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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…

Probability · Mathematics 2018-04-17 Sharif Rahman

As the share of renewables in the grid increases, the operation of power systems becomes more challenging. The present paper proposes a method to formulate and solve chance-constrained optimal power flow while explicitly considering the…

Systems and Control · Computer Science 2019-04-04 T. Mühlpfordt , L. Roald , V. Hagenmeyer , T. Faulwasser , S. Misra

Addressing the uncertainty introduced by increasing renewable integration is crucial for secure power system operation, yet capturing it while preserving the full nonlinear physics of the grid remains a significant challenge. This paper…

Systems and Control · Electrical Eng. & Systems 2025-10-06 Ghulam Mohy-ud-din , Yunqi Wang , Rahmat Heidari , Frederik Geth

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

Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful sparse regression solvers to approximate computer models with…

Numerical Analysis · Mathematics 2021-05-20 Nora Lüthen , Stefano Marelli , Bruno Sudret

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

Surrogate modelling techniques have opened up new possibilities to overcome the limitations of computationally intensive numerical models in various areas of engineering and science. However, while fundamental in many engineering…

Numerical Analysis · Mathematics 2024-02-20 José Calos García-Marino , Carmen Calvo-Jurado , Enrique García-Macías

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

This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…

Computation · Statistics 2017-04-05 Negin Alemazkoor , Hadi Meidani

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…

Computation · Statistics 2018-10-17 Negin Alemazkoor , Hadi Meidani

The formation and accretion of ice on the leading edge of a wing can be detrimental to airplane performance. Complicating this reality is the fact that even a small amount of uncertainty in the shape of the accreted ice may result in a…

Data Analysis, Statistics and Probability · Physics 2014-11-14 Anthony M. DeGennaro , Clarence W. Rowley , Luigi Martinelli

The surrogate model-based uncertainty quantification method has drawn much attention in many engineering fields. Polynomial chaos expansion (PCE) and deep learning (DL) are powerful methods for building a surrogate model. However, PCE needs…

Machine Learning · Computer Science 2022-03-02 Wen Yao , Xiaohu Zheng , Jun Zhang , Ning Wang , Guijian Tang

The effective management of stochastic characteristics of renewable power generations is vital for ensuring the stable and secure operation of power systems. This paper addresses the task of optimizing the chance-constrained…

Systems and Control · Electrical Eng. & Systems 2024-01-05 Yuanxi Wu , Zhi Wu , Yijun Xu , Huan Long , Wei Gu , Shu Zheng , Jingtao Zhao

Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, is unavoidable. Polynomial Chaos Expansion (PCE) is widely…

Computational Engineering, Finance, and Science · Computer Science 2025-11-04 Bahador Bahmani , Ioannis G. Kevrekidis , Michael D. Shields

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

Operator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its main applications is learning the solution operator of…

Machine Learning · Statistics 2025-08-29 Himanshu Sharma , Lukáš Novák , Michael D. Shields

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

The intermittent nature of renewable power availability is one of the major sources of uncertainty in power systems. While markets can guarantee that the demand is covered by the available generation, transmission system operators have to…

Systems and Control · Electrical Eng. & Systems 2025-10-28 Oleksii Molodchyk , Hendrik Drögehorn , Martin Lindner , Mario Kendziorski , Timm Faulwasser

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

Considering the increasing penetration of renewable energy sources and electrical vehicles in utility distribution feeders, it is imperative to study the impacts of the resulting increasing uncertainty on the delivery capability of a…

Signal Processing · Electrical Eng. & Systems 2018-04-11 Hao Sheng , Xiaozhe Wang