MathModDB is a database of mathematical models developed by the Mathematical Research Data Initiative (MaRDI). MathModDB defines a data model with classes (Mathematical Model, Mathematical Formulation, Acadmic Discipline, Research Problem, Quantity [Kind], Computational Task, Publication), object properties/relations, data properties and annotation properties as an ontology. This ontology is populated with individuals/data from various fields of applied mathematics, making it a knowledge graph.
For more detailed information on the ontology and the knowledge graph please refer to the MathModDB page on the MaRDI portal. For a high level description and evolutionary history of MathModDB please refer to our papers listed in the References subsection.
This version is in OWL and automatically generated from the MaRDI Portal version, which is always the most up-to-date version. The portal version is powered by the Wikibase technology.
Version 2.0.0
Released on 2026-07-28
- Aurela Shehu, Weierstrass Institute Berlin for Applied Analysis and Stochastics
- Björn Schembera, University of Stuttgart
- Burkhard Schmidt, Weierstrass Institute Berlin for Applied Analysis and Stochastics
- Christine Biedinger, Fraunhofer Institute for Industrial Mathematics ITWM
- Jochen Fiedler, Fraunhofer Institute for Industrial Mathematics ITWM
- Marco Reidelbach, Zuse Institute Berlin
- Thomas Koprucki, Weierstrass Institute Berlin for Applied Analysis and Stochastics
The ontology and the data included is represented in OWL, serialized as RDF/XML in the two files in this repository.
MathModDB.owlis the version as designed by the MathModDB team members. This "lean" version includes, for example, only one direction of object property relations -- the other direction can be easily inferred automatically by a reasoner, if the inverses are defined.
These files can opened with Protégé or any other tool for that purpose.
A detailed description of the main concepts, classes and relations of the ontology as well as their individuals can be found on https://mardi4nfdi.github.io/MathModDB/. This documentation is created with Widoco. More high level descriptions can be found in the References section.
An educational toy example where MathModDB is used to model falling apples (as described here) can be found on the branch tutorial_material, where the only individuals are those needed for the example.
In case you are refering to or using MathModDB, please use the following citation:
Shehu, A., Schembera, B., Schmidt, B., Biedinger, C., Fiedler, J., Reidelbach, M., Koprucki, T. (2025): MathModDB - An Ontology and Knowledge Graph for Mathematical Models. https://doi.org/10.5281/zenodo.14887915
Schembera, B., Wübbeling, F., Kleikamp, H., Schmidt, B., Shehu, A., Reidelbach, M., Biedinger, C., Fiedler, J., Koprucki, T., Iglezakis, D. and Göddeke, D., 2025. Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics. In Research Conference on Metadata and Semantics Research (pp. 95–109). Springer Nature. https://doi.org/10.1007/978-3-031-81974-2_8
Schembera, B., Wübbeling, F., Kleikamp, H., Biedinger, C., Fiedler, J., Reidelbach, M., Shehu, A., Schmidt, B., Koprucki, T., Iglezakis, D. and Göddeke, D., 2024. Ontologies for models and algorithms in applied mathematics and related disciplines. In Research Conference on Metadata and Semantics Research (pp. 161-168). Cham: Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-65990-4_14
Schembera, B., Wübbeling, F., Koprucki, T., Biedinger, C., Reidelbach, M., Schmidt, B., Göddeke, D. and Fiedler, J., 2023, September. Building Ontologies and Knowledge Graphs for Mathematics and its Applications. In Proceedings of the Conference on Research Data Infrastructure (Vol. 1). https://doi.org/10.52825/cordi.v1i.255
The ontology MathModDB is licensed under CC-BY 4.0.
The work has been funded by the DFG (German Research Foundation), project number 460135501, NFDI 29/1 “MaRDI – Mathematische Forschungsdateninitiative”.
