Predicting Elastic Properties of Materials from Electronic Charge Density Using 3D Deep Convolutional Neural Networks

Materials representation plays a key role in machine learning-based prediction of materials properties and new materials discovery. Currently both graph and three-dimensional (3D) voxel representation methods are based on the heterogeneous elements of the crystal structures. Here, we propose to use electronic charge density (ECD) as a generic unified 3D descriptor for materials property prediction with the advantage of possessing close relation with the physical and chemical properties of materials. We developed an ECD-based 3D convolutional neural networks (CNNs) for predicting the elastic properties of materials, in which CNNs can learn effective hierarchical features with multiple convolving and pooling operations. Extensive benchmark experiments over 2170 Fm3̅m face-centered-cubic materials show that our ECD-based CNNs can achieve good performance for elasticity prediction. Especially, our CNN models based on the fusion of elemental Materials-Agnostic Platform for Informatics and Exploration features and ECD descriptors achieved the best fivefold cross-validation performance. More importantly, we showed that our ECD-based CNN models can achieve significantly better extrapolation performance when evaluated over nonredundant data sets, where there are few neighbor-training samples around test samples. As an additional validation, we evaluated the predictive performance of our models on 329 materials of space group Fm3̅m by comparing to density functional theory calculated values, which shows a better prediction power of our model for bulk modulus than shear modulus. Because of the unified representation power of ECD, it is expected that our ECD-based CNN approach can also be applied to predict other physical and chemical properties of crystalline materials.