Δ‑EGNNMethod Accelerates the Constructionof Machine Learning Potential

Recent advancements in molecular simulations highlight the substantial computational demands of generating high-precision quantum mechanical labels for training neural network potentials. These challenges emphasize the need for improvements in delta-machine learning techniques. The Equivariant Graph Neural Network (EGNN) framework, grounded in a message-passing mechanism that preserves structural equivariance, enables refined atomic representations through interaction-driven updates. We introduce the Δ-EGNN model, which achieves high prediction accuracy for both molecular and condensed-phase systems. For example, in periodic water box systems, a mean absolute error of 1.722 meV/atom for energy (global property) and 0.0027 e for partial charge (local property) were achieved with training on just 800 labels. Δ-EGNN is computationally efficient, achieving speedups of 1–2 orders of magnitude compared to conventional methods at the MP2 level. In contrast to models directly trained on total energies, such as NequIP, MACE, and Allegro, the Δ-EGNN model employs delta-machine learning to predict the difference between energies derived from low- and high-level electronic structure methods, providing a significant advantage in reducing computational costs while preserving high accuracy. In summary, Δ-EGNN opens a new avenue for exploring energy landscapes and constructing machine learning potentials with afforable computational overhead, facilitating routine quantum mechanical calculations for complex molecular systems.