Reproduction of Melting and Crystallization of Sodium by Machine-Learning Interatomic Potential Based on Artificial Neural Networks

The training requirements for machine-learning interatomic potential based on artificial neural networks (ANN) are investigated to reproduce melting and crystallization of sodium. Only when the virial stress tensor, as well as the potential energy and atomic forces, is considered in the training, the constructed ANN potential precisely mimics the temperature dependence of the phase behavior obtained by first-principles molecular dynamics simulations. The melting temperature is estimated from the Helmholtz free energy, which is calculated by thermodynamic integration using the ANN potential. This study also discusses the dependence of the obtained melting temperature on the system size and the number of sampling k points.