Efficient determination of the Hamiltonian and electronic properties using graph neural network with complete local coordinates

Abstract Despite the successes of machine learning methods in physical sciences, the prediction of the Hamiltonian, and thus the electronic properties, is still unsatisfactory. Based on graph neural network (NN) architecture, we present an extendable NN model to determine the Hamiltonian from ab initio data, with only local atomic structures as inputs. The rotational equivariance of the Hamiltonian is achieved by our complete local coordinates (LCs). The LC information, encoded using a convolutional NN and designed to preserve Hermitian symmetry, is used to map hopping parameters onto local structures. We demonstrate the performance of our model using graphene and SiGe random alloys as examples. We show that our NN model, although trained using small-size systems, can predict the Hamiltonian, as well as electronic properties such as band structures and densities of states for large-size systems within the ab initio accuracy, justifying its extensibility. In combination with the high efficiency of our model, which takes only seconds to get the Hamiltonian of a 1728-atom system, the present work provides a general framework to predict electronic properties efficiently and accurately, which provides new insights into computational physics and will accelerate the research for large-scale materials.