MathModDB Knowledge Graph -- From Documentation to Validation of Mathematical Models

The systematic documentation, discovery, and reuse of mathematical models remains a significant challenge, particularly across disparate academic disciplines. As part of the Mathematical Research Data Initiative (MaRDI) within Germany’s National Research Data Infrastructure (NFDI), we are tackling the problem of documenting and reusing mathematical models across disciplines. To this end, we developed MathModDB, an ontology-based database and knowledge graph designed to formalize the representation of mathematical models. By providing semantic descriptions, MathModDB directly supports the FAIR (Findable, Accessible, Interoperable, and Reusable) principles.

Currently, the database contains over 20,000 semantic statements covering more than 200 models in fields such as chemical kinetics, semiconductor physics, and computational mechanics. Recently, MathModDB has been integrated into the MaRDI Portal web service,  a gateway to open mathematical research data based on Wikibase technology. There, MathModDB is now interlinked with MathAlgoDB, a related ontology-based database for mathematical algorithms and their implementation and scientific context. This creates a unified ecosystem that connects mathematical models with their algorithmic counterparts. Moreover, the pair of knowledge graphs is connected to numerous publications, datasets, and other resources available within the MaRDI portal.

In a next step, we intend to go beyond a mere documentation of mathematical models and algorithms: We strive to create an active simulation environment where models become directly executable. The spectrum of functionality ranges from automated code generation for analytical approaches to the integration of high-performance software packages for numerical solutions of, e.g., systems of partial differential equations. Thus, by intuitively linking modeling and computation, the next stage of the MathModDB platform aims at making a vital contribution to the reproducibility of simulation results and establishes itself as a central tool for systematic benchmarking, verification and validation of models and methods.