Global Universal Scaling and Ultra-Small Parameterization in Machine Learning Interatomic Potentials with Super-Linearity

Significance Global scaling, such as the well-known universal equation of states (UEOS), usually exists as a fundamental law and covers different states of matter in nature. However, the state-of-the-art machine-learning models of potential energy surface (PES) and interatomic potentials lack such physical constraints, leading to problems in generalizability and physical scalability. This paper presents an approach of naturally incorporating global-scaling constraints into a machine-learning potential model by scaling different interatomic interactions into a universal form as revealed by the UEOS. The resulting model is able to construct a physically scalable PES and machine-learning interatomic potentials (MLIPs) with ultrasmall parameterization and exceptional computational efficiency. This work also sheds light on incorporating physical constraints into an artificial-intelligence model for materials simulation.