Machine learning enhanced empirical potentials for metals and alloys
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Interatomic potential (i.e. force-field) plays a vital role in atomistic simulation of materials. Empirical potentials like the embedded atom method (EAM) and its variant angular-dependent potential (ADP) have proven successful in many metals. In the past few years, machine learning has become a compelling approach for modeling interatomic interactions. Powered by big data and efficient optimizers, machine learning interatomic potentials can generally approximate to the accuracy of the first-principles calculations based on the quantum mechanics theory. In this works, we successfully developed a route to express EAM and ADP within machine learning framework in highly-vectorizable form and further incorporated several physical constraints into the training. As it is proved in this work, the performances of empirical potentials can be significantly boosted with few training data. For energy and force predictions, machine tuned EAM and ADP, can be almost as accurate as the computationally expensive spectral neighbor analysis potential (SNAP) on the fcc Ni, bcc Mo and Mo-Ni alloy systems. Machine learned EAM and ADP can also reproduce some key materials properties, such as elastic constants, melting temperatures and surface energies, close to the first-principles accuracy. Our results suggest a new and systematic route for developing machine learning interatomic potentials. All the new algorithms have been implemented in our program TensorAlloy.
原子间势（Interatomic Potential，即力场）在材料的原子尺度模拟中发挥着至关重要的作用。诸如嵌入原子法（Embedded Atom Method, EAM）及其变体角相关势（Angular-Dependent Potential, ADP）等经验势函数，已在诸多金属体系中得到广泛且成功的应用。过去数年间，机器学习已成为模拟原子间相互作用的极具吸引力的研究手段。依托大数据与高效优化器的支撑，基于机器学习的原子间势通常能够达到基于量子力学理论的第一性原理计算的精度水平。在本研究中，我们成功开发出一种可高度向量化的机器学习框架下的EAM与ADP势函数表达方案，并在训练过程中引入了多项物理约束条件。本研究证实，仅需少量训练数据，即可大幅提升经验势函数的预测性能。在面心立方（Face-Centered Cubic, fcc）镍、体心立方（Body-Centered Cubic, bcc）钼以及钼镍合金体系的能量与原子力预测任务中，经机器学习优化的EAM与ADP势函数，其精度几乎可与计算成本高昂的谱邻域分析势（Spectral Neighbor Analysis Potential, SNAP）相媲美。经机器学习训练的EAM与ADP势函数，还能够复现弹性常数、熔点与表面能等关键材料属性，其精度接近第一性原理计算结果。本研究结果为机器学习原子间势的开发提供了一条全新且系统化的研究路径。所有新型算法均已在我们开发的TensorAlloy程序中完成实现。
