Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics

Schembera, Björn; Wübbeling, Frank; Kleikamp, Hendrik; Schmidt, Burkhard; Shehu, Aurela; Reidelbach, Marco; Biedinger, Christine; Fiedler, Jochen; Koprucki, Thomas; Iglezakis, Dorothea; Göddeke, Dominik

Abstract

Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this research data FAIR, two previously distinct ontologies were merged and extended, becoming a living knowledge graph. The link between the two ontologies is established by introducing computational tasks, as they occur in modeling, corresponding to algorithmic tasks. Moreover, controlled vocabularies are incorporated and a new class, distinguishing base quantities from specific use case quantities, was introduced. Also, both models and algorithms can now be enriched with metadata. Subject-specific metadata is particularly relevant here, such as the symmetry of a matrix or the linearity of a mathematical model. This is the only way to express specific workflows with concrete models and algorithms, as the feasible solution algorithm can only be determined if the mathematical properties of a model are known. We demonstrate this using two examples from different application areas of applied mathematics. In addition, we have already integrated over 250 research assets from applied mathematics into our knowledge graph.