A Challenging problem: Identification of Bayesian posteriors of high-dimension polynomial chaos expansions of random fields using partial and limited experimental data

Abstract : We propose an approach to solve the very challeging problem relative to the use of the Bayesian methods for identifying the posterior probability model of the random coefficients of the polynomial chaos expansion in very high dimension (several millions of random coefficients). The available experimental data are assumed to be partial and limited, and are made up of partial observations of the reponses of a stochastic boundary value problem for which the parameter which must be identified is an unknown non-Gaussian tensor-valued random field which is represented by the high-dimension polynomial chaos expansion. The complete methodology is presented and is applied to a three dimensional elastic microstructure constituted of a non-homogeneous and anisotropic linear elastic material.