Parameter space exploration with Gaussian process trees

Computer experiments often require dense sweeps over input parameters to obtain a qualitative understanding of their response. Such sweeps can be prohibitively expensive, and are unnecessary in regions where the response is easy predicted; well-chosen designs could allow a mapping of the response with far fewer simulation runs. Thus, there is a need for computationally inexpensive surrogate models and an accompanying method for selecting small designs. We explore a general methodology for addressing this need that uses non-stationary Gaussian processes. Binary trees partition the input space to facilitate non-stationarity and a Bayesian interpretation provides an explicit measure of predictive uncertainty that can be used to guide sampling. Our methods are illustrated on several examples, including a motivating example involving computational fluid dynamics simulation of a NASA reentry vehicle.

• Type: Conference
• Year: 2004
• Where: ICML
• Authors: Robert B. Gramacy, Herbert K. H. Lee, William G. Macready
• Keywords: Fewer Simulation Runs, Fluid Dynamics Simulation, ICML 2004, Machine Learning, Non-stationary Gaussian Processes