A novel sparse polynomial chaos expansion technique with high adaptiveness for surrogate modelling

Abstract

In this paper, a novel adaptive modelling framework for sparse polynomial chaos expansion is proposed, which can automatically determine adequate truncation degree and training sample set simultaneously. Moreover, the curse of dimensionality issue in polynomial chaos expansion, which generally arises in dealing with high input dimension or large truncation degree, can be alleviated to a large extent. In this framework, a new basis selection strategy, which leverages basis expansion, pruning and refinement, is pursued to adaptively select the polynomial terms of proper degree during the modelling process. Besides, an outstanding sequential sampling strategy is adopted to collect samples of high quality and in relatively small quantity for training polynomial chaos expansion model, and a sparse representation method, Bayesian compressive sensing, is employed for regression calculation. To reconcile the sequential sampling and adaptive basis selection in a consistent framework, a stability evaluation process which works in parallel with the sequential sampling process is performed. The performance of the proposed adaptive modelling framework is evaluated on two benchmark functions and a physical model through comparison with an existing adaptive polynomial chaos expansion modelling technique, a sequential sampling-only approach, and several basis adaptivity strategies. Results demonstrate that the proposed method has high adaptiveness in building surrogate models for various problems. It outperforms the existing adaptive polynomial chaos expansion modelling technique in terms of modelling precision and convergence rate, and it has similar performance with the sequential sampling-only method while lessening the burden in regression calculation and enabling adaptive determination of the truncation degree. Limitations of the proposed method are also summarized after comparing it with various basis adaptivity strategies.