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An efficient methodology for modeling complex computer codes with Gaussian processes

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  • Marrel, Amandine
  • Iooss, Bertrand
  • Van Dorpe, François
  • Volkova, Elena

Abstract

Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this inconvenience consists in replacing the complex computer code by a reduced model, called a metamodel, or a response surface that represents the computer code and requires acceptable calculation time. One particular class of metamodels is studied: the Gaussian process model that is characterized by its mean and covariance functions. A specific estimation procedure is developed to adjust a Gaussian process model in complex cases (non-linear relations, highly dispersed or discontinuous output, high-dimensional input, inadequate sampling designs, etc.). The efficiency of this algorithm is compared to the efficiency of other existing algorithms on an analytical test case. The proposed methodology is also illustrated for the case of a complex hydrogeological computer code, simulating radionuclide transport in groundwater.

Suggested Citation

  • Marrel, Amandine & Iooss, Bertrand & Van Dorpe, François & Volkova, Elena, 2008. "An efficient methodology for modeling complex computer codes with Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4731-4744, June.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:10:p:4731-4744
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    Cited by:

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    3. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204, arXiv.org, revised May 2018.
    4. Betancourt, José & Bachoc, François & Klein, Thierry & Idier, Déborah & Pedreros, Rodrigo & Rohmer, Jérémy, 2020. "Gaussian process metamodeling of functional-input code for coastal flood hazard assessment," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    5. Picheny, Victor & Ginsbourger, David, 2014. "Noisy kriging-based optimization methods: A unified implementation within the DiceOptim package," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1035-1053.
    6. Marrel, Amandine & Iooss, Bertrand & Laurent, Béatrice & Roustant, Olivier, 2009. "Calculations of Sobol indices for the Gaussian process metamodel," Reliability Engineering and System Safety, Elsevier, vol. 94(3), pages 742-751.
    7. Simon Nanty & Céline Helbert & Amandine Marrel & Nadia Pérot & Clémentine Prieur, 2017. "Uncertainty quantification for functional dependent random variables," Computational Statistics, Springer, vol. 32(2), pages 559-583, June.
    8. Ge, Qiao & Ciuffo, Biagio & Menendez, Monica, 2015. "Combining screening and metamodel-based methods: An efficient sequential approach for the sensitivity analysis of model outputs," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 334-344.
    9. Touzani, Samir & Busby, Daniel, 2013. "Smoothing spline analysis of variance approach for global sensitivity analysis of computer codes," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 67-81.
    10. Ye, Dongwei & Nikishova, Anna & Veen, Lourens & Zun, Pavel & Hoekstra, Alfons G., 2021. "Non-intrusive and semi-intrusive uncertainty quantification of a multiscale in-stent restenosis model," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    11. Lee, Dongjin & Kramer, Boris, 2023. "Multifidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos-Kriging," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    12. Storlie, Curtis B. & Reich, Brian J. & Helton, Jon C. & Swiler, Laura P. & Sallaberry, Cedric J., 2013. "Analysis of computationally demanding models with continuous and categorical inputs," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 30-41.
    13. Veiga, Sébastien Da & Marrel, Amandine, 2020. "Gaussian process regression with linear inequality constraints," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    14. Christophette Blanchet-Scalliet & Céline Helbert & Mélina Ribaud & Céline Vial, 2019. "Four algorithms to construct a sparse kriging kernel for dimensionality reduction," Computational Statistics, Springer, vol. 34(4), pages 1889-1909, December.
    15. Radaideh, Majdi I. & Kozlowski, Tomasz, 2020. "Surrogate modeling of advanced computer simulations using deep Gaussian processes," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    16. Storlie, Curtis B. & Swiler, Laura P. & Helton, Jon C. & Sallaberry, Cedric J., 2009. "Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1735-1763.
    17. Echard, B. & Gayton, N. & Lemaire, M. & Relun, N., 2013. "A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 232-240.
    18. Kapusuzoglu, Berkcan & Mahadevan, Sankaran, 2021. "Information fusion and machine learning for sensitivity analysis using physics knowledge and experimental data," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    19. Marrel, A. & Marie, N. & De Lozzo, M., 2015. "Advanced surrogate model and sensitivity analysis methods for sodium fast reactor accident assessment," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 232-241.
    20. Chevalier, Clément & Picheny, Victor & Ginsbourger, David, 2014. "KrigInv: An efficient and user-friendly implementation of batch-sequential inversion strategies based on kriging," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1021-1034.
    21. Auffray, Yves & Barbillon, Pierre & Marin, Jean-Michel, 2014. "Bounding rare event probabilities in computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 153-166.
    22. Bachoc, François, 2013. "Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 55-69.
    23. Iooss, Bertrand & Le Gratiet, Loïc, 2019. "Uncertainty and sensitivity analysis of functional risk curves based on Gaussian processes," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 58-66.

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