Surrogate modeling of high-dimensional problems via data-driven polynomial chaos expansions and sparse partial least square

Abstract

Surrogate modeling techniques such as polynomial chaos expansion (PCE) are widely used to simulate the behavior of manufactured and physical systems for uncertainty quantification. An inherent limitation of many surrogate modeling methods is their susceptibility to the curse of dimensionality, that is, the computational cost becomes intractable for problems involving a high-dimensionality of the uncertain input parameters. In the paper, we address the issue by proposing a novel surrogate modeling method that enables the solution of high dimensional problems. The proposed surrogate model relies on a dimension reduction technique, called sparse partial least squares (SPLS), to identify the projection directions with largest predictive significance in the PCE surrogate. Moreover, the method does not require (or even assume the existence of) a functional form of the distribution of input variables, since a data-driven construction, which can ensure that the polynomial basis maintains the orthogonality for arbitrary mutually dependent randomness, is applied to surrogate modeling. To assess the performance of the method, a detailed comparison is made with several well-established surrogate modeling methods. The results show that the proposed method can provide an accurate representation of the response of high-dimensional problems.