Generating Approximate Thermal Models from Physical Principles

Ringo Ling and Louis Steinberg

This paper describes a framework and a system for generating mathematical models (i.e. sets of equations) for analyzing physical systems. The models are derived from physical principles, and include not only models based on algebraic and ordinary differential equations (i.e. "lumped" models), but also those based on partial differential equations (i.e. "distributed" models). We are motivated the need for analysis models to be used in designing artifacts, and focus on the domain of thermal manufacturing. Our framework involves three sequential subtasks: identify regions of interest on the artifact, determine and identify the relevant physical processes, transform the set of individual processes into equations and carry out mathematical simplification. We take the view that understanding the task of model generation is fundamental to our future research on approximate modeling in design.

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