Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Generalized spectral decomposition for stochastic nonlinear problems
Journal of Computational Physics
Polynomial chaos representation of spatio-temporal random fields from experimental measurements
Journal of Computational Physics
Identification of Bayesian posteriors for coefficients of chaos expansions
Journal of Computational Physics
Time-dependent generalized polynomial chaos
Journal of Computational Physics
Adaptive sparse polynomial chaos expansion based on least angle regression
Journal of Computational Physics
SIAM Journal on Matrix Analysis and Applications
Iterative Solvers for the Stochastic Finite Element Method
SIAM Journal on Scientific Computing
Eigenvalues of the Jacobian of a Galerkin-Projected Uncertain ODE System
SIAM Journal on Scientific Computing
Data-free inference of the joint distribution of uncertain model parameters
Journal of Computational Physics
Bayesian inference with optimal maps
Journal of Computational Physics
Journal of Computational Physics
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
A one-time truncate and encode multiresolution stochastic framework
Journal of Computational Physics
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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 mathematical problem can be defined. This measure space is defined on a product measure associated with the collection of basic random variables. This paper clarifies the mathematical structure of this space and its relationship to the underlying spaces associated with each of the random variables. Cases of both dependent and independent basic random variables are addressed. Bases on the product space are developed that can be viewed as generalizations of the standard polynomial chaos approximation. Moreover, two numerical constructions of approximations in this space are presented along with the associated convergence analysis.