Typed Category-Theoretic Semantic Representations for AI-Assisted Engineering of Cyber-Physical Systems

Complex cyber-physical systems (CPSs) combine physical processes, computation, communication, sensing, and actuation across subsystems developed with different tools and assumptions. When a composite model is reduced to implementation code, its component boundaries, interface assumptions, and governing laws can become difficult to recover for reconfiguration, analysis, and assurance. Large language models (LLMs) can generate such implementations rapidly, but their outputs remain difficult to verify and reuse. Applied category theory (ACT) provides mathematical abstractions for describing how scientific systems are organized and composed; categorical CPS models use wiring diagrams to retain subsystem interfaces and compositional structure. Building on this foundation, this paper constructs a compositional abstraction for CPS, enriches it with a reusable domain knowledge base, and makes it accessible to LLM agents through an executable domain-specific language and deterministic validation workflow. Categorical composition is mapped to executable DAEs through a structure-preserving interpretation that retains the typed system schema. The 1R1C example demonstrates how this interpretation commutes with composition, while larger thermal systems and a deterministic mixed-CPS fragment test its application to more complex composites. We then evaluate the ACT-based DSL within an agentic workflow under five different configurations. Across six building-control tasks, access to the ACT-based DSL and engineering skills substantially improves validator pass rates and engineering representation quality relative to direct code generation, although performance remains bounded by primitive-library coverage. The results support reusable and verifiable AI-assisted CPS model development through the combination of formal abstraction, domain knowledge, and agent-oriented tooling.