Surrogate modeling based on resampled polynomial chaos expansions

Abstract : In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the randommodel responses, which are computationally expensive and usually obtained by deterministic numericalmodeling approaches including finite-element and finite-difference time-domain methods. Recently, eortshave been made on improving the prediction performance of the PCE-based model and building efficiencyby only selecting the influential basis polynomials (e.g., via the approach of least angle regression). Thispaper proposes an approach, named as resampled PCE (rPCE), to further optimize the selection by makinguse of the knowledge that the true model is fixed despite the statistical uncertainty inherent to samplingin the training. By simulating data variation via resampling (k-fold division utilized here) and collectingthe selected polynomials with respect to all resamples, polynomials are ranked mainly according to theselection frequency. The resampling scheme (the value of k here) matters much and various configurationsare considered and compared. The proposed resampled PCE is implemented with two popular selectiontechniques, namely least angle regression and orthogonal matching pursuit, and a combination thereof. Theperformance of the proposed algorithm is demonstrated on two analytical examples, a benchmark problemin structural mechanics, as well as a realistic case study in computational dosimetry.