Equation Model Generation: Where do Equations Come From?

Reference: Iwasaki, Y. & Doshi, K. Equation Model Generation: Where do Equations Come From? Knowledge Systems Laboratory, August, 1990.

Abstract: In all disciplines of physical and social sciences, a set of simultaneous equations is an essential tool for describing the relations that hold among parameters of objects and that govern their behavior over time. The two main stages of using equations for this purpose are (1) characterization of a system in terms of functional relations among parameters and, (2) prediction of the system behaviour using the equations through various analytic, numeric, or qualitative techniques. As the second stage has been studied extensively in many fields including applied mathematics and numerical simulation, there exist many computer programs for performing the second stage. Compared to the second stage, much less attempts have been made to automate the first stage. Some of the reasons for this are: 1. Model building is a process that requires a large amount of knowledge of the domain under study. 2. Appropriate selection of parameters and equations also requires much heuristic and commonsense knowledge in order to determine the appropriate set of phenomena to model and the temporal grain size depending on the goal of the analysis [4,8]. This paper discusses different types of physical knowledge required for model generation. The paper will then focus on two issues is particular that we have found problematic in model building. As principles to guide the model generation process, de Kleer and Brown have stressed the importance of locality principle and no-function-in-structure principle [1]. Forbus has put forth the process-oriented approach [3], and Iwasaki and Simon require that model equations to be structural [6]. After studying the various sources of equations, we think that none of these principles alone is sufficient nor has been articulated well enough to allow systematic construction of models. One reason for this is that what is considered to be processes, mechanisms, components, and connections can vary widely from domain to domain. Also, even when one limits the problem to a particular domain, what is an appropriate model still deppends on the levels of abstraction and what are considered to be the primitives at each level. We need more detailed examination of different types of physical principles underlying equations and further refinement of these principles in order to formulate a computation tehory of model generation.

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