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.

FAIR GraphRAG: A Retrieval-Augmented Generation Approach for Semantic Data Analysis

Retrieval-Augmented Generation (RAG) addresses the limitations of Large Language Models (LLMs) when providing responses to domain-specific questions. Graph-based RAG approaches, such as GraphRAG, enhance retrieval by capturing semantic relationships within knowledge graphs (KGs). While the FAIR principles (Findability, Accessibility, Interoperability, and Reusability) are becoming prevalent for scientific data management, especially in complex domains such as medicine, existing RAG approaches lack a structured FAIRification of the underlying knowledge resources. This lack limits their potential for FAIR information retrieval in these domains. To address this gap, we introduce FAIR GraphRAG, a novel framework that integrates FAIR Digital Objects (FDOs) as the fundamental units of a graph-based retrieval system. Each graph node represents an FDO that incorporates core data, metadata, persistent identifiers, and semantic links. We leverage LLMs to support schema construction and automated extraction of content and metadata from data sources. The framework was co-designed by physicians and computer scientists to ensure technical and clinical relevance. We apply FAIR GraphRAG to a biomedical dataset in gastroenterology, demonstrating its applicability to RNA-sequencing data. Beyond ensuring adherence to the FAIR principles, FAIR GraphRAG significantly improves question answering accuracy, coverage, and explainability, particularly for complex queries involving metadata and ontology links. This work shows the feasibility of combining FAIR data practices with graph-based retrieval techniques. We see potential for applying our approach to other specialized fields such as education and business.