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Gaussian process regression of two nested computer codes

Abstract : This thesis deals with the Gaussian process regression of two nested codes. The term "nested codes" refers to a system of two chained computer codes: the output of the first code is one of the inputs of the second code. The two codes are computationally expensive. In order to perform a sensitivity analysis, we aim at emulating the output of the nested code from a small number of observations. Three types of observations of the system exist: those of the chained code, those of the first code only and those of the second code only. The surrogate model has to be accurate on the most likely regions of the input domain of the nested code. In this work, the surrogate models are constructed using the Universal Kriging framework, with a Bayesian approach. First, the case when there is no information about the intermediary variable (the output of the first code) is addressed. An innovative parametrization of the mean function of the Gaussian process modeling the nested code is proposed. It is based on the coupling of two polynomials. Then, the case with intermediary observations is addressed. A stochastic predictor based on the coupling of the predictors associated with the two codes is proposed. Methods aiming at computing quickly the mean and the variance of this predictor are proposed. Finally, the methods obtained for the case of codes with scalar outputs are extended to the case of codes with high dimensional vectorial outputs. We propose an efficient dimension reduction method of the high dimensional vectorial input of the second code in order to facilitate the Gaussian process regression of this code. All the proposed methods are applied to numerical examples.
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Contributor : Sophie Marque-Pucheu <>
Submitted on : Sunday, October 27, 2019 - 6:23:33 PM
Last modification on : Thursday, March 26, 2020 - 9:25:56 PM


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  • HAL Id : tel-02092072, version 3




Sophie Marque-Pucheu. Gaussian process regression of two nested computer codes. Mathematics [math]. Université Paris-Diderot - Paris VII, 2018. English. ⟨tel-02092072v3⟩



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