An ontological conceptualization of multiscale models

Multiscale modeling has recently been widely used in various fields of science and engineering. A few research efforts have attempted to generalize existing applications mainly by means of classifying multiscale modeling paradigms, to reach a general understanding of multiscale modeling. However, these existing efforts have been largely inductive and abstracting from the applications the researchers were familiar with. This has inevitably caused inconsistencies within the results of different researchers. Further, existing work has not provided a precise definition for the fundamental concepts such as scale, which arguably has been the main source of confusion. In this work, we attempt to address this issue through developing a coherent conceptualization framework. Instead of starting with existing applications, our work is built upon a conceptualization of general systems, from which precise definitions of scale and inter-scale relations are derived. This is further followed by a precise specification of the composition of a multiscale model and subsequently a classification of multiscale models, all through rigorous definitions. This conceptualization framework is represented in form of an ontology by means of a set-theoretic language. It reuses part of an existing ontology (the BWW ontology). The key concepts in this framework are illustrated through two modeling examples judiciously chosen from the field of chemical engineering. In comparison with existing results, the key contribution of this framework is not a classification but rather a generic conceptual foundation for a better understanding of multiscale modeling, which is intended to be sharable by researchers from different backgrounds. On the other hand, it is demonstrated that a rigorously defined classification can be derived from this conceptual foundation. It is also shown that the classifications of multiscale modeling proposed in other works can be interpreted by means of the suggested conceptualization framework in a precise manner.