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Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics

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Metadata and Semantic Research (MTSR 2024)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 2331))

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Abstract

Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. To make this research data FAIR, we present how two previously distinct ontologies, MathAlgoDB for algorithms and MathModDB for models, were merged and extended into a living knowledge graph as the key outcome. This was achieved by connecting the ontologies through computational tasks that correspond to algorithmic tasks. Moreover, we show how models and algorithms can be enriched with subject-specific metadata, such as matrix symmetry or model linearity, essential for defining workflows and determining suitable algorithms. Additionally, we propose controlled vocabularies to be added, along with a new class that differentiates base quantities from specific use case quantities. We illustrate the capabilities of the developed knowledge graph using two detailed examples from different application areas of applied mathematics, having already integrated over 250 research assets into the knowledge graph.

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Notes

  1. 1.

    https://www.wikidata.org/wiki/Q2465832.

  2. 2.

    https://orkg.org/fields.

  3. 3.

    https://qudt.org/vocab/quantitykind/Voltage.

  4. 4.

    https://www.wikidata.org/wiki/Q25428.

  5. 5.

    https://portal.mardi4nfdi.de/wiki/Portal.

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Acknowledgments

The co-authors C.B., J.F., M.R., A.S., B.S., B.S. acknowledge funding by MaRDI, funded by the DFG (German Research Foundation), project number 460135501, NFDI 29/1 “MaRDI - Mathematische Forschungsdateninitiative”. The co-authors H.K. and F.W. acknowledge funding by the DFG under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics- Geometry- Structure.The co-author D.G. acknowledges funding by the DFG under Germany’s Excellence Strategy EXC 2075: Data-Integrated Simulation Science (SimTech), project number 390740016.

Author information

Authors and Affiliations

  1. Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Stuttgart, Germany

    Björn Schembera & Dominik Göddeke

  2. Institute of Applied Mathematics: Analysis and Numerics, University of Münster, Münster, Germany

    Frank Wübbeling & Hendrik Kleikamp

  3. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Burkhard Schmidt, Aurela Shehu & Thomas Koprucki

  4. Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany

    Christine Biedinger & Jochen Fiedler

  5. Mathematics of Complex Systems, Zuse Institute Berlin, Berlin, Germany

    Marco Reidelbach

  6. University Library, University of Stuttgart, Stuttgart, Germany

    Dorothea Iglezakis

  7. Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, Stuttgart, Germany

    Dominik Göddeke

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  1. Björn Schembera
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Correspondence to Björn Schembera .

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Editors and Affiliations

  1. Ionian University, Corfu, Greece

    Michalis Sfakakis

  2. International Hellenic University, Thessaloniki, Greece

    Emmanouel Garoufallou

  3. Ionian University, Corfu, Greece

    Matthew Damigos

  4. Kent State University, Kent, OH, USA

    Athena Salaba

  5. National and Kapodistrian University of Athens, Athens, Greece

    Christos Papatheodorou

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Schembera, B. et al. (2025). Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics. In: Sfakakis, M., Garoufallou, E., Damigos, M., Salaba, A., Papatheodorou, C. (eds) Metadata and Semantic Research. MTSR 2024. Communications in Computer and Information Science, vol 2331. Springer, Cham. https://doi.org/10.1007/978-3-031-81974-2_8

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