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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…

Computation · Statistics 2018-02-14 Mohammad Hadigol , Alireza Doostan

For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. This paper presents, within the context of uncertainty…

Computation · Statistics 2018-06-13 Jerrad Hampton , Alireza Doostan

Sub-terahertz (subTHz) antennas will play an important role in the next generations of wireless communication systems. However, when comes to the subTHz frequency spectrum, the antenna fabrication tolerance needs to be accurately considered…

Information Theory · Computer Science 2024-04-09 Aristeides D. Papadopoulos , Yihan Ma , Qi Luo , George C. Alexandropoulos

Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs. PCEs for models with independent inputs have been extensively explored in…

Systems and Control · Electrical Eng. & Systems 2021-06-02 Zhanlin Liu , Youngjun Choe

In an ever-increasing interest for Machine Learning (ML) and a favorable data development context, we here propose an original methodology for data-based prediction of two-dimensional physical fields. Polynomial Chaos Expansion (PCE),…

Computational Physics · Physics 2021-02-03 Rem-Sophia Mouradi , Cédric Goeury , Olivier Thual , Fabrice Zaoui , Pablo Tassi

In this paper we present a basis selection method that can be used with $\ell_1$-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets…

Numerical Analysis · Computer Science 2015-06-22 John D. Jakeman , Michael S. Eldred , Khachik Sargsyan

In this letter, we compare three polynomial chaos expansion (PCE)-based methods for ANCOVA (ANalysis of COVAriance) indices based global sensitivity analysis for correlated random inputs in two power system applications. Surprisingly, the…

Signal Processing · Electrical Eng. & Systems 2023-07-17 Xiaoting Wang , Rong-Peng Liu , Xiaozhe Wang , François Bouffard

Optimal Bayesian design techniques provide an estimate for the best parameters of an experiment in order to maximize the value of measurements prior to the actual collection of data. In other words, these techniques explore the space of…

Computational Physics · Physics 2020-08-11 Alexander Tarakanov , Ahmed H. Elsheikh

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 interest with respect to multivariate orthonormal basis…

Numerical Analysis · Mathematics 2019-11-12 Sharif Rahman

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…

Machine Learning · Computer Science 2025-05-29 Dominik Polke , Tim Kösters , Elmar Ahle , Dirk Söffker

The Polynomial Chaos Expansion (PCE) technique recovers a finite second order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochas- tic quantity {\xi}, hence acting as a…

Computational Finance · Quantitative Finance 2016-10-31 Luca Di Persio , Michele Bonollo , Gregorio Pellegrini

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…

Numerical Analysis · Mathematics 2023-11-29 Julian Clausnitzer , Andreas Kleefeld

Reliability analysis typically relies on deterministic simulators, which yield repeatable outputs for identical inputs. However, many real-world systems display intrinsic randomness, requiring stochastic simulators whose outputs are random…

Methodology · Statistics 2025-07-08 A. Pires , M. Moustapha , S. Marelli , B. Sudret

We apply the Tensor Train (TT) decomposition to construct the tensor product Polynomial Chaos Expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some…

Numerical Analysis · Mathematics 2015-03-12 Sergey Dolgov , Boris N. Khoromskij , Alexander Litvinenko , Hermann G. Matthies

Polynomial chaos expansions (PCE) have seen widespread use in the context of uncertainty quantification. However, their application to structural reliability problems has been hindered by the limited performance of PCE in the tails of the…

Computation · Statistics 2018-08-10 S. Marelli , B. Sudret

Accurate modeling of radio wave propagation over irregular terrains is crucial for designing reliable wireless communication systems in such environments, yet uncertainties in the antenna configuration are not quantified within…

Signal Processing · Electrical Eng. & Systems 2026-03-04 Sicheng An , Luca Di Rienzo , Hao Qin , Xingqi Zhang , Lorenzo Codecasa

The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos…

Numerical Analysis · Mathematics 2022-12-22 Xiaoshu Zeng , Roger Ghanem

This work introduces a method to equip data-driven polynomial chaos expansion surrogate models with intervals that quantify the predictive uncertainty of the surrogate. To that end, jackknife-based conformal prediction is integrated into…

Methodology · Statistics 2025-12-18 Dimitrios Loukrezis , Dimitris G. Giovanis

This paper presents a method for performing Uncertainty Quantification in high-dimensional uncertain spaces by combining arbitrary polynomial chaos with a recently proposed scheme for sensitivity enhancement (1). Including available…

Numerical Analysis · Mathematics 2024-02-09 Nick Pepper , Francesco Montomoli , Kyriakos Kantarakias

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a…

Machine Learning · Statistics 2024-11-11 Dimitris G. Giovanis , Dimitrios Loukrezis , Ioannis G. Kevrekidis , Michael D. Shields