Efficiently Trained Deep Learning Potential for Graphane

We have developed an accurate and efficient deep-learning potential (DP) for graphane, which is a fully hydrogenated version of graphene, using a very small training set consisting of 1000 snapshots from a 0.5 ps density functional theory (DFT) molecular dynamics simulation at 1000 K. We have assessed the ability of the DP to extrapolate to system sizes, temperatures, and lattice strains not included in the training set. The DP performs surprisingly well, outperforming an empirical many-body potential when compared with DFT data for the phonon density of states, thermodynamic properties, velocity autocorrelation function, and stress–strain curve up to the yield point. This indicates that our DP can reliably extrapolate beyond the limit of the training data. We have computed the thermal fluctuations as a function of system size for graphane. We found that graphane has larger thermal fluctuations compared with graphene, but having about the same out-of-plane stiffness.我们开发了一款针对石墨烷的高精度、高效率的深度学习势（deep-learning potential, DP）——石墨烷是石墨烯的完全氢化形式，其训练集规模极小，仅包含1000 K下0.5皮秒（ps）密度泛函理论（density functional theory, DFT）分子动力学模拟得到的1000个结构快照。我们评估了该深度学习势（DP）对训练集未涵盖的体系尺寸、温度以及晶格应变条件下的外推能力。该深度学习势（DP）表现出人意料的优异，在声子态密度、热力学性质、速度自相关函数以及直至屈服点的应力应变曲线等指标上，与DFT参考数据的对比结果显示其性能优于经验多体势。这表明我们开发的深度学习势（DP）能够可靠地外推至训练数据范围之外。我们计算了石墨烷的热涨落随体系尺寸的变化关系。我们发现，与石墨烯相比，石墨烷的热涨落更大，但面外刚度与石墨烯大致相当。