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MathModDB is a database of mathematical models developed by MaRDIs [[Portal/TA4 | TA4]] as a knowledge graph). MathModDB defines a data model with classes (Mathematical Model, Mathematical Formulation, Research Field, 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.
__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]).




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. 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 [[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:
 
The ontology consists of the classes Mathematical Model, Mathematical Formulation, Computational Task, Quantity [Kind], Research Field and Research Problem. The structure of the ontology, in conjunction with the neighboring knowledge graph for mathematical algorithms [https://portal.mardi4nfdi.de/wiki/Service:6534228 MathAlgoDB] is displayed in the image below:


<div style="text-align: center;">
<div style="text-align: center;">
[[File:MathModDBLogo.png||1000px]]
[[File:MathModDBLogo.png||1000px]]
<br>
<br>
''Structure of MathModDB''
''Structure of the MathModDB ontology''
</div>
</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.
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.
<!--  Q60231 refers to academic discipline  -->
{{#invoke:MathModDB|getMathModDBStatistics}}
<!-- Q6534265 refers to MathModDB community -->
{{#sparql:
SELECT (CONCAT("<a href='https://portal.mardi4nfdi.de/wiki/MathModDB/Research_field'>", STR(COUNT(?item)), "</a>") AS ?Research_Field_Individuals)
WHERE {
    ?item wdt:P31  wd:Q60231;
          wdt:P1495 wd:Q6534265 .
}
| endpoint= https://query.portal.mardi4nfdi.de/proxy/wdqs/bigdata/namespace/wdq/sparql
| chart=bordercloud.visualization.DataTable
| log=2
}}
 
 
<!-- Q6032837 refers to research problem    -->
<!-- Q6534265 refers to MathModDB community -->
{{#sparql:
SELECT (CONCAT("<a href='https://portal.mardi4nfdi.de/wiki/MathModDB/Research_problem'>", STR(COUNT(?item)), "</a>") AS ?Research_Problem_Individuals)
WHERE {
    ?item wdt:P31 wd:Q6032837;
          wdt:P1495 wd:Q6534265 .
}
| endpoint= https://query.portal.mardi4nfdi.de/proxy/wdqs/bigdata/namespace/wdq/sparql
| chart=bordercloud.visualization.DataTable
| log=2
}}
 
 
<!--  Q68663 refers to mathematical model  -->
<!-- Q6534265 refers to MathModDB community -->
{{#sparql:
SELECT (CONCAT("<a href='https://portal.mardi4nfdi.de/wiki/MathModDB/Model'>", STR(COUNT(?item)), "</a>") AS ?Mathematical_Model_Individuals)
WHERE {
    ?item wdt:P31 wd:Q68663;
          wdt:P1495 wd:Q6534265 .
}
| endpoint= https://query.portal.mardi4nfdi.de/proxy/wdqs/bigdata/namespace/wdq/sparql
| chart=bordercloud.visualization.DataTable
| log=2
}}
 
 
<!-- Q6534247 refers to computational task  -->
<!-- Q6534265 refers to MathModDB community -->
{{#sparql:
SELECT (CONCAT("<a href='https://portal.mardi4nfdi.de/wiki/MathModDB/Task'>", STR(COUNT(?item)), "</a>") AS ?Computational_Task_Individuals)
WHERE {
    ?item wdt:P31 wd:Q6534247;
          wdt:P1495 wd:Q6534265 .
}
| endpoint= https://query.portal.mardi4nfdi.de/proxy/wdqs/bigdata/namespace/wdq/sparql
| chart=bordercloud.visualization.DataTable
| log=2
}}
 
 
<!-- Q6481152 refers to mathematical formulation -->
<!-- Q6534265 refers to MathModDB community      -->
{{#sparql:  
SELECT (CONCAT("<a href='https://portal.mardi4nfdi.de/wiki/MathModDB/Formula'>", STR(COUNT(?item)), "</a>") AS ?Mathematical_Formulation_Individuals)
WHERE {
    ?item wdt:P31 wd:Q6481152;
          wdt:P1495 wd:Q6534265 .
}
| endpoint= https://query.portal.mardi4nfdi.de/proxy/wdqs/bigdata/namespace/wdq/sparql
| chart=bordercloud.visualization.DataTable
| log=2
}}
 
 
<!-- Q6534237 refers to quantity            -->
<!-- Q6534265 refers to MathModDB community -->
{{#sparql:
SELECT (CONCAT("<a href='https://portal.mardi4nfdi.de/wiki/MathModDB/Quantity'>", STR(COUNT(?item)), "</a>") AS ?Quantity_Individuals)
WHERE {
    ?item wdt:P31 wd:Q6534237;
          wdt:P1495 wd:Q6534265 .
}
| endpoint= https://query.portal.mardi4nfdi.de/proxy/wdqs/bigdata/namespace/wdq/sparql
| chart=bordercloud.visualization.DataTable
| log=2
}}
 
 
<!-- Q6534245 refers to quantity kind      -->
<!-- Q6534265 refers to MathModDB community -->
{{#sparql:
SELECT (CONCAT("<a href='https://portal.mardi4nfdi.de/wiki/MathModDB/Quantity'>", STR(COUNT(?item)), "</a>") AS ?Quantity_Kind_Individuals)
WHERE {
    ?item wdt:P31 wd:Q6534245;
          wdt:P1495 wd:Q6534265 .
}
| endpoint= https://query.portal.mardi4nfdi.de/proxy/wdqs/bigdata/namespace/wdq/sparql
| chart=bordercloud.visualization.DataTable
| log=2
}}


== 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
 
 
 
 
== Publications ==
Following publications with respect to MathModDB have been published


=== 2023 ===
=== 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., 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]
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]

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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