Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics

2024-08-19

arXiv.org

AI Summary

Application mathematical models and algorithms suffer from insufficient semantic representation, hindering compliance with the FAIR (Findable, Accessible, Interoperable, Reusable) principles. Method: This paper constructs the first application-mathematics-oriented knowledge graph for models and algorithms. It systematically introduces the knowledge graph paradigm into core methodological modeling, integrating ontology engineering, LaTeX formula structural extraction, mathematical semantic parsing, and expert-validated semi-automatic knowledge fusion. The graph explicitly encodes multi-dimensional semantic relationships—including definitions, assumptions, derivation logic, applicability conditions, and numerical implementations. Contribution/Results: It enables cross-domain algorithm provenance tracking, explainability verification, and automatic reasoning-chain construction. We release the first structured version covering differential equations, optimization, and numerical linear algebra, supporting SPARQL queries and traceable algorithm recommendations—significantly enhancing mathematical knowledge findability, interoperability, and reusability.

Technology Category

• Knowledge Representation and Reasoning: Applications
• Data Mining & Knowledge Management: Linked Open Data, Knowledge Graphs & KB Completion
• Machine Learning: Graph-based Machine Learning

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Problem

• Semantically represent mathematical models and algorithms
• Merge and extend ontologies for FAIR research data
• Enrich models and algorithms with subject-specific metadata

Innovation

• Merged ontologies for semantic representation
• Introduced computational tasks linking models
• Enriched models with subject-specific metadata