Identification of Polynomial Chaos Representations in High Dimension from a Set of Realizations

This paper deals with the identification in high dimensions of a 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 induce a numerical bias. This bias becomes very detrimental to the convergence analysis of polynomial chaos identification in high dimensions. 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 detail and illustrated using two examples.