Material informatics (MI) is a promising approach to liberate us from the time-consuming Edisonian (trial and error) process for material discoveries, driven by machine-learning algorithms. Several descriptors, which are encoded material features to feed computers, were proposed in the last few decades. Especially to solid systems, however, their insufficient representations of three dimensionality of field quantities such as electron distributions and local potentials have critically hindered broad and practical successes of the solid-state MI. We develop a simple, generic 3D voxel descriptor that compacts any field quantities, in such a suitable way to implement convolutional neural networks (CNNs). We examine the 3D voxel descriptor encoded from the electron distribution by a regression test with 680 oxides data. The present scheme outperforms other existing descriptors in the prediction of Hartree energies that are significantly relevant to the long-wavelength distribution of the valence electrons. The results indicate that this scheme can forecast any functionals of field quantities just by learning sufficient amount of data, if there is an explicit correlation between the target properties and field quantities. This 3D descriptor opens a way to import prominent CNNs-based algorithms of supervised, semi-supervised and reinforcement learnings into the solid-state MI.
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