Related papers: Automatic selection of basis-adaptive sparse polyn…
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising measure-consistent multivariate orthonormal polynomials in dependent random variables. Unlike existing PCEs, whether classical or generalized, no…
Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos…
The polynomial chaos (PC) expansion has been widely used as a surrogate model in the Bayesian inference to speed up the Markov chain Monte Carlo (MCMC) calculations. However, the use of a PC surrogate introduces the modeling error, that may…
To date, the analysis of high-dimensional, computationally expensive engineering models remains a difficult challenge in risk and reliability engineering. We use a combination of dimensionality reduction and surrogate modelling termed…
We present a regression technique for data-driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive…
Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…
Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computational approach to solve stochastic partial differential…
As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling…
As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly…
This work develops a novel basis-adaptive method for constructing anisotropic polynomial chaos expansions of multidimensional (vector-valued, multi-output) model responses. The adaptive basis selection is based on multivariate sensitivity…
Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper…
We introduce a new algorithm, called adaptive sparse backfitting algorithm, for solving high dimensional Sparse Additive Model (SpAM) utilizing symmetric, non-negative definite smoothers. Unlike the previous sparse backfitting algorithm,…
We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the…
Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…
The paper presents a novel methodology to build surrogate models of complicated functions by an active learning-based sequential decomposition of the input random space and construction of localized polynomial chaos expansions, referred to…
We propose a non-intrusive reduced-order modeling method based on proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for stochastic representations in uncertainty quantification (UQ) analysis. Firstly, POD provides…
We consider the numerical approximation of different ordinary differential equations (ODEs) and partial differential equations (PDEs) with periodic boundary conditions involving a one-dimensional random parameter, comparing the intrusive…
Software engineers often have to estimate the performance of a software system before having full knowledge of the system parameters, such as workload and operational profile. These uncertain parameters inevitably affect the accuracy of…
A new approximation format for solutions of partial differential equations depending on infinitely many parameters is introduced. By combining low-rank tensor approximation in a selected subset of variables with a sparse polynomial…
Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…