Ground state charge density prediction in C-BN nanoflakes using rotation equivariant feature-free artificial neural networks

Abstract Ab initio methods have been the workhorse for the computational investigation of new materials during the past few decades. In spite of the improvements regarding the efficiency and scalability achieved by various implementations, the self-consistent solution of the Konhn-Sham equations remains challenging as the size of the system increases. We propose here machine learning methods based on a feature-free deep ANN approach that are able to predict the ground state charge density by starting from readily accessible ’free-atom’ charge densities, thus bypassing the usual Hamiltonian diagonalization. We validate our approach on hybrid C-BN nanoflakes with random atomic configurations by comparing the predicted charge density to that computed by DFT. The ANN architecture is optimized in order to reach the high prediction accuracy required to extract ground state based material properties. In order to correlate the effect of spatial rotations in the input-output mapping, we introduce a novel rotational equivariant network (RE-ANN), by properly symmetrizing the synaptic weights during training. This regularization procedure enhances the prediction accuracy, provides consistent results under rotation operations and also increases the sparsity of the weight matrix. These methods have the potential to speed-up DFT simulations and can be used as high throughput investigation tools.