Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines

TL;DR

This paper discusses the development and application of ontologies and knowledge graphs to represent mathematical models and algorithms, enhancing data FAIRness in applied mathematics.

Contribution

It introduces ontologies for mathematical models and algorithms, demonstrating their use in representing complex mathematical research data with semantic technology.

Findings

Ontologies improve data documentation and sharing in applied mathematics.

Knowledge graphs facilitate understanding of mathematical models and algorithms.

Application example in microfracture analysis illustrates practical benefits.

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.