Using a Domain Theory to Guide Automated Modeling of Complex Physical Phenomena

Abstract

Choosing appropriate models is crucial in analyzing complex physical phenomena, especially when supercomputing resources and complex partial differential equations are involved. This paper presents an approach to formulating mathematical models guided by the structure of a domain theory and the gross behavior of a physical problem. The approach is motivated by the observation that many physical domains, though complex and computationally expensive to analyze, have strong domain theories based on a few fundamental conservation laws and well-defined physical processes. Furthermore, modeling decisions have to be guided by the behavior specific to a physical problem that the system is trying to model. By exploiting a domain theory and using problem specific behavior, the approach offers an uniform and efficient way of formulating models of various complexity, ranging from algebraic, ordinary to partial differential equations. The approach has been implemented in a computer program, MSG, and tested in the heat transfer domain.