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Despite the successes of machine learning methods in physical sciences,prediction of the Hamiltonian, and thus electronic properties, is stillunsatisfactory. Here, based on graph neural network architecture, we present anextendable neural network model to determine the Hamiltonian from ab initiodata, with only local atomic structures as inputs. Rotational equivariance ofthe Hamiltonian is achieved by our complete local coordinates. The localcoordinates information, encoded using the convolutional neural network anddesigned to preserve Hermitian symmetry, is used to map hopping parameters ontolocal structures. We demonstrate the performance of our model using grapheneand SiGe random alloys as examples. We show that our neural network model,although trained using small-size systems, can predict the Hamiltonian, as wellas electronic properties such as band structures and densities of states (DOS)for large-size systems within the ab initio accuracy, justifying itsextensibility. In combination with the high efficiency of our model, whichtakes only seconds to get the Hamiltonian of a 1728-atom system, present workprovides a general framework to predict electronic properties efficiently andaccurately, which provides new insights into computational physics and willaccelerate the research for large-scale materials.

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