From Physical Principles to ML-Ready Representations: A Unified Framework for Scanning Tunneling Microscopy

Scanning tunneling microscopy (STM) enables atomic-resolution imaging, but quantitative interpretation remains difficult because tunneling current depends nonlinearly on both surface geometry and electronic structure. We propose a physics-informed representation based on bond valence and tip-height deviation from the covalent surface, which captures the local chemical environment while incorporating permutational invariance and the nearsightedness principle. This representation maps the STM-structure relationship onto a low-dimensional manifold and demonstrates strong transferability across iron carbide stoichiometries and surface orientations. Combined with a compact XGBoost model, it predicts STM images accurately while reducing computation from hours to seconds. Integrated with surface structure filters, the method forms a high-throughput pipeline for candidate screening, image prediction, and experimental validation through an online virtual STM laboratory. The framework can be further expanded in the future to atomic force microscopy and other scanning probe techniques, which establishes a physically grounded framework for efficient, data-driven surface structure determination.