Abstract
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.
Highlights
A critical obstacle to wide-spectrum applications of the Material informatics (MI) is absence of descriptors for field quantities
The proposed voxel descriptor inherently keeps the invariances of the translation, commutation of atomic labels, and unit-cell selection; the three-dimensional convolutional neural networks (CNNs) learn the rotation invariance with augmented input data which are rotated from the original voxel data
The reciprocal 3D voxel space (R3DVS) data are augmented by copies with non-zero-angle rotations of the original R3DVS data; namely, none of the rotated replicas is identical to the original
Summary
Even though the practical applications should aim at predictions of properties such as non-equilibrium quantities that are difficult to be obtained by usual simulations, this study uses objective variables obtained by ab-initio methods for the purpose of the assessment of the present scheme. We randomly select 680 oxides which contain less than 50 atoms in the each unit cell from the inorganic crystal structure database (ICSD; https://icsd.fiz-karlsruhe.de). The selected oxides are calculated by VASP33 which is a program package of electronic-state calculations based on density functional theory. Exchange-correlation functional is expressed by the Perdew-Berke-Ernzerhof type of generalised gradient approximation[34], a plane wave basis set with a cutoff energy of 500 eV is used to expand one-electron wave function, and the projector-augmented-wave method is used to describe interactions between the valence electrons and ion cores[35]. We adopt energy terms that constitute a total energy E of a unit cell as objective variables for the regression tests. Cohesive energy and band gap are added to the objective variables
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