Physical Experimental Design in Support of Computer Model Development
Max D. Morris · Technometrics · 2014
Computer models of physical systems are often written based on known theory or “first principles” of a system, reflecting substantial knowledge of each component or subsystem, but also the need to use a numerical approach to mimic the more complex behavior of the entire system of interest. However, in some cases, there is insufficient known theory to encode all necessary aspects of the system, and empirical studies are required to generate approximate functional forms. We consider the question of how a physical experiment might be designed to approximate one module or subroutine of a computer model that can otherwise be written from first principles. The concept of preposterior analysis is used to suggest an approach to generating a kind of I-optimal design for this purpose, when the remainder of the computer model is a composition of nonlinear functions that can be directly evaluated as part of the design process. Extensions are then described for situations in which one or more known components must themselves be approximated by metamodels due to the large number of evaluations needed, and for computer models that have iterative structure. A simple “toy” model is used to demonstrate the ideas. Online supplementary material accompanies this article.