea of 𝓁 1-minimization is the basis of the widely adopted compressive sensing
method for function approximation. In this paper, we extend its application to high …