Hybrid Models Bridge to Neuro-Symbolic AI for Better Uncertainty.

Hybrid mechanistic-data-driven models, which combine scientific first principles with machine learning components, are gaining traction in fields like process engineering and scientific machine learning. However, these models often lack a standardized semantic interface for comparison and verification across domains, and they pay insufficient attention to quantifying epistemic uncertainty within their mechanistic parts. This research proposes a novel approach to bridge hybrid modeling with neuro-symbolic (NeSy) AI. It reconstructs existing hybrid designs as instances of a NeSy interface, effectively translating them into a framework where mechanistic knowledge resides on the language side, learned modules on the belief side, and validity domains and constraints on the logic side. This translation, termed Hybrid-to-NeSy (H2N), provides an explicit NeSy inference functional and a logic-belief decomposition for each hybrid design. From this decomposition, two new metrics are derived: structural violation rate (SVR), which measures how well learned beliefs adhere to the mechanistic structure, and belief dispersion (BD), which quantifies the concentration of learned plausibility, serving as a measure of epistemic uncertainty. A case study on a structured hybrid model for binary classification under label noise demonstrated that models with higher SVR and BD exhibited greater variability in accuracy. H2N also effectively quantifies model uncertainty during extrapolations under structural distribution shifts, offering insights that test accuracy alone reveals only retrospectively.