Convolutional neural network learning of self-consistent electron density via field-projected atomic fingerprints

While density functional theory (DFT) has been established as the standard approach for first-principles materials simulations, with the significant increase of computational costs with the system size, the practical use of the DFT is typically limited to systems containing less than a few hundred atoms. Herein, we develop the machine learning scheme DeepSCF to predict the map between the initial guess density and the converged electron density within the self-consistent field (SCF) loop based on the three-dimensional (3D) convolutional neural network. To successfully enable the objective, we devise on field-projected atomic fingerprints of materials that encode the structural and chemical information of target materials into 3D real-space grid. To incorporate diverse chemical bonding information, we train our model by adopting a molecular database that includes different bonding configurations and also augment the training datasets to maximize the model transferability. Next, using the trained model, we examine various electronic structures of the test dataset and confirm that the quality of our DeepSCF is comparable to that of DFT counterparts. Finally, we demonstrate the size-extensibility and transferability of the DeepSCF model with crystalline polyethylene, graphene and composite DNA-carbon nanotube structures.