原子系统张量性质的对称自适应机器学习
Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
摘要：
统计学习方法在提供材料和分子性质的准确预测方面显示出巨大的潜力，同时最大限度地减少了对计算要求高的电子结构计算的需求。这些模型的准确性和可转移性显着增加编码到学习过程中的基本对称性的旋转和置换不变性的标量属性。然而，张量性质的预测要求模型在参考系旋转时遵守适当的几何变换，而不是不变性。我们介绍了一种形式主义，可用于执行机器学习的一般分子几何形状的任意秩的张量属性。为了证明这一点，我们推导出一个张量核适应旋转对称性，这是自然推广的平滑重叠原子位置（SOAP）内核通常用于预测标量属性在原子尺度。该方法的性能和一般性证明了通过学习的瞬时电响应的水低聚物的复杂性不断增加，从孤立的分子到凝聚相。
英文摘要：
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and transferability of these models are increased significantly by encoding into the learning procedure the fundamental symmetries of rotational and permutational invariance of scalar properties. However, the prediction of tensorial properties requires that the model respects the appropriate geometric transformations, rather than invariance, when the reference frame is rotated. We introduce a formalism that can be used to perform machine-learning of tensorial properties of arbitrary rank for general molecular geometries. To demonstrate it, we derive a tensor kernel adapted to rotational symmetry, which is the natural generalization of the smooth overlap of atomic positions (SOAP) kernel commonly used for the prediction of scalar properties at the atomic scale. The performance and generality of the approach is demonstrated by learning the instantaneous electrical response of water oligomers of increasing complexity, from the isolated molecule to the condensed phase.
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