Functional error modeling for uncertainty quantification in hydrogeology

Détails

Ressource 1Télécharger: BIB_66B2D2B7F80C.P001.pdf (5715.47 [Ko])
Etat: Public
Version: Author's accepted manuscript
ID Serval
serval:BIB_66B2D2B7F80C
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Functional error modeling for uncertainty quantification in hydrogeology
Périodique
Water Resources Research
Auteur(s)
Josset L., Ginsbourger D., Lunati I.
ISSN
0043-1397
Statut éditorial
Publié
Date de publication
2015
Peer-reviewed
Oui
Volume
51
Pages
1050-1068
Langue
anglais
Résumé
Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.
Open Access
Oui
Création de la notice
10/02/2015 19:05
Dernière modification de la notice
20/08/2019 15:22
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