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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

The global sensitivity analysis method, used to quantify the influence of uncertain input variables on the response variability of a numerical model, is applicable to deterministic computer code (for which the same set of input variables…

Methodology · Statistics 2009-06-08 Bertrand Iooss , Mathieu Ribatet , Amandine Marrel

Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model…

Methodology · Statistics 2008-02-08 Amandine Marrel , Bertrand Iooss , Beatrice Laurent , Olivier Roustant

Explainable machine learning techniques have gained increasing attention in engineering applications, especially in aerospace design and analysis, where understanding how input variables influence data-driven models is essential. Partial…

Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a…

Computation · Statistics 2021-06-01 X. Zhu , B. Sudret

Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attributing to each variable its relative contribution to the…

Computation · Statistics 2018-12-19 Joseph Hart , Pierre Gremaud

Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a…

Computational Engineering, Finance, and Science · Computer Science 2019-09-05 Alexander Tarakanov , Ahmed H. Elsheikh

Global sensitivity analysis (GSA) aims at quantifying the contribution of input variables over the variability of model outputs. In the frame of functional outputs, a common goal is to compute sensitivity maps (SM), i.e sensitivity indices…

Statistics Theory · Mathematics 2024-12-12 Yuri Sao , Olivier Roustant , Geraldo de Freitas Maciel

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

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

Polynomial chaos expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…

Numerical Analysis · Mathematics 2016-04-25 H. Cagan Ozen , Guillaume Bal

The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimate, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are…

Statistics Theory · Mathematics 2019-11-26 Bertrand Iooss , Clémentine Prieur

Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully…

Methodology · Statistics 2025-10-30 Kellin N. Rumsey , Devin Francom , Graham C. Gibson , J. Derek Tucker , Gabriel Huerta

Variance based global sensitivity analysis measures the relevance of inputs to a single output using Sobol' indices. This paper extends the definition in a natural way to multiple outputs, directly measuring the relevance of inputs to the…

Statistics Theory · Mathematics 2025-03-25 Robert A. Milton , Solomon F. Brown

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

Global Sensitivity Analysis (GSA) is the study of the influence of any given inputs on the outputs of a model. In the context of engineering design, GSA has been widely used to understand both individual and collective contributions of…

Machine Learning · Statistics 2024-03-06 Yigitcan Comlek , Liwei Wang , Wei Chen

Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for…

Computational Engineering, Finance, and Science · Computer Science 2023-07-26 Niklas Georg , Ulrich Römer

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

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

Sparse polynomial chaos expansions (PCE) are an efficient and widely used surrogate modeling method in uncertainty quantification for engineering problems with computationally expensive models. To make use of the available information in…

Computation · Statistics 2021-07-26 Nora Lüthen , Stefano Marelli , Bruno Sudret