Gradient-enhanced high dimensional model representation via Bayesian inference

Recently, gradient-enhanced surrogate models have drawn extensive attention for function approximation, in which the gradient information is utilized to improve the surrogate model accuracy. In this work, gradient-enhanced high dimensional model representation (HDMR) is established based on Bayesian inference technique. The proposed method first assigns Gaussian process prior for the model response function and its partial derivative functions (with respect to all the input variables). Then the auto-covariance functions and the cross-covariance functions of these random processes are established respectively by the HDMR basis functions. Finally, the posterior distribution of the response function is analytically obtained through Bayes theorem. The proposed method combines the sample information and gradient information in a seamless way to yield a highly accurate HDMR prediction model. We demonstrate our method via several examples, and the results all suggest that combining gradient information with sample information provides more accurate prediction results at reduced computational cost.