Björn Schembera

Björn Schembera, Frank Wübbeling, Hendrik Kleikamp et al.

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.

Björn Schembera, Frank Wübbeling, Hendrik Kleikamp et al.

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.

Marco Reidelbach, Björn Schembera, Marcus Weber

Modeling-Simulation-Optimization workflows play a fundamental role in applied mathematics. The Mathematical Research Data Initiative, MaRDI, responded to this by developing a FAIR and machine-interpretable template for a comprehensive documentation of such workflows. MaRDMO, a Plugin for the Research Data Management Organiser, enables scientists from diverse fields to document and publish their workflows on the MaRDI Portal seamlessly using the MaRDI template. Central to these workflows are mathematical models. MaRDI addresses them with the MathModDB ontology, offering a structured formal model description. Here, we showcase the interaction between MaRDMO and the MathModDB Knowledge Graph through an algebraic modeling workflow from the Digital Humanities. This demonstration underscores the versatility of both services beyond their original numerical domain.

Björn Schembera, Dorothea Iglezakis

Computational engineering generates knowledge through the analysis and interpretation of research data, which is produced by computer simulation. Supercomputers produce huge amounts of research data. To address a research question, a lot of simulations are run over a large parameter space. Therefore, handling this data and keeping an overview becomes a challenge. Data documentation is mostly handled by file and folder names in inflexible file systems, making it almost impossible for data to be findable, accessible, interopable and hence reusable. To enable and improve a structured documentation of research data from computational engineering, we developed EngMeta as a metadata model. We built this model by incorporating existing standards for general descriptive and technical information and adding metadata fields for disciplinespecific information like the components and parameters of the simulated target system and information about the research process like the used methods, software and computational environment. EngMeta functions, in practical use, as the descriptive core for an institutional repository. In order to reduce the burden of description on scientists, we have developed an approach for automatically extracting metadata information from the output and log files of computer simulations. Through a qualitative analysis, we show that EngMeta fulfills the criteria of a good metadata model. Through a quantitative survey, we can show that it meets the needs of engineering scientists.

Martin Thomas Horsch, Silvia Chiacchiera, Björn Schembera et al.

The European Materials and Modelling Ontology (EMMO) has recently been advanced in the computational molecular engineering and multiscale modelling communities as a top-level ontology, aiming to support semantic interoperability and data integration solutions, e.g., for research data infrastructures. The present work explores how top-level ontologies that are based on the same paradigm - the same set of fundamental postulates - as the EMMO can be applied to models of physical systems and their use in computational engineering practice. This paradigm, which combines mereology (in its extension as mereotopology) and semiotics (following Peirce's approach), is here referred to as mereosemiotics. Multiple conceivable ways of implementing mereosemiotics are compared, and the design space consisting of the possible types of top-level ontologies following this paradigm is characterized.