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Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
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 Roosbroecks 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 MMS as research data and
opens the way towards more MKM services for models
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