arXiv subjects

Björn Schembera

Publications and source records attributed to Björn Schembera.

9 recordsLinked to original sources

arXiv2026

Making Mathematical Knowledge Explainable, Accessible and Interoperable Through Large Language Model Integration

Mathematical models are central to formalizing research problems, yet their documentation often falls short of FAIR principles. Knowledge bases such as the Mathematical Model Database (MathModDB) address this gap by providing curated, semantically rich representations of mathematical models. Built on Wikibase, the same open-source infrastructure underlying Wikidata, MathModDB utilizes Semantic Web technologies to support Linked Open Data, collaborative editing, and the storage of semantically enriched metadata, making it a domain-specific knowledge graph within the broader Wikidata ecosystem. However, access to MathModDB currently requires either navigating a complex web interface or proficiency in SPARQL and Wikibase APIs, posing significant barriers for potential users. In addition, the combination of such curated knowledge bases with actual research data stored, e.g., in Dataverse repository instances, remains a challenge. To overcome these limitations, we propose integrating Large Language Models (LLMs) with MathModDB via a Model Context Protocol (MCP) server that exposes a vector-indexed schema retrieval and Steiner-tree-based join planner, combining dialogue-based natural language interaction with curated, epistemically grounded knowledge. Although instantiated on MathModDB, the architecture can be applied to other Wikibase-based systems. We demonstrate that this approach enables epistemically grounded LLM usage, improves model explainability and accessibility beyond what the standard Wikibase interface offers, and simplifies interoperability with external databases and tools, such as Dataverse data repositories. We illustrate the benefits of combining the accessibility of an LLM with the epistemic safety of a curated knowledge base through the adaptability of the MCP protocol by two use cases involving mathematical models in the fields of continuum mechanics and enzyme kinetics.

cs.AI↗

arXiv2026

MathModDB: A Database for Mathematical Models

When researchers need a mathematical model for a research problem, they face a fragmented landscape: relevant formulas, quantities, assumptions, and model variants are scattered across publications and domain-specific conventions. The Mathematical Models Database (MathModDB) addresses this challenge by providing a curated knowledge graph for mathematical models, deployed on the MaRDI Portal as part of the German National Research Data Infrastructure (NFDI). Building on ontology designs presented in earlier work, this paper focuses on MathModDB as a publicly available service. It addresses researchers who use mathematical models in their work -- whether in applied mathematics, engineering, or the natural sciences. We describe its deployment on the Wikibase-powered MaRDI Portal, report on its current scale, and demonstrate its practical use through a walkthrough of an electric discharge modeling use case from plasma physics. We further discuss the ecosystem around MathModDB, including its connection to the MathAlgoDB knowledge graph for numerical algorithms and the MaRDMO documentation tool.

cs.DL↗

arXiv2025

Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics

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.

cs.AI↗

arXiv2024

Towards a FAIR Documentation of Workflows and Models in Applied Mathematics

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.

cs.AI↗

arXiv2024

Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines

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.

cs.AI↗

arXiv2022

Research-Data Management Planning in the German Mathematical Community

In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring research-data management plans to mathematicians' research processes and discuss their usage all along the data life cycle.

math.HO↗

arXiv2021

Semantic interoperability based on the European Materials and Modelling Ontology and its ontological paradigm: Mereosemiotics

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.

cs.AI↗

arXiv2020

EngMeta -- Metadata for Computational Engineering

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.

cs.IR↗

arXiv2017

Optimized Secure Position Sharing with Non-trusted Servers

Today, location-based applications and services such as friend finders and geo-social networks are very popular. However, storing private position information on third-party location servers leads to privacy problems. In our previous work, we proposed a position sharing approach for secure management of positions on non-trusted servers, which distributes position shares of limited precision among servers of several providers. In this paper, we propose two novel contributions to improve the original approach. First, we optimize the placement of shares among servers by taking their trustworthiness into account. Second, we optimize the location update protocols to minimize the number of messages between mobile device and location servers.

cs.DC↗