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Gaussian processes (GPs) are widely used as surrogate models for emulatingcomputer code, which simulate complex physical phenomena. In many problems,additional boundary information (i.e., the behavior of the phenomena alonginput boundaries) is known beforehand, either from governing physics orscientific knowledge. While there has been recent work on incorporatingboundary information within GPs, such models do not provide theoreticalinsights on improved convergence rates. To this end, we propose a new GP model,called BdryGP, for incorporating boundary information. We show that BdryGP notonly has improved convergence rates over existing GP models (which do notincorporate boundaries), but is also more resistant to the"curse-of-dimensionality" in nonparametric regression. Our proofs make use of anovel connection between GP interpolation and finite-element modeling.

BdryGP: a new Gaussian process model for incorporating boundary information