An efficient and robust adaptive sampling method for polynomial chaos expansion in sparse Bayesian learning framework

Abstract

Sparse polynomial chaos expansion has been widely used to tackle problems of function approximation in the field of uncertain quantification. The accuracy of PCE depends on how to construct the experimental design. Therefore, adaptive sampling methods of designs of experiment are raised. Classic designs of experiment for PCE are based on least-square minimization techniques, where the design space is only defined by the inputs without involving the responses of the system. To overcome this limitation, a novel adaptive sampling method is introduced in sparse Bayesian learning framework. The design point is enriched sequentially by maximizing a generalized expectation of loss function criterion which allows an effective use of all the information available, on which two adaptive strategies are derived to get a balance between the global exploration and the local exposition via the error information from the previous iteration. The numerical results show that the proposed method is superior to classic design of experiment in terms of efficiency and robustness.