Interpretability in the modeling spectrum: A conceptual framework and a quantification index

This paper addresses the challenge of enhancing interpretability in the construction of mathematical models, which are essential for understanding and optimizing complex systems. The primary motivation lies in the need to establish a common conceptual framework across the modeling spectrum and to improve the interpretability of mathematical models, particularly in the context of first principles based semi-physical models (FPBSM). The importance of physical interpretation in models, especially within biotechnological or ecological processes, is highlighted, starting from the difficulty in establishing clear boundaries when searching for constitutive equations in such models, while maintaining a balance between fit accuracy and model interpretability. To meet this challenge, we propose a novel conceptual framework for addressing interpretability within the mathematical modeling spectrum and introduce a mathematical index for quantifying interpretability in FPBSM. Furthermore, the existing modeling methodology is extended by integrating interpretability as an additional criterion in determining the level of specification at which the search for constitutive equations should be stopped. The utility of the index and the proposed methodology is evaluated using a growth model of the grapevine moth (Lobesia botrana).