Multi-fidelity Gaussian process modeling with boundary information

Multi-fidelity simulations are widely employed in engineering. When the simulators are time consuming to run, an autoregressive Gaussian process (AGP) model fitted with data from a nested space-filling design can be employed as emulator. However, the AGP model assumes the simulators at different levels of fidelity share the same inputs. This article considers bi-fidelity simulations with a high-fidelity (HF) simulator and a low-fidelity (LF) simulator, where the HF simulator contains a vector of inputs not shared with the LF simulator, called augmented input. The augmented input captures finer modeling details neglected by the LF simulator, and the HF simulator reduces to the LF simulator when some or all components of the augmented input tend to zero. To ensure this boundary constraint in the domain of the augmented input is satisfied, we propose a modified AGP model that uses covariance functions (CFs) constructed from covariances of integrated stochastic processes, called integrated CFs. Five families of integrated CFs are compared in two numerical examples based on finite element simulators and in numerical simulations based on four test functions with analytical forms. It is demonstrated that certain choices of integrated CFs yield substantial improvements in prediction performance attained by the modified AGP model. Matlab codes for reproducing reported results are given in the Supporting Information.