45 citations · 88 across the 7 of their papers we have counts for
13 papers
A Spline Dimensional Decomposition for Uncertainty Quantification in High Dimensions
Sharif Rahman, Ramin Jahanbin
This study debuts a new spline dimensional decomposition (SDD) for uncertainty quantification analysis of high-dimensional functions, including those endowed with high nonlinearity…
A Spline Chaos Expansion
Sharif Rahman
A spline chaos expansion, referred to as SCE, is introduced for uncertainty quantification analysis. The expansion provides a means for representing an output random variable of in…
Dimension-wise Multivariate Orthogonal Polynomials in General Probability Spaces
Sharif Rahman
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogo…
A Galerkin Isogeometric Method for Karhunen-Loeve Approximation of Random Fields
Sharif Rahman
This paper marks the debut of a Galerkin isogeometric method for solving a Fredholm integral eigenvalue problem, enabling random field discretization by means of the Karhunen-Loeve…
A Polynomial Chaos Expansion in Dependent Random Variables
Sharif Rahman
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising measure-consistent multivariate orthonormal polynomials in dependent random variables. Unlike ex…
Mathematical Properties of Polynomial Dimensional Decomposition
Sharif Rahman
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of rando…
Wiener-Hermite Polynomial Expansion for Multivariate Gaussian Probability Measures
Sharif Rahman
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising multivariate Hermite orthogonal polynomials in dependent Gaussian random variables. The second-m…
The -Sensitivity Index
Sharif Rahman
This article presents a general multivariate -sensitivity index, rooted in the -divergence between the unconditional and conditional probability measures of a stochastic resp…
A Generalized ANOVA Dimensional Decomposition for Dependent Probability Measures
Sharif Rahman
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties…
Adaptive-Sparse Polynomial Dimensional Decomposition Methods for High-Dimensional Stochastic Computing
Vaibhav Yadav, Sharif Rahman
This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational…
Novel Computational Methods for High-Dimensional Stochastic Sensitivity Analysis
Sharif Rahman, Xuchun Ren
This paper presents three new computational methods for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to rando…
Uncertainty Quantification by Alternative Decompositions of Multivariate Functions
Sharif Rahman
This article advocates factorized and hybrid dimensional decompositions (FDD/HDD), as alternatives to analysis-of-variance dimensional decomposition (ADD), for second-moment statis…
Approximation Errors in Truncated Dimensional Decompositions
Sharif Rahman
The main theme of this paper is error analysis for approximations derived from two variants of dimensional decomposition of a multivariate function: the referential dimensional dec…