Automated mathematical modeling from experimental data: an application to material science

Automated model formulation is a crucial issue toward the construction of computational environments that can reason about the behavior of a physical system. The procedure of mathematically modeling a given physical system is quite complex and basically involves three fundamental entities: the experimental data, a set of candidate models, and rules for determining in such a set the ''best" model that reproduces the measured data. The construction of the candidate models is domain dependent and based on specific knowledge and techniques of the application domain. The choice of the best model is guided by the data themselves; a first rough guess, which is suggested by the qualitative properties of the observed behavior, is refined through system identification techniques so that the quantitative properties of the observed behavior are assessed. Therefore, automating such a procedure requires handling and integrating different formalisms and methods, both qualitative and quantitative. This paper describes a comprehensive environment that aims at the automated formulation of an accurate quantitative model of the mechanical behavior of an actual viscoelastic material in accordance with the observed response of the material to standard experiments, To this end, algorithms and methods for both the generation of an exhaustive library of models of ideal materials and the selection of the most "accurate" model of a real material have been designed and implemented. The model selection phase occurs in two main stages; at first, the subset of most plausible candidate models for the material is drawn out from the library in accordance with the qualitative properties of the material that are highlighted by the experimental data; then, the most accurate model of the material is identified within such a set by exploiting both statistical and numerical methods.