Abstract
With advances in mathematical modeling and computational methods, complex phenomena (e.g., universe formations, rocket propulsion) can now be reliably simulated via computer code. This code solves a complicated system of equations representing the underlying science of the problem. Such simulations can be very time-intensive, requiring months of computation for a single run. Gaussian processes (GPs) are widely used as predictive models for “emulating” this expensive computer code. Yet with limited training data on a high-dimensional parameter space, such models can suffer from poor predictive performance and poor interpretability. Fortunately, in many physical applications, there is additional boundary information on the code beforehand, either from governing physics or scientific knowledge. We propose a new BdryGP model which incorporates such boundary information for prediction. We show that BdryGP enjoys improved convergence rates over standard GP models which do not incorporate boundaries. We then demonstrate the improved predictive performance and posterior contraction of the BdryGP model on a suite of numerical experiments and a real-world application.