Gaussian process modeling with boundary information

Gaussian process (GP) models are widely used to approximate time consuming deterministic computer codes, which are often models of physical systems based on partial differential equations (PDEs). Limiting or boundary behavior of the PDE solutions (e.g., behavior when an input tends to infinity) is often known based on physical considerations or mathematical analysis. However, widely used stationary GP priors do not take this information into account. It should be expected that if the GP prior is forced to reproduce the known limiting behavior, it will give better prediction accuracy and extrapolation capability. This paper shows how a GP prior that reproduce known boundary behavior of the computer model can be constructed. Real examples are given to demonstrate the improved prediction performance of the proposed approach.