Adaptive Design and Analysis Via Partitioning Trees for Emulation of a Complex Computer Code

Abstract

Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the model. Gaussian process regression has been the almost ubiquitous choice for a fast statistical emulator for such a computer model, due to its flexible form and analytical expressions for measures of predictive uncertainty. However, even this statistical emulator can be computationally intractable for large designs, due to computing time increasing with the cube of the design size. Multiple methods have been proposed for addressing this problem. We discuss several of them, and compare their predictive and computational performance in several scenarios. We propose solving this problem using a new method, adaptive design and analysis via partitioning trees (ADAPT). The new approach is motivated by the idea that most computer models are only complex in particular regions of the input space. By taking a data-adaptive approach to the development of a design, and choosing to partition the space in the regions of highest variability, we obtain a higher density of points in these regions and hence accurate prediction. Supplemental files for this article are available online.