Linear-Scaling Potential-Free Data-Driven Molecular Dynamics for Arbitrary-Sized Water Clusters $(\text{H}_2\text{O})_n$

Conventional molecular dynamics (MD) simulation approaches, such as $\textit{ab initio}$ MD (AIMD) and empirical force field MD (EFFMD), face significant trade-offs between physical accuracy and computational efficiency. This work presents a linear-scaling potential-free data-driven molecular dynamics (PDMD) framework for predicting system energy and atomic forces of arbitrary-sized water clusters $(\text{H}_2\text{O})_n$. Specifically, PDMD employs a Gaussian-based atomic geometry descriptor to generate high-dimensional, equivariant features, then leverages ChemGNN, a graph neural network model that adaptively learns the atomic chemical environments without requiring $\textit{a priori}$ knowledge. Through an iterative self-consistent training approach, the converged PDMD achieves a mean absolute error of 1.39 meV/atom for energy and 50.7 meV/angstrom for forces, outperforming the state-of-the-art DeepMD by $\sim$5x in energy accuracy and $\sim$3x in force accuracy. As a result, the linear-scaling PDMD can reproduce the AIMD properties of water clusters at orders-of-magnitude lower computational cost, as illustrated by simulations of systems consisting of thousands or more molecules. These results demonstrate that the proposed PDMD offers multiphase predictive power and enables ultra-fast, general-purpose MD simulations while retaining AIMD-level accuracy. This accuracy is achieved by efficiently capturing many-body potentials that are critical in numerous polyatomic systems but are often missing in EFFMD. Moreover, we have constructed an $\textit{ab initio}$ dataset with over 300,000 $(\text{H}_2\text{O})_n$ structures, standardized in a unified PyTorch Geometric framework, to support scalable evaluation of artificial intelligence methods for molecular dynamics.