Parameter Space Exploration with Gaussian Process Trees

Abstract

Computer experiments often require dense sweeps over input parameters toobtain a qualitative understanding of their response. Such sweeps can beprohibitively expensive, and are unnecessary in regions where the response iseasy predicted; well-chosen designs could allow a mapping of the response withfar fewer simulation runs. Thus, there is a need for computationallyinexpensive surrogate models and an accompanying method for selecting smalldesigns. We explore a general methodology for addressing this need that usesnon-stationary Gaussian processes. Binary trees partition the input space tofacilitate non-stationarity and a Bayesian interpretation provides an explicitmeasure of predictive uncertainty that can be used to guide sampling. Ourmethods are illustrated on several examples, including a motivating exampleinvolving computational fluid dynamics simulation of a NASA reentry vehicle.