A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry

Pierric Kersaudy 1, 2 Bruno Sudret 3, 4 Nadège Varsier 2 Odile Picon 1 Joe Wiart 2
1 ESYCOM - Electronique, Systèmes de communication et Microsystèmes
2 Whist Lab
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
4 ETH Zürich - Eidgenössische Technische Hochschule [Zürich]
Abstract : In numerical dosimetry, the recent advances in high performance computing led to a strong reduction of the required computational time to assess the specific absorption rate (SAR) characterizing the human exposure to electromagnetic waves. However, this procedure remains time-consuming and a single simulation can request several hours. As a consequence, the influence of uncertain input parameters onto the SAR cannot be analyzed using crude Monte Carlo simulation. The solution presented here to perform such an analysis is surrogate modeling. This paper proposes a novel approach to build such a surrogate model from a design of experiments. Considering a sparse representation of the polynomial chaos expansions using least-angle regression as a selection algorithm to retain the most influential polynomials, this paper proposes to use the selected polynomials as regression functions for the universal Kriging model. The leave-one-out cross validation is used to select the optimal number of polynomials in the deterministic part of the Kriging model. The proposed approach, called LARS-Kriging-PC modeling, is applied onto three benchmark examples and then onto a full-scale metamodeling problem involving the exposure of a numerical fetus model to a femtocell device. The performances of the LARS-Kriging-PC are compared to an ordinary Kriging model and to a classical sparse polynomial chaos expansion. The LARS-Kriging-PC appears to have better performances than the two other approaches. A significant accuracy improvement is observed compared to the ordinary Kriging or to the sparse polynomial chaos depending on the studied case. This approach seems to be an optimal solution between the two other classical approaches. A global sensitivity analysis is finally performed onto the LARS-Kriging-PC model of the fetus exposure problem.
Keywords : polynomial chaos expansions Kriging least-angle regression dosimetry specific absorption rate
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Article dans une revue
Journal of Computational Physics, Elsevier, 2015, 286, pp.130-117. 〈10.1016/j.jcp.2015.01.034〉
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Pierric Kersaudy, Bruno Sudret, Nadège Varsier, Odile Picon, Joe Wiart. A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry. Journal of Computational Physics, Elsevier, 2015, 286, pp.130-117. 〈10.1016/j.jcp.2015.01.034〉. 〈hal-01143146〉

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