# Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines

arXiv: https://arxiv.org/abs/2310.20443 · HTML: https://mlsanity.com/paper/2310.20443/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 27 references that are in the map.
- First posted on arXiv 31 Oct 2023.

## Builds on (most cited first, 1 of 1)

- [EngMeta -- Metadata for Computational Engineering](https://mlsanity.com/paper/2005.01637/) (2020)

## Built on by (most cited first, 3 of 3)

- [Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics](https://mlsanity.com/paper/2408.10003/) (2024)
- [Towards a FAIR Documentation of Workflows and Models in Applied Mathematics](https://mlsanity.com/paper/2403.17778/) (2024)
- [Making Mathematical Knowledge Explainable, Accessible and Interoperable Through Large Language Model Integration](https://mlsanity.com/paper/2607.24512/) (2026)

## Abstract (arXiv)

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.