MathModDB: Difference between revisions

Revision as of 12:57, 28 April 2025

MathModDB is a database of mathematical models developed by MaRDIs 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.

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).

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 MathAlgoDB is displayed in the image below:

File:MathModDB.png
Structure of MathModDB

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.

Models

Following models have been integrated into MathModDB:

TODO

Publications

Following publications with respect to MathModDB have been published

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:2310.20443.

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

@@ Line 1: / Line 1: @@
-MathModDB is the database for mathematical models developed by MaRDIs [[Portal/TA4 | TA4]] as a knowledge graph. The [https://mtsr2024.m1.mardi.ovh/static/widoco/v1/index-en.html Algorithm Knowledge Graph 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.
+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.
-[[File:MathModDB Feb2024.png|1000px|MathModDB and its connection to MathAlgoDB via the Mathematical Task class, as of February 2024]]
+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).
+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;">
+[[File:MathModDB.png||1000px]]
+<br>
+''Structure of MathModDB''
+</div>
+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  -->
+<!-- Q6534265 refers to MathModDB community -->
+{{#sparql:
+SELECT (CONCAT("<a href='https://staging.mardi4nfdi.org/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
+}}
-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].