Nested polynomial trends for the improvement of Gaussian process-based predictors

Abstract : The role of simulation has kept increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only can be not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process-based regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, which mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parameterization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.
Type de document :
Pré-publication, Document de travail
2016
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01298861
Contributeur : Guillaume Perrin <>
Soumis le : mercredi 6 avril 2016 - 17:18:39
Dernière modification le : lundi 29 mai 2017 - 14:25:08
Document(s) archivé(s) le : lundi 14 novembre 2016 - 18:29:20

Fichier

PERRIN_JCP2016.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01298861, version 1

Collections

Citation

Guillaume Perrin, Christian Soize, Josselin Garnier, Marque-Pucheu Sophie. Nested polynomial trends for the improvement of Gaussian process-based predictors. 2016. <hal-01298861>

Partager

Métriques

Consultations de
la notice

361

Téléchargements du document

76