Mathematical Models as Research Data via Flexiformal Theory Graphs
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. While the problems of classifying, archiving and making accessible are largely solved for data and first frameworks and systems are emerging for software, the question of how to deal with mathematical models is completely open.
In this paper we propose a solution – to cover all aspects of mathematical models: the underlying mathematical knowledge, the equations, boundary conditions, numeric approximations, and documents in a flexiformal framework, which has enough structure to support the various uses of models in scientific and technology workflows.
Concretely we propose to use the OMDoc/MMT framework to formalize mathematical models and show the adequacy of this approach by modeling a simple, but non-trivial model: van Roosbroeck’s drift-diffusion model for one-dimensional devices. This formalization – and future extensions – allows us to support the modeler by e.g., flexibly composing models, visualizing Model Pathway Diagrams, and annotating model equations in documents as induced from the formalized documents by flattening. This directly solves some of the problems in treating mathematical models as “research data” and opens the way towards more MKM services for models.
We gratefully acknowledge EU funding for the OpenDreamKit project in the Horizon 2020 framework under grant 676541. Our discussions have particularly profited from contributions by Florian Rabe (Mmt advice) and Wolfram Sperber (general math background). Finally, Marcel Rupprecht has developed the MPD viewer mentioned in Sect. 4.
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