MathModDB and MathAlgoDB: Knowledge Graphs for Mathematical Models and Numerical Algorithms
Schmidt, Burkhard; Biedinger, Christine; Fiedler, Jochen; Reidelbach, Marco; Schembera, Björn; Shehu, Aurela; Koprucki, Thomas
- Publisher
- Zenodo
- Language
- en
Abstract
Key components in applied mathematics and computational sciences and engineering are mathematical models, for the application of mathematical methods to real-world problems, and mathematical algorithms, for solving underlying equations or for data processing. In this contribution, we introduce MathModDB and MathAlgoDB, the ontologies and knowledge graphs for mathematical models and algorithms, respectively. They provide a semantic description of these key components, thus facilitating the discovery of existing, alternative, competing, or complementary models and/or algorithms within and across disciplines. Embedded into the MaRDI knowledge graph, MathModDB and MathAlgoDB support and enhance the search for information on models and algorithms, related literature and software conducted by researchers at all levels beyond a classical keyword search, making it a valuable resource for diverse academic and research needs. In summary, the MathModDB and MathAlgoDB ontologies provide semantically rich metadata descriptions for models and algorithms, thus implementing the FAIR principles.
Full text
MaRDI Mathematical Research Data Initiative MathModDB and MathAlgoDB: Knowledge Graphs for Mathematical Models and Numerical Algorithms Burkhard Schmidt Weierstrass Institute for Applied Analysis and Stochastics
2 MaRDI: The Mathematical Research Data Initiative Image: WIAS, from the MaRDI proposal, see DOI:10.5281/zenodo.6552436
3 Mathematical Models: Attempt for a definition
4 MathModDB: From ontology to knowledge graph academic discipline strength of materials materials science continuum mechanics research problem plate with a hole prototypical concrete structures mathematical model linear elasticity model mathematical expression computational domain Cauchy momentum equation plane stress quantity stress & strain tensors Young‘s modulus Poisson‘s ratio quantity kind stress & strain physical constant dimensionless number computational task analytical solution finite element discretization variational solution contains used by specialized by Plate with a hole Cooperation: Sjard Rosenbusch & Jörg Unger (BAM) NFDI4Ing
5 MathModDB knowledge graph: current status (December 2025)
6 MathModDB: “Landing page” at the MaRDI Portal https://portal.mardi4nfdi.de/wiki/MathModDB
7 MathModDB development and documentation of OWL To do: Zenodo https://github.com/MaRDI4NFDI/MathModDB https://zenodo.org/records/14887915 https://mardi4nfdi.github.io/MathModDB/
8 MaRDI portal and MaRDI knowledge graph https://portal.mardi4nfdi.de/wiki/Portal https://portal.mardi4nfdi.de/wiki/Service:MaRDI_KG
9 Wikibase technology stack at the MaRDI portal Using Wikibase technology •Wikidata, world‘s largest free knowledge graph •Machine & human readable •Unique identifiers: items, properties •Linked Open Data web •Useful through semantic queries -> SPARQL Concept of qualifiers •Expand, annotate, or contextualize statements (property-value pair) •Describe or refine the value of a property given in a statement •Add metadata about statements
where * may stand for: •initial condition •final condition •boundary condition •constraint condition • coupling condition • physical law • constitutive equation where ** may stand for: • input • output • parameter • constant •objective Mathematical Model Mathematical Formulation Quantity [Kind] Research Problem Academic Discipline Computational Task used by MathModDB (TA4) uses Algorithm Software Benchmar k Algorithmic Task MathAlgoDB (TA2) equivalent MathModDB meets MathAlgoDB Frank Wübbeling Hendrik Kleikamp Mario Ohlberger Stefan Rave
18 Linear Equations Problem: Algorithmic Task (MathAlgoDB) Use of qualifiers •Roles of quantities in algorithmic tasks Mathematical algorithm •Links to software •Links to benchmarks
19 NFDI4Ing: Benchmarks for concrete plate with a hole JörgUnger Sjard Rosenbusch Bundesanstalt für Materialforschung und -prüfung
20 NFDI4BioImage: Electrical barrier discharge in Argon Leibniz-Institut für Plasmaforschung und Technologie e.V. (INP) Markus Becker HV f= 60 kHz, U0= 1–3 kV Modelling approaches 1D 2D Unstable occurrence of striated and non-striated discharges Fluid-Poisson model implemented in 1D or 2D model geometries allows to study the underlaying physical effects
21 MathModDB at the MaRDI portal: Summary and Perspective •Migration from OWL to Wikibase finished: -Loss of ontological strictness -Loss of automated reasoning +MaRDI portal: one stop shop +Use of qualifiers to add metadata about statements +Compatibility with Wikidata •Available: Input of mathematical models using MaRDMO Frontend: Rendering templates using LUA scripts •Coming soon: MathModDB (TA4) --- MathAlgoDB (TA2) •Not so soon (?): Curation of external contributions (TA5)
22 Thank you! Thomas Koprucki Björn Schembera Aurela Shehu Jochen Fiedler Christine Biedinger Marco Reidelbach TA5: Eloi Ferrer
23 Conference papers
