Accurate interatomic force fields via machine learning with covariant kernels
Accurate interatomic force fields via machine learning with covariant kernels
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DOI：
10.1103/physrevb.95.214302
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发表时间：
2017-06-08
影响因子：
3.7
通讯作者：
De Vita, Alessandro
中科院分区：
文献类型：
--
作者：
Glielmo, Aldo;Sollich, Peter;De Vita, Alessandro
我们提出了一个新的计划，准确地预测原子力的矢量量，而不是标量分量的集合，高斯过程（GP）回归。这是基于矩阵值核函数，我们施加的要求，预测力旋转的目标配置，是独立的任何旋转应用到配置数据库条目。我们表明，这样的协变GP核可以通过对旋转群SO（d）的元素进行积分来获得。值得注意的是，在特定情况下，积分可以进行分析，并产生一个保守的力场，可以重铸成一对相互作用的形式。最后，我们表明，限制的整合，在一个有限的点群的元素有关的目标系统的总和是足以恢复一个准确的GP。我们的内核在预测量子力学力在真实的材料的准确性进行了研究，通过测试纯和有缺陷的镍，铁，硅晶体系统。
We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian process (GP) regression. This is based on matrix-valued kernel functions, on which we impose the requirements that the predicted force rotates with the target configuration and is independent of any rotations applied to the configuration database entries. We show that such covariant GP kernels can be obtained by integration over the elements of the rotation group SO(d) for the relevant dimensionality d. Remarkably, in specific cases the integration can be carried out analytically and yields a conservative force field that can be recast into a pair interaction form. Finally, we show that restricting the integration to a summation over the elements of a finite point group relevant to the target system is sufficient to recover an accurate GP. The accuracy of our kernels in predicting quantum-mechanical forces in real materials is investigated by tests on pure and defective Ni, Fe, and Si crystalline systems.