Graph-based neural networks and, specifically, message-passing neural networks (MPNNs) have shown great potential in predicting physical properties of solids. In this work, we train an MPNN to first classify materials through density functional theory data from the AFLOW database as being metallic or semiconducting/insulating. We then perform a neural-architecture search to explore the model architecture and hyperparameter space of MPNNs to predict the band gaps of the materials identified as non-metals. The parameters in the search include the number of message-passing steps, latent size, and activation-function, among others. The top-performing models from the search are pooled into an ensemble that significantly outperforms existing models from the literature. Uncertainty quantification is evaluated with Monte-Carlo Dropout and ensembling, with the ensemble method proving superior. The domain of applicability of the ensemble model is analyzed with respect to the crystal systems, the inclusion of a Hubbard parameter in the density functional calculations, and the atomic species building up the materials.
We verified that the deep learning method named reading periodic table introduced by ref. Deep Learning Model for Finding New Superconductors, which utilizes deep learning to read the periodic table and the laws of the elements, is applicable not only for superconductors, for which the method was originally applied but also for other problems of materials by demonstrating band gap estimations. We then extended the method to learn the laws better by directly learning the cylindrical periodicity between the right- and left-most columns in the periodic table at the learning representation level, that is, by considering the left- and right-most columns to be adjacent to each other. Thus, while the original method handles the table as is, the extended method treats the periodic table as if its two edges are connected. This is achieved using novel layers named periodic convolution layers, which can handle inputs exhibiting periodicity and may be applied to other problems related to computer vision, time series, and so on for data that possess some periodicity. In the reading periodic table method, no material feature or descriptor is required as input. We demonstrated two types of deep learning estimation: methods to estimate the existence of a bandgap, and methods to estimate the value of the bandgap given when the existence of the bandgap in the materials is known. Finally, we discuss the limitations of the dataset and model evaluation method. We may be unable to distinguish good models based on the random train-test split scheme; thus, we must prepare an appropriate dataset where the training and test data are temporally separate. The code and data are open.