Leibniz MMS Days 2018 - Abstract
Koprucki, Thomas
Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines. It is common to categorize the involved numerical data and to some extent the corresponding scientific software as research data. But both have their origin in mathematical models, therefore any holistic approach to research data in MMS should cover all three aspects: data, software, and models.
However, finding an appropriate representation for models is far less obvious than for numerical data and software. The current practice of representing models is a mixture of mathematical formulae and natural language in scientific publications. This (rigorous, but) informal approach creates ambiguity, potential incompleteness of the presentation, less reproducibility and often "re-invention of the wheel".
We present a concept for a machine-actionable as well as human-understandable of mathematical models based on Model Pathway Diagrams (MPD). MPDs specify the physical quantities that are described in the model as well as the relations between them (laws, constitutive equations) and informal documentation about them. MPDs provide a visual tool for understanding the structural properties of models as well as algorithms for numerical simulations.
For a formalized representation of mathematical models and their underlying physics, we use the OMDoc/MMT, a special machine-readable description language for mathematical documents, that allows specifying the mathematical vocabulary of models, i.e. the concepts, their properties, and relations.
We illustrate our approach by application to the van Roosbroeck system describing the carrier transport in semiconductors by drift and diffusion. We introduce an approach for the block-based composition of models from simpler components.