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相关论文: Adaptive Polynomial Chaos Expansion for Uncertaint…

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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…

概率论 · 数学 2018-04-17 Sharif Rahman

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…

信号处理 · 电气工程与系统科学 2023-07-17 Xiaoting Wang , Rong-Peng Liu , Xiaozhe Wang , François Bouffard

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…

计算工程、金融与科学 · 计算机科学 2025-11-04 Bahador Bahmani , Ioannis G. Kevrekidis , Michael D. Shields

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…

数值分析 · 数学 2021-05-20 Nora Lüthen , Stefano Marelli , Bruno Sudret

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…

数值分析 · 数学 2014-06-23 Maria Navarro , Jeroen Witteveen , Joke Blom

The increasing uncertainty level caused by growing renewable energy sources (RES) and aging transmission networks poses a great challenge in the assessment of total transfer capability (TTC) and available transfer capability (ATC). In this…

信号处理 · 电气工程与系统科学 2020-10-29 Xiaoting Wang , Xiaozhe Wang , Hao Sheng , Xi Lin

In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach…

数值分析 · 数学 2024-03-19 Gianluca Geraci , Kayla Clements , Aaron J Olson

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,…

数值分析 · 数学 2021-05-04 John Jakeman , Fabian Franzelin , Akil Narayan , Michael Eldred , Dirk Plfueger

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…

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…

数值分析 · 计算机科学 2015-06-22 John D. Jakeman , Michael S. Eldred , Khachik Sargsyan

Automating the design of microstrip antennas has been an active area of research for the past decade. By leveraging machine learning techniques such as Genetic Algorithms (GAs) or, more recently, Deep Neural Networks (DNNs), a number of…

信号处理 · 电气工程与系统科学 2024-10-07 Ali Al-Zawqari , Ali Safa , Gert Vandersteen

In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses, which are computationally expensive and usually obtained by deterministic numerical modeling approaches including finite…

统计计算 · 统计学 2020-06-01 Z. Liu , D. Lesselier , B. Sudret , J. Wiart

Surrogate modeling of costly mathematical models representing physical systems is challenging since it is typically not possible to create a large experimental design. Thus, it is beneficial to constrain the approximation to adhere to the…

机器学习 · 计算机科学 2023-09-06 Lukáš Novák , Himanshu Sharma , Michael D. Shields

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…

机器学习 · 统计学 2019-04-02 E. Torre , S. Marelli , P. Embrechts , B. Sudret

Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with high-dimensional random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter,…

概率论 · 数学 2015-06-22 Jerrad Hampton , Alireza Doostan

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…

数值分析 · 数学 2019-11-12 Sharif Rahman

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…

数值分析 · 数学 2017-09-27 Melvin Leok , Gautam Wilkins

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide…

数值分析 · 数学 2016-08-24 Katerina Konakli , Bruno Sudret

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…

系统与控制 · 电气工程与系统科学 2024-01-05 Yuanxi Wu , Zhi Wu , Yijun Xu , Huan Long , Wei Gu , Shu Zheng , Jingtao Zhao

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…

系统与控制 · 电气工程与系统科学 2026-03-24 Le Fang , Wangkun Xu , Fei Teng