research-article

Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation

Authors:

Pietro M. Congedo,

Rémi AbgrallAuthors Info & Claims

Journal of Computational Physics, Volume 314, Issue C

Pages 557 - 589

https://doi.org/10.1016/j.jcp.2016.03.026

Published: 01 June 2016 Publication History

Abstract

The Polynomial Dimensional Decomposition (PDD) is employed in this work for the global sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to a moderate to large number of input random variables. Due to the intimate connection between the PDD and the Analysis of Variance (ANOVA) approaches, PDD is able to provide a simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to the Polynomial Chaos expansion (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of standard methods unaffordable for real engineering applications. In order to address the problem of the curse of dimensionality, this work proposes essentially variance-based adaptive strategies aiming to build a cheap meta-model (i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed by regression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionality for ANOVA component functions, 2) the active dimension technique especially for second- and higher-order parameter interactions, and 3) the stepwise regression approach designed to retain only the most influential polynomials in the PDD expansion. During this adaptive procedure featuring stepwise regressions, the surrogate model representation keeps containing few terms, so that the cost to resolve repeatedly the linear systems of the least-squares regression problem is negligible. The size of the finally obtained sparse PDD representation is much smaller than the one of the full expansion, since only significant terms are eventually retained. Consequently, a much smaller number of calls to the deterministic model is required to compute the final PDD coefficients.

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Wang GSahu SLiao Q(2023)An Adaptive ANOVA Stochastic Galerkin Method for Partial Differential Equations with High-dimensional Random InputsJournal of Scientific Computing10.1007/s10915-023-02417-w98:1Online publication date: 15-Dec-2023
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He WLi GZhong CWang Y(2023)A novel data-driven sparse polynomial chaos expansion for high-dimensional problems based on active subspace and sparse Bayesian learningStructural and Multidisciplinary Optimization10.1007/s00158-022-03475-866:1Online publication date: 14-Jan-2023
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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 314, Issue C

June 2016

911 pages

ISSN:0021-9991

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Copyright © Elsevier Inc.

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Academic Press Professional, Inc.

United States

Publication History

Published: 01 June 2016

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Cited By

Wang GSahu SLiao Q(2023)An Adaptive ANOVA Stochastic Galerkin Method for Partial Differential Equations with High-dimensional Random InputsJournal of Scientific Computing10.1007/s10915-023-02417-w98:1Online publication date: 15-Dec-2023
https://dl.acm.org/doi/10.1007/s10915-023-02417-w
Zhao YLiu JHe Z(2023)A general multi-fidelity metamodeling framework for models with various output correlationStructural and Multidisciplinary Optimization10.1007/s00158-023-03537-566:5Online publication date: 13-Apr-2023
https://dl.acm.org/doi/10.1007/s00158-023-03537-5
He WLi GZhong CWang Y(2023)A novel data-driven sparse polynomial chaos expansion for high-dimensional problems based on active subspace and sparse Bayesian learningStructural and Multidisciplinary Optimization10.1007/s00158-022-03475-866:1Online publication date: 14-Jan-2023
https://dl.acm.org/doi/10.1007/s00158-022-03475-8
He WLi GNie Z(2022)An adaptive sparse polynomial dimensional decomposition based on Bayesian compressive sensing and cross-entropyStructural and Multidisciplinary Optimization10.1007/s00158-021-03120-w65:1Online publication date: 5-Jan-2022
https://dl.acm.org/doi/10.1007/s00158-021-03120-w
Cheng KLu ZLing CZhou S(2020)Surrogate-assisted global sensitivity analysis: an overviewStructural and Multidisciplinary Optimization10.1007/s00158-019-02413-561:3(1187-1213)Online publication date: 17-Jan-2020
https://dl.acm.org/doi/10.1007/s00158-019-02413-5
Wang CCheng XChen SLi GZhang H(2018)A SVM-based Sensitivity Analysis Approach for Data-Driven Modeling of Ship Motion2018 IEEE International Conference on Mechatronics and Automation (ICMA)10.1109/ICMA.2018.8484531(803-808)Online publication date: 5-Aug-2018
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Margheri LSagaut P(2016)A hybrid anchored-ANOVA - POD/Kriging method for uncertainty quantification in unsteady high-fidelity CFD simulationsJournal of Computational Physics10.1016/j.jcp.2016.07.036324:C(137-173)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1016/j.jcp.2016.07.036

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