A scalable machine learning multi-local regression framework for potential energy surface fitting across diverse chemical landscapes.

The accurate characterization of the potential energy surface (PES) is fundamental to understanding molecular structures and chemical reaction mechanisms. Traditional approaches, such as ab initio calculations and empirical force fields, struggle to balance computational efficiency and accuracy, particularly for high-dimensional systems. Machine learning methods have demonstrated remarkable efficacy in addressing chemical problems, yet two critical challenges remain: (1) Inadequate representation of high-energy structures (e.g., transition states) in training data due to their scarcity and inherent complexity, leading to biased PES predictions; and (2) insufficient adaptability of data-driven models to dynamic chemical scenarios, as they rely on static benchmark datasets and lack explicit integration with mechanistic knowledge. This study proposes a Clustering and Local Regression Network (CLRNet), a chemical-principle-guided hierarchical framework for PES construction, which integrates data-driven modeling with quantum mechanical insights. CLRNet employs graph neural networks to extract molecular features, integrating unsupervised clustering of features with local potential energy surface regression. CLRNet has outstanding advantages in accommodating high-energy structures and has achieved a balance between model capacity and computing power. This work not only offers a new approach to PES analysis but also bridges the gap between data-driven modeling and chemical intuition. It has great application prospects in downstream tasks such as transition state energy calculation and PES fitting of catalysis and chemical kinetics in physical chemistry.