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Metamodel-Based Sensitivity Analysis: Polynomial Chaos Expansions and Gaussian Processes

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Handbook of Uncertainty Quantification

Abstract

Global sensitivity analysis is now established as a powerful approach for determining the key random input parameters that drive the uncertainty of model output predictions. Yet the classical computation of the so-called Sobol’ indices is based on Monte Carlo simulation, which is not affordable when computationally expensive models are used, as it is the case in most applications in engineering and applied sciences. In this respect metamodels such as polynomial chaos expansions (PCE) and Gaussian processes (GP) have received tremendous attention in the last few years, as they allow one to replace the original, taxing model by a surrogate which is built from an experimental design of limited size. Then the surrogate can be used to compute the sensitivity indices in negligible time. In this chapter an introduction to each technique is given, with an emphasis on their strengths and limitations in the context of global sensitivity analysis. In particular, Sobol’ (resp. total Sobol’) indices can be computed analytically from the PCE coefficients. In contrast, confidence intervals on sensitivity indices can be derived straightforwardly from the properties of GPs. The performance of the two techniques is finally compared on three well-known analytical benchmarks (Ishigami, G-Sobol’, and Morris functions) as well as on a realistic engineering application (deflection of a truss structure).

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Authors and Affiliations

  1. EDF R&D, 6 quai Watier, 78401, Chatou, France

    Loïc Le Gratiet

  2. Chair of Risk, Safety & Uncertainty Quantification, ETH Zürich, Stefano-Franscini-Platz 5, CH-8093, Zürich, Switzerland

    Stefano Marelli

  3. Chair of Risk, Safety & Uncertainty Quantification, ETH Zürich, Stefano-Franscini-Platz 5, CH-8093, Zürich, Switzerland

    Bruno Sudret

Authors
  1. Loïc Le Gratiet
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  2. Stefano Marelli
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  3. Bruno Sudret
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Correspondence to Loïc Le Gratiet .

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Editors and Affiliations

  1. Viterbi School of Engineering, University of Southern California, Los Angeles, California, USA

    Roger Ghanem

  2. Los Alamos National Laboratory, Los Alamos, New Mexico, USA

    David Higdon

  3. California Institute of Technology , Pasadena, California, USA

    Houman Owhadi

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Gratiet, L., Marelli, S., Sudret, B. (2015). Metamodel-Based Sensitivity Analysis: Polynomial Chaos Expansions and Gaussian Processes. In: Ghanem, R., Higdon, D., Owhadi, H. (eds) Handbook of Uncertainty Quantification. Springer, Cham. https://doi.org/10.1007/978-3-319-11259-6_38-1

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  • DOI: https://doi.org/10.1007/978-3-319-11259-6_38-1

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