Beyond Semantic Similarity: Contrastive Learning for Cross-Domain Structural Isomorphism Detection

We present a contrastive learning approach to detect deep structural isomorphism across scientific domains, moving beyond surface semantic similarity. Our contributions include: SIBD Benchmark: The first Structural Isomorphism Benchmark Dataset with 84 mathematical structure types and 1,214 cross-domain natural language descriptions Fine-tuned Model: A sentence-transformer achieving Silhouette Score 0.85 (from -0.01) and Retrieval@5 of 100% (from 20%) Large-scale Discovery: Application to 500 scientific phenomena yielding 3,017 cross-domain matches, of which 684 passed LLM screening and 6 were verified at the equation level All code, data, and models are open-source at GitHub.