Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines

TL;DR

The paper addresses the lack of interoperable semantic representations for mathematical models and numerical algorithms in modeling-simulation-optimization (MSO) workflows. It introduces two ontologies, MathModDB for mathematical models and AlgoData for algorithms, and demonstrates their merger into a knowledge graph that connects models, application problems, algorithms, literature, and software within the FAIR framework. A detailed X-RCT porous-media use case shows how the combined ontology enables end-to-end tracing from application domains to mathematical formulations and corresponding algorithmic solutions. The work highlights the practical impact of standardized, queryable metadata for reuse across disciplines and outlines plans to integrate with existing vocabularies and process/upper ontologies to realize a living knowledge graph for mathematics.

Abstract

In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data, the Mathematical Research Data Initiative has developed, merged and implemented ontologies and knowledge graphs. This contributes to making mathematical research data FAIR by introducing semantic technology and documenting the mathematical foundations accordingly. Using the concrete example of microfracture analysis of porous media, it is shown how the knowledge of the underlying mathematical model and the corresponding numerical algorithms for its solution can be represented by the ontologies.

Figures (2)

• Figure 1: Typical MSO workflow and resulting competency questions MaRDI2022.
• Figure 2: The ontologies for algorithms (AlgoData, light blue) and models (MathModDB, dark blue). The ontologies are connected between the Mathematical Model and the Algorithmic Problem classes.