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An efficient dimension reduction for the Gaussian process emulation of two nested codes with functional outputs

Author

Listed:
  • Sophie Marque-Pucheu

    (CEA/DAM/DIF
    Université Paris Diderot)

  • Guillaume Perrin

    (CEA/DAM/DIF)

  • Josselin Garnier

    (Ecole Polytechnique)

Abstract

In this paper, we first propose an efficient method for the dimension reduction of the functional input of a code with functional output. It is based on the approximation of the output by a model which is linear with respect to the functional input. This approximation has a sparse structure, whose parameters can be accurately estimated from a small set of observations of the code. The Gaussian predictor based on this projection basis is significantly more accurate than the one based on a projection obtained with Partial Least Squares. Secondly, the surrogate modeling of two nested codes with functional outputs is considered. In such a case, the functional output of the first code is one of the inputs of the second code. The Gaussian process regression of the second code is performed using the proposed dimension reduction. A Gaussian predictor of the nested code is obtained by composing the predictors of the two codes and linearizing this composition. Moreover, two sequential design criteria are proposed. Since we aim at performing a sensitivity analysis, these criteria are based on a minimization of the prediction variance. Moreover, one of the criteria enables to choose, if it is possible, which of the two codes to run. Thus, the computational budget is optimally allocated between the two codes and the prediction error is substantially reduced.

Suggested Citation

  • Sophie Marque-Pucheu & Guillaume Perrin & Josselin Garnier, 2020. "An efficient dimension reduction for the Gaussian process emulation of two nested codes with functional outputs," Computational Statistics, Springer, vol. 35(3), pages 1059-1099, September.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:3:d:10.1007_s00180-019-00926-7
    DOI: 10.1007/s00180-019-00926-7
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    References listed on IDEAS

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    1. S. Conti & J. P. Gosling & J. E. Oakley & A. O'Hagan, 2009. "Gaussian process emulation of dynamic computer codes," Biometrika, Biometrika Trust, vol. 96(3), pages 663-676.
    2. 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.
    3. Higdon, Dave & Gattiker, James & Williams, Brian & Rightley, Maria, 2008. "Computer Model Calibration Using High-Dimensional Output," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 570-583, June.
    4. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
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