Automated selection of an accurate model of a visco-elastic material

A major problem in the development of a computational environment that can reason about physical systems is its ability to formulate a model. The work here described is part of a research effort aimed at developing a comprehensive environment that automates the formulation of the constitutive law of an actual visco-elastic material. In outline, we approached the problem in two main stages: at first, a library of models of ideal materials is generated, and then an accurate model of an actual material, which explains the observed response of the material to standard experiments, is selected. The models library includes both models of ideal materials and their qualitative response to standard experiments. The models are generated in two different formalisms (Rheological Formulae (RF) and Ordinary Differential Equations (ODE)), by following an enumerative procedure and an approach which is grounded both on a component-connection paradigm and on internal state variables. A class of candidate models, i.e. a class of ODEs, for the material is selected from the model space through the comparison of the observed behavior, qualitatively interpreted, with the qualitative behaviors generated directly from the rheological structures. Then, the most ``accurate'' model for the real material is chosen within the selected class so that both the goodness of experimental data fitting and the number of parameters in the model are ``reasonable''. This paper mainly concentrates on the methods and algorithms, both qualitative and quantitative, of model selection.