Equation model generation: where do equations come from?

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[[abstract::In all disciplines of physical and social sciences, a set of simultaneousequations is an essential tool for describing the relations that hold amongparameters of objects and that govern their behavior over time. The two mainstages of using equations for this purpose are (1) characterization of asystem in terms of functional relations among parameters and, (2) predictionof the system behaviour using the equations through various analytic, numeric,or qualitative techniques. As the second stage has been studied extensivelyin many fields including applied mathematics and numerical simulation, thereexist many computer programs for performing the second stage. Compared to thesecond 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 ofthe domain under study.2. Appropriate selection of parameters and equations also requires muchheuristic and commonsense knowledge in order to determine the appropriate setof phenomena to model and the temporal grain size depending on the goal of theanalysis [4,8].This paper discusses different types of physical knowledge required for modelgeneration. The paper will then focus on two issues is particular that wehave found problematic in model building.As principles to guide the model generation process, de Kleer and Brown havestressed the importance of locality principle and no-function-in-structureprinciple [1]. Forbus has put forth the process-oriented approach [3], andIwasaki and Simon require that model equations to be structural [6]. Afterstudying the various sources of equations, we think that none of theseprinciples alone is sufficient nor has been articulated well enough to allowsystematic construction of models. One reason for this is that what isconsidered to be processes, mechanisms, components, and connections can varywidely from domain to domain. Also, even when one limits the problem to aparticular domain, what is an appropriate model still deppends on the levelsof abstraction and what are considered to be the primitives at each level. Weneed more detailed examination of different types of physical principlesunderlying equations and further refinement of these principles in order toformulate a computation tehory of model generation.|]]

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abstract: In all disciplines of physical and social sciences, a set of simultaneousequations is an essential tool for describing the relations that hold amongparameters of objects and that govern their behavior over time. The two mainstages of using equations for this purpose are (1) characterization of asystem in terms of functional relations among parameters and, (2) predictionof the system behaviour using the equations through various analytic, numeric,or qualitative techniques. As the second stage has been studied extensivelyin many fields including applied mathematics and numerical simulation, thereexist many computer programs for performing the second stage. Compared to thesecond 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 ofthe domain under study.2. Appropriate selection of parameters and equations also requires muchheuristic and commonsense knowledge in order to determine the appropriate setof phenomena to model and the temporal grain size depending on the goal of theanalysis [4,8].This paper discusses different types of physical knowledge required for modelgeneration. The paper will then focus on two issues is particular that wehave found problematic in model building.As principles to guide the model generation process, de Kleer and Brown havestressed the importance of locality principle and no-function-in-structureprinciple [1]. Forbus has put forth the process-oriented approach [3], andIwasaki and Simon require that model equations to be structural [6]. Afterstudying the various sources of equations, we think that none of theseprinciples alone is sufficient nor has been articulated well enough to allowsystematic construction of models. One reason for this is that what isconsidered to be processes, mechanisms, components, and connections can varywidely from domain to domain. Also, even when one limits the problem to aparticular domain, what is an appropriate model still deppends on the levelsof abstraction and what are considered to be the primitives at each level. Weneed more detailed examination of different types of physical principlesunderlying equations and further refinement of these principles in order toformulate a computation tehory of model generation.

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