形成能机器学习模型的晶体结构表示
Crystal Structure Representations for Machine Learning Models of Formation Energies
摘要：
我们介绍和评估一组特征向量表示的晶体结构的机器学习（ML）模型的固体形成能。ML模型的原子化能量的有机分子已成功地使用库仑矩阵表示的分子。我们考虑了三种将这种表示推广到周期系统的方法：（i）一个矩阵，其中每个元素都与晶格上重复的两个不同原子之间静电相互作用的Ewald和有关;（ii）一个扩展的类库仑矩阵，它考虑了许多相邻的单元格;以及（iii）通过使用原子的晶体坐标的正弦函数来模拟埃瓦尔德和矩阵中的元素的周期性和基本特征的Ancor。的表示比较与曼哈顿规范的拉普拉斯内核，训练再生形成能量使用的数据集的3938晶体结构从材料项目。对于由3000个晶体组成的训练集，预测新结构的形成能的泛化误差对应于各自表示的（i）0.49、（ii）0.64和（iii）0.37 eV/原子。
英文摘要：
We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an Ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix by using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a data set of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37 eV/atom for the respective representations.
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