  The combination of deep learning and ab initio materials calculations is
emerging as a trending frontier of materials science research, with
deep-learning density functional theory (DFT) electronic structure being
particularly promising. In this work, we introduce a neural-network method for
modeling the DFT density matrix, a fundamental yet previously unexplored
quantity in deep-learning electronic structure. Utilizing an advanced neural
network framework that leverages the nearsightedness and equivariance
properties of the density matrix, the method demonstrates high accuracy and
excellent generalizability in multiple example studies, as well as capability
to precisely predict charge density and reproduce other electronic structure
properties. Given the pivotal role of the density matrix in DFT as well as
other computational methods, the current research introduces a novel approach
to the deep-learning study of electronic structure properties, opening up new
opportunities for deep-learning enhanced computational materials study.
