Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines 

The ontologies for algorithms (AlgoData, light blue) and models(MathModDB, dark blue). The ontologies are connected between the Mathematical Model and the Algorithmic Problem classes

Björn Schembera, Frank Wübbeling, Hendrik Kleikamp, Christine Biedinger, Jochen Fiedler, Marco Reidelbach, Aurela Shehu, Burkhard Schmidt, Thomas Koprucki, Dorothea Iglezakis, Dominik Göddeke 

In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data, the Mathematical Research Data Initiative has developed, merged and implemented ontologies and knowledge graphs. This contributes to making mathematical research data FAIR by introducing semantic technology and documenting the mathematical foundations accordingly. Using the concrete example of microfracture analysis of porous media, it is shown how the knowledge of the underlying mathematical model and the corresponding numerical algorithms for its solution can be represented by the ontologies. 

17th International Conference on Metadata and Semantics Research
(Milano/Italy, Oct. 25-27, 2023)