Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

José Daniel Betancourt (1, 2) , François Bachoc (1) , Thierry Klein (2, 1) , Déborah Idier (3) , Rodrigo Pedreros (3) , Jeremy Rohmer (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 ENAC - Ecole Nationale de l'Aviation Civile
3 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)

In this article we investigate the construction of metamodels when the numerical code has functional inputs. We compare diverse Gaussian process metamodeling approaches that take into account the functional structure of the data. We discuss two methods to tune the dimension of the projection when functional inputs are decomposed on a functional basis: (i) based on the error of the projection; (ii) based on the performance of the metamodel. We further propose a methodology that allows to detect the optimal projection of the input function. We apply this methodology to the real case study of coastal flooding in the peninsula of Gâvres. Results show that the approach based on the error of the projection, being the common practice nowadays, may lead to unnecessarily large projection dimensions. In contrast, the approach based on metamodel performance presents the virtue of directly pointing to the final objective of building a fast and accurate metamodel.

Mots clés: Computer code experiments; Metamodeling; Functional inputs; Gaussian processes

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

José Daniel Betancourt, François Bachoc, Thierry Klein, Déborah Idier, Rodrigo Pedreros, et al.. Gaussian process metamodeling of functional-input code for coastal flood hazard assessment. 2019. ⟨hal-01998724v1⟩