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Solving the electronic structure problem with machine learning
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DOI：10.1038/s41524-019-0162-7.png)
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Abstract
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Simulations based on solving the Kohn-Sham (KS) equation of density functional theory (DFT) have become a vital component of modern materials and chemical sciences research and development portfolios. Despite its versatility, routine DFT calculations are usually limited to a few hundred atoms due to the computational bottleneck posed by the KS equation. Here we introduce a machine-learning-based scheme to efficiently assimilate the function of the KS equation, and by-pass it to directly, rapidly, and accurately predict the electronic structure of a material or a molecule, given just its atomic configuration. A new rotationally invariant representation is utilized to map the atomic environment around a grid-point to the electron density and local density of states at that grid-point. This mapping is learned using a neural network trained on previously generated reference DFT results at millions of grid-points. The proposed paradigm allows for the high-fidelity emulation of KS DFT, but orders of magnitude faster than the direct solution. Moreover, the machine learning prediction scheme is strictly linear-scaling with system size.
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