AMS2004-4: Parameter Space Exploration With Gaussian Process Trees

Robert B. Gramacy, Herbert K. H. Lee, William Macready
12/31/2004 09:00 AM
Applied Mathematics & Statistics
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 uses non-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.