MathModDB: The Knowledge Graph for FAIR Storage of Mathematical Models used in Applied Sciences

MaRDI Mathematical Research Data Initiative MathModDB: The Knowledge Graph for FAIR Storage of Mathematical Models used in Applied Sciences Jochen Fiedler1, Christine Biedinger1, Michael Burger1, Dominik Göddeke2, Thomas Koprucki3, Marco Reidelbach4, Björn Schembera2, Aurela Schehu3, Burkhard Schmidt3, Marcus Weber4 1Fraunhofer ITWM, 2Universität Stuttgart, 3WIAS Berlin, 4ZIB 2 •R&D teams often rely on mathematical models and concepts •Models are often scattered across manifold publications and internal documents •Finding the right model for a new research project (including assumptions, scope, required quantities, and references) is timeconsuming •Leads to fragmented knowledge and missed opportunities •Improve discoverability of models (including versions, variants, and application domains) •Provide transparency and thorough documentation of necessary formulations and assumptions •Connect and link research questions and domains to specific models •Enable easy search, maximum synergies and unique identification →Making mathematical models FAIR! Motivation: Create central repository for mathematical models Challenges Goals MaRDI within the NFDI 5 MaRDI: The Mathematical Research Data Initiative •Start: November 2021 •15 Member institutions •28 (full-time equivalent) employees •10 million Euro funding over 5 years 6 MaRDI aims and services MaRDI aims •Develop robust Mathematical Research Data Infrastructure •Set standards and confirmable workflows for certified Mathematical Research Data •Provide services to both the mathematical and wider scientific community Services The structure of MathModDB 8 Introduction: FAIR traded apples in MathModDB Free Fall models as mathematical research data •Simple model without air drag: ሶ𝑣 = 𝑔 •More complex model with air drag: ሶ𝑣 = 𝑔 − 𝜌𝐶𝐷𝐴𝑣2 2𝑚 Sir Isaac Newton (1666) What and how to store such a model in a meaningful way? →Utilization of ontologies! 10 MathModDB: Ontology specification Version 1.0.0 published in February 11 The free fall model in our ontology Mathematical Model: Free fall with air drag Mathematical Formulation: ሶ𝑣 = 𝑔 − 𝜌𝐶𝐷𝐴𝑣2 2𝑚 Quantities: Free Fall Velocity 𝑣 Gravitational acceleration 𝑔 Density of air 𝜌 Drag coefficient 𝐶𝐷 Cross section 𝐴of the apple Mass of the apple 𝑚 Computational Task: Calculate free fall time Research Field: “Pomology” Research Problem: Gravitational effects on fruit Sir Isaac Newton (1666) 18 Implementation on graphserver in Münster •Operated by MaRDI-colleagues for MathAlgoDB •Intuitive graphical surface •Connection between algorithms and mathematical models https://cordi2025.m1.mardi.ovh/ 19 MaRDI portal: One-stop-shop for MaRDI services •MaRDI technology stack •Wikibase technology –interface to Wikidata •Identifier for individuals •Work in progress https://portal.mardi4nfdi.de/wiki/Item:Q6675414 20 Summary and outlook •MathModDB is a repository for mathematical model research data •It connects models, formulas, research questions, etc. with semantics and enables synergies •It grows in content and its ecosystem size •Potential connections to other repositories •Experience from researchers will help to improve it further!