用大模型让数学模型库更易懂、好用且能互通。
Making Mathematical Knowledge Explainable, Accessible and Interoperable Through Large Language Model Integration
- 通过大模型接口实现自然语言查询数学模型
- 提升模型解释性与跨系统数据互通能力
- 适合科研人员快速获取可信数学知识
数学模型是形式化研究问题的核心，但其文档常不符合FAIR原则。MathModDB作为基于Wikibase的领域知识图谱，提供语义丰富的模型表示，支持链接开放数据和协作编辑。然而，当前访问需掌握SPARQL或复杂网页操作，且难以与如Dataverse等外部数据存储系统集成。为此，我们提出通过模型上下文协议（MCP）服务器，将大语言模型（LLMs）与MathModDB结合，实现向量索引的模式检索与斯坦纳树驱动的连接规划，支持对话式自然语言交互，并保持知识的本体可靠性。该架构不仅提升了模型可解释性与可访问性，还简化了与外部数据库的互操作。我们在连续介质力学和酶动力学两个案例中验证了该方法的有效性，展示了大模型与经验证知识库融合带来的灵活性与安全性。
原文摘要 · Abstract (English)
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.
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