@inproceedings{SchemberaWuebbelingKleikampetal.2025, author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Kleikamp, Hendrik and Schmidt, Burkhard and Shehu, Aurela and Reidelbach, Marco and Biedinger, Christine and Fiedler, Jochen and Koprucki, Thomas and Iglezakis, Dorothea and G{\"o}ddeke, Dominik}, title = {Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics}, volume = {2331}, booktitle = {Metadata and Semantic Research. MTSR 2024}, publisher = {Springer Nature Switzerland}, address = {Cham}, isbn = {9783031819735}, issn = {1865-0929}, doi = {10.1007/978-3-031-81974-2_8}, pages = {95 -- 109}, year = {2025}, 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.}, language = {en} } @inproceedings{SchemberaWuebbelingKleikampetal.2023, author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Kleikamp, Hendrik and Biedinger, Christine and Fiedler, Jochen and Reidelbach, Marco and Shehu, Aurela and Schmidt, Burkhard and Koprucki, Thomas and Iglezakis, Dotothea and G{\"o}ddeke, Dominik}, title = {Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines}, booktitle = {Metadata and Semantic Research - MTSR 2023}, edition = {Communications in Computer and Information Science}, publisher = {Springer Nature Switzerland}, address = {Cham}, arxiv = {http://arxiv.org/abs/2310.20443}, doi = {10.1007/978-3-031-65990-4_14}, pages = {161 -- 168}, year = {2023}, abstract = {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.}, language = {en} } @article{SchemberaWuebbelingKopruckietal.2023, author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Koprucki, Thomas and Biedinger, Christine and Reidelbach, Marco and Schmidt, Burkhard and G{\"o}ddeke, Dominik and Fiedler, Jochen}, title = {Building Ontologies and Knowledge Graphs for Mathematics and its Applications}, volume = {1}, journal = {Proceedings of the Conference on Research Data Infrastructure}, publisher = {TIB Open Publishing}, issn = {2941-296X}, doi = {10.52825/cordi.v1i.255}, year = {2023}, abstract = {Ontologies and knowledge graphs for mathematical algorithms and models are presented, that have been developed by the Mathematical Research Data Initiative. This enables FAIR data handling in mathematics and the applied disciplines. Moreover, challenges of harmonization during the ontology development are discussed.}, language = {en} } @article{SchemberaWuebbelingShehuetal.2025, author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Shehu, Aurela and Biedinger, Christine and Fiedler, Jochen and Reidelbach, Marco and Schmidt, Burkhard and Ferrer, Eloi and Koprucki, Thomas}, title = {FAIR Representation of Mathematical Research Data: MathModDB and MathAlgoDB as Knowledge Graphs for Mathematical Models and Numerical Algorithms}, journal = {2nd Conference on Research Data Infrastructure (CoRDI)}, doi = {10.5281/zenodo.16735911}, year = {2025}, language = {en} }