Identification of polynomial chaos representations in high dimension from a set of realizations

Guillaume Perrin (1, 2, 3) , Christian Soize (1) , Denis Duhamel (4) , Christine Fünfschilling (3)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 navier umr 8205 - Laboratoire Navier
3 SNCF - Direction de l'Innovation et de la Recherche
4 Dynamique des structures et identification

This paper deals with the identification in high dimension of polynomial chaos expansion of random vectors from a set of realizations. Due to numerical and memory constraints, the usual polynomial chaos identification methods are based on a series of truncations that induces a numerical bias. This bias becomes very detrimental to the convergence analysis of polynomial chaos identification in high dimension. This paper therefore proposes a new formulation of the usual polynomial chaos identification algorithms to avoid this numerical bias. After a review of the polynomial chaos identification method, the influence of the numerical bias on the identification accuracy is quantified. The new formulation is then described in details, and illustrated on two examples.

Mots clés: polynomial chaos expansion; high dimension; identification; statistical inverse method; uncertainty quantification; computation

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Mécanique [physics.med-ph]

Guillaume Perrin, Christian Soize, Denis Duhamel, Christine Fünfschilling. Identification of polynomial chaos representations in high dimension from a set of realizations. SIAM Journal on Scientific Computing, 2012, 34 (6), pp.A2917-A2945. ⟨10.1137/11084950X⟩. ⟨hal-00770006⟩