Global sensitivity analysis using polynomial chaos expansion enhanced Gaussian process regression method

Global sensitivity analysis (GSA) is a commonly used approach to explore the contribution of input variables to the model output and identify the most important variables. However, performing GSA typically requires a large number of model evaluations, which can result in a heavy computational burden, particularly when the model is computationally expensive. To address this issue, an efficient Sobol index estimator is proposed in this paper using polynomial chaos expansion (PCE) enhanced Gaussian process regression (GPR) method, namely PCEGPR. The orthogonal polynomial functions of PCE method are incorporated into GPR surrogate model to construct the kernel function. An estimation scheme based on fixed-point iteration and leave-one-out cross-validation error is presented to determine the optimal parameters of PCEGPR method. The analytical expressions of main and total sensitivity indices are also derived by considering the posterior predictor and covariance of PCEGPR surrogate model. The effectiveness of the proposed estimator is demonstrated by four numerical examples.