Global universal scaling and ultrasmall parameterization in machine-learning interatomic potentials with superlinearity.

Using machine learning (ML) to construct interatomic interactions and thus potential energy surface (PES) has become a common strategy for materials design and simulations. However, those current models of machine-learning interatomic potential (MLIP) consider no relevant physical constraints or global scaling and thus may owe intrinsic out-of-domain difficulty which underlies the challenges of model generalizability and physical scalability. Here, by incorporating the global universal scaling law, we develop an ultrasmall parameterized MLIP with superlinear expressive capability, named SUS(2)-MLIP. Due to the global scaling derived from the universal equation of state (UEOS), SUS(2)-MLIP not only has significantly reduced parameters by decoupling the element space from coordinate space but also naturally outcomes the out-of-domain difficulty and endows the model with inherent generalizability and scalability even with relatively small training dataset. The non-linearity-embedding transformation in radial function endows the model with superlinear expressive capability. SUS(2)-MLIP outperforms the state-of-the-art MLIP models with its exceptional computational efficiency, especially for multiple-element materials and physical scalability in property prediction. This work not only presents a highly efficient universal MLIP model but also sheds light on incorporating physical constraints into AI-aided materials simulation.