Partial gradient-enhanced multi-output sparse polynomial chaos expansion method for model representation

Polynomial chaos expansion (PCE) serves as a common surrogate model to approximate the computational models. Two typical strategies for enhancing surrogate model performance involve integrating the distinct outputs and model gradients. However, incorporating both types of information into the PCE method presents a significant challenge in terms of computational efforts. To address this challenge, a partial gradient-enhanced multi-output sparse PCE (PGMSPCE) surrogate model is proposed. Inspired by the multivariate Gaussian process, a gradient-enhanced multi-output sparse PCE method is derived by incorporating the multi-output correlation and gradient information. A fixed-point iteration scheme is derived to estimate the optimal hyper-parameters and induce a sparse structure. Additionally, a screening strategy based on multi-output derivative-based sensitivity index is developed to assess the impact of input variables on model outputs. Subsequently, the partial set of gradient information, corresponding to the significant input variables, is selected to construct PGMSPCE, thereby reducing computational efforts. The benchmark functions and an engineering example verify the performance of PGMSPCE, which indicates that PGMSPCE makes a tradeoff between efficiency and accuracy for model representation.