MathModDB: Difference between revisions

Latest revision as of 12:17, 24 July 2025

Proper documentation and storage of research data, adhering to FAIR principles, are crucial for reproducibility and scientific integrity. Applied mathematics, producing diverse numerical and symbolic data, heavily relies on models that must be well-documented for replication and future use. Here, we present MathModDB, an ontology for mathematical models, along with a knowledge graph containing over 1200 elements. The work is conducted within the NFDI project entitled Mathematical Research Data Initiative (MaRDI).

MathModDB is a database of mathematical models developed by MaRDI's Task Area 4 as an ontology/knowledge graph. MathModDB defines a data model with classes, object properties/relations, data and annotation properties as an ontology. The ontology consists of the classes Mathematical Model, Mathematical Formulation, Computational Task, Quantity [Kind], Research Field and Research Problem. The structure of the ontology is displayed in the image below:

Structure of the MathModDB ontology

The ontology is populated with individuals/data from various fields of applied mathematics, making it a knowledge graph. Next, we show the total number of individuals per class and a detailed list of the individuals, when you click on the respective total number of individuals.

Research Fields: 1
Research Problems: 1
Mathematical Models: 1
Computational Tasks: 1
Mathematical Expressions: 1
Quantities: 1
Quantity Kinds: 1

Publications

2025

Schembera, Björn, Frank Wübbeling, Hendrik Kleikamp, Burkhard Schmidt, Aurela Shehu, Marco Reidelbach, Christine Biedinger et al. "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

2024

Schembera, B., Wübbeling, F., Kleikamp, H., Biedinger, C., Fiedler, J., Reidelbach, M., Shehu, A., Schmidt, B., Koprucki, T., Iglezakis, D. and Göddeke, D., 2023. Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines. In: Garoufallou, E. and Sartori, F. (eds) Metadata and Semantic Research (MTSR 2023). Communications in Computer and Information Science, vol 2048. Springer, Cham. https://doi.org/10.1007/978-3-031-65990-4_14

2023

Schembera, B., Riethmüller, C. and Göddeke, D., Enabling FAIR Data in Computational Science, Engineering and Mathematics through Knowledge Graphs.

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

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-MathModDB is the database for mathematical models developed by MaRDIs [[Portal/TA4 | TA4]] as a knowledge graph. The ontology, which serves as the data model for the knowledge graph, encompasses seven classes (as of January 2024: "Research Field," "Research Problem," "Mathematical Model," "Mathematical Formulation," "Mathematical Task," "QuantityKind," and "Quantity.") It also captures the relationships between these classes, such as the association indicating that a model addresses a specific research problem. Furthermore, these entities are enriched with various attributes, including metadata like the mathematical formulations in LaTeX. This provides a thorough description of mathematical models and has been derived from the requirements stemming from the use case studies in M4.1. Initial datasets, exemplified by mathematical models such as Navier-Stokes (fluid dynamics), Michaelis-Menten (chemical kinetics), quantum dynamics (molecules and semiconductor devices), Line Planning, or Röntgen Transformation, have been seamlessly integrated into MathModDB.
+__NOTOC__ <!-- Removes table of content -->
+Proper documentation and storage of research data, adhering to FAIR principles, are crucial for reproducibility and scientific integrity. Applied mathematics, producing diverse numerical and symbolic data, heavily relies on models that must be well-documented for replication and future use. Here, we present MathModDB, an ontology for mathematical models, along with a knowledge graph containing over 1200 elements. The work is conducted within the NFDI project entitled Mathematical Research Data Initiative ([https://www.mardi4nfdi.de/about/mission MaRDI]).
-In collaboration with [[Portal/TA2]], the integration of MathModDB with MathAlgoDB was accomplished, underscoring the inherent connection between mathematical models and algorithms within the modeling-simulation workflow. This collaborative effort was showcased at various conferences, earning recognition with the [https://www.f08.uni-stuttgart.de/mathematik/aktuelles/news/Best-Paper-Award-beim-MTSR2023-fuer-Bjoern-Schembera-und-Dominik-Goeddeke/ Best Paper Award at MTSR 2023].
+MathModDB is a database of mathematical models developed by MaRDI's [[Portal/TA4 | Task Area 4]] as an ontology/knowledge graph. MathModDB defines a data model with classes, object properties/relations, data and annotation properties as an ontology. The ontology consists of the classes Mathematical Model, Mathematical Formulation, Computational Task, Quantity [Kind], Research Field and Research Problem. The structure of the ontology is displayed in the image below:
+<div style="text-align: center;">
+[[File:MathModDBLogo.png||1000px]]
+<br>
+''Structure of the MathModDB ontology''
+</div>
+The ontology is populated with individuals/data from various fields of applied mathematics, making it a knowledge graph.
+Next, we show the total number of individuals per class and a detailed list of the individuals, when you click on the respective total number of individuals.
+{{#invoke:MathModDB|getMathModDBStatistics}}
-== Models ==
+== Publications ==
-Following models have been integrated into MathModDB:
-TODO
+=== 2025 ===
+Schembera, Björn, Frank Wübbeling, Hendrik Kleikamp, Burkhard Schmidt, Aurela Shehu, Marco Reidelbach, Christine Biedinger et al. "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
-== Publications ==
+=== 2024 ===
-Following publications with respect to MathModDB have been published
+Schembera, B., Wübbeling, F., Kleikamp, H., Biedinger, C., Fiedler, J., Reidelbach, M., Shehu, A., Schmidt, B., Koprucki, T., Iglezakis, D. and Göddeke, D., 2023. Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines. In: Garoufallou, E. and Sartori, F. (eds) Metadata and Semantic Research (MTSR 2023). Communications in Computer and Information Science, vol 2048. Springer, Cham. https://doi.org/10.1007/978-3-031-65990-4_14
 === 2023 ===
-Schembera, B., Wübbeling, F., Kleikamp, H., Biedinger, C., Fiedler, J., Reidelbach, M., Shehu, A., Schmidt, B., Koprucki, T., Iglezakis, D. and Göddeke, D., 2023. Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines. arXiv preprint arXiv:[https://arxiv.org/pdf/2310.20443 2310.20443].
 Schembera, B., Riethmüller, C. and Göddeke, D., [https://www.simtech2023.uni-stuttgart.de/documents/Theme-4/Schembera-Bjoern.pdf Enabling FAIR Data in Computational Science, Engineering and Mathematics through Knowledge Graphs.]
 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 https://doi.org/10.52825/cordi.v1i.255]