Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data

This paper is devoted to the identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data. The experimental data sets correspond to partial experimental data made up of an observation vector which is the response of a stochastic boundary value problem depending on the tensor-valued random field which has to be identified. So an inverse stochastic problem has to be solved to carry out the identification of the random field. A complete methodology is proposed to solve this challenging problem and consists in introducing a family of prior probability models, in identifying an optimal prior model in the constructed family using the experimental data, in constructing a statistical reduced order optimal prior model, in constructing the polynomial chaos expansion with deterministic vector-valued coefficients of the reduced order optimal prior model and finally, in constructing the probability distribution of random coefficients of the polynomial chaos expansion and in identifying the parameters using experimental data. An application is presented for which several millions of random coefficients are identified solving an inverse stochastic problem.