An integrated quantitative-qualitative approach to automated modeling of visco-elastic materials from experimental data

This paper illustrates, through a case study in the domain of Material Science, how AI and Mathematics techniques can be suitably combined within a unified and robust approach to provide an intelligent tool for modeling. Given a physical system, the modeling problem we address consists in finding an adequate mathematical description (the constitutive equation) R(s,e)=0 of the cause-effect relation between two state variables s(t), e(t) , where e(t) is the response elicited on the system by an input signal s(t) applied over time t. The model structure, i.e. the mathematical form of operator R, is closely related to the physical domain knowledge and the modeling assumptions. Much of the modeling activity performed by the skilled human expert regards the definition of the model space, that is the set of all the model structures constrained by the physical and modeling assumptions. The process of obtaining, usually through an optimization loop and parameter estimation techniques, from a given set of candidate model structures and experimental data, the "best performing" quantitative model is called as a whole System Identification (SI).