  Despite the successes of machine learning methods in physical sciences,
prediction of the Hamiltonian, and thus electronic properties, is still
unsatisfactory. Here, based on graph neural network architecture, we present an
extendable neural network model to determine the Hamiltonian from ab initio
data, with only local atomic structures as inputs. Rotational equivariance of
the Hamiltonian is achieved by our complete local coordinates. The local
coordinates information, encoded using the convolutional neural network 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 neural network model,
although trained using small-size systems, can predict the Hamiltonian, as well
as electronic properties such as band structures and densities of states (DOS)
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, 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.
