Optimized sparse polynomial chaos expansion with entropy regularization

Abstract

Sparse Polynomial Chaos Expansion (PCE) is widely used in various engineering fields to quantitatively analyse the influence of uncertainty, while alleviating the problem of dimensionality curse. However, current sparse PCE techniques focus on choosing features with the largest coefficients, which may ignore uncertainties propagated with high order features. Hence, this paper proposes the idea of selecting polynomial chaos basis based on information entropy, which aims to retain the advantages of existing sparse techniques while considering entropy change as output uncertainty. A novel entropy-based optimization method is proposed to update the state-of-the-art sparse PCE models. This work further develops an entropy-based synthetic sparse model, which has higher computational efficiency. Two benchmark functions and a computational fluid dynamics (CFD) experiment are used to compare the accuracy and efficiency between the proposed method and classical methods. The results show that entropy-based methods can better capture the features of uncertainty propagation, improving accuracy and reducing sparsity while avoiding over-fitting problems.