Solving the electronic structure problem with machine learning

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.