Adaptive design of supercomputer experiments
Robert B. Gramacy, Herbert K. H. Lee · arXiv (Cornell University) · 2008
Computer experiments are often performed to allow modeling of a response surface of a physical experi-ment that can be too costly or difficult to run except using a simulator. Running the experiment over a dense grid can be prohibitively expensive, yet running over a sparse design chosen in advance can result in obtaining insufficient information in parts of the space, particularly when the surface is nonstation-ary. We propose an approach which automatically explores the space while simultaneously fitting the response surface, using predictive uncertainty to guide subsequent experimental runs. The newly devel-oped Bayesian treed Gaussian process is used as the surrogate model, and a fully Bayesian approach allows explicit nonstationary measures of uncertainty. Our adaptive sequential design framework has been developed to cope with an asynchronous, random, agent-based supercomputing environment. We take a hybrid approach which melds optimal strategies from the statistics literature with flexible strate-gies from the active learning literature. The merits of this approach are borne out in several examples, including the motivating example of a computational fluid dynamics simulation of rocket booster. Key words: nonstationary spatial model, treed partitioning, sequential design, active learning 1