Useful properties of phenomenological-based models

Abstract

This work compiles the conceptual and practical proposals of various research groups regarding interesting properties of mathematical models. Although different types of mathematical models are mentioned, phenomenological-based semi-physical models (PBSM) are the main focus of this paper. The partitioning of the process to be modeled, the scalability of the model, and the interpretability of its parameters are presented as important properties of the model that help to understand and use the mathematical model. The use of these properties is illustrated with examples, providing the respective bibliographical reference where an expanded presentation of each example can be reviewed. The importance of each model property presented is explained from the inherent condition of the model as a mathematical object and from the expectation of the final users of the model. The confidence in the model is increased when the user knows how the model is obtained. These properties provide valuable information to the end use of the model. Therefore, the modeler must understand and apply this knowledge during model deduction and write, in the model report, how the mentioned properties were tested.