An active sparse polynomial chaos expansion approach based on sequential relevance vector machine

Abstract

Polynomial chaos expansion (PCE) is a popular surrogate modeling approach employed in uncertainty quantification for a variety of engineering problems. However, the challenges for full PCE lie in the “curse of dimensionality” of the expansion coefficients. In this paper, we propose a new sparse PCE approach by introducing active learning technique and sequence relevance vector machine (SRVM). As an active learning technique, efficient loss function based on expected improvement (EI-based ELF) is introduced to search for the best next sampling point and enrich the training samples. Relevance vector machine (RVM) is a superior machine learning technique due to the sparsity of its adopted model. SRVM leads to the maximization of marginal likelihood by sequentially selecting basis functions. To assess the performance of the proposed method, four examples are investigated, and the results show that the proposed method outperforms the classical sparse PCE in terms of both accuracy and efficiency.