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.

中文翻译：

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基于人工神经网络的机器学习原子间势再现钠的熔化和结晶

研究了基于人工神经网络 (ANN) 的机器学习原子间势的训练要求，以重现钠的熔化和结晶。只有在训练中考虑了力应力张量以及势能和原子力时，构建的 ANN 势才能精确地模拟通过第一性原理分子动力学模拟获得的相行为的温度依赖性。熔化温度是根据亥姆霍兹自由能估算的，该自由能是使用 ANN 势通过热力学积分计算的。本研究还讨论了获得的熔化温度对系统尺寸和采样k点数量的依赖性。