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Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response…

Computation · Statistics 2023-06-14 Paul-Christian Bürkner , Ilja Kröker , Sergey Oladyshkin , Wolfgang Nowak

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…

Computation · Statistics 2022-06-20 Max Ehre , Iason Papaioannou , Bruno Sudret , Daniel Straub

Polynomial Chaos Expansions (PCEs) are widely recognized for their efficient computational performance in surrogate modeling. Yet, a robust framework to quantify local model errors is still lacking. While the local uncertainty of PCE…

Methodology · Statistics 2026-01-26 A. Hatstatt , X. Zhu , B. Sudret

The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…

Systems and Control · Electrical Eng. & Systems 2026-03-24 Le Fang , Wangkun Xu , Fei Teng

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…

Numerical Analysis · Mathematics 2019-02-20 Liang Yan , Tao Zhou

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…

Optimization and Control · Mathematics 2019-10-16 David Métivier , Marc Vuffray , Sidhant Misra

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 (PCE) have proven efficiency in a number of fields for propagating parametric uncertainties through computational models of complex systems, namely structural and fluid mechanics, chemical reactions and…

Computation · Statistics 2017-04-13 Chu V. Mai , Bruno Sudret

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

The application of polynomial chaos expansions (PCEs) to the propagation of uncertainties in stochastic dynamical models is well-known to face challenging issues. The accuracy of PCEs degenerates quickly in time. Thus maintaining a…

Methodology · Statistics 2016-04-27 C. V. Mai , M. D. Spiridonakos , E. N. Chatzi , B. Sudret

Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial…

Neural and Evolutionary Computing · Computer Science 2024-02-14 Sergey Oladyshkin , Timothy Praditia , Ilja Kröker , Farid Mohammadi , Wolfgang Nowak , Sebastian Otte

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…

Numerical Analysis · Mathematics 2017-09-27 Melvin Leok , Gautam Wilkins

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 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

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

In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this…

Methodology · Statistics 2018-05-09 Paul Diaz , Alireza Doostan , Jerrad Hampton

Frequency response functions (FRFs) are important for assessing the behavior of stochastic linear dynamic systems. For large systems, their evaluations are time-consuming even for a single simulation. In such cases, uncertainty…

Computation · Statistics 2017-03-23 V. Yaghoubi , S. Marelli , B. Sudret , T. Abrahamsson

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

This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…

Machine Learning · Computer Science 2021-10-27 Alexander Henkes , Ismail Caylak , Rolf Mahnken

Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for evaluating PCE coefficients. In contrast,…

Numerical Analysis · Mathematics 2021-05-04 John Jakeman , Fabian Franzelin , Akil Narayan , Michael Eldred , Dirk Plfueger