  The many-body Green's function provides access to electronic properties
beyond density functional theory level in ab inito calculations. In this
manuscript, we propose a deep learning framework for predicting the
finite-temperature Green's function in atomic orbital space, aiming to achieve
a balance between accuracy and efficiency. By predicting the self-energy
matrices in Lehmann representation using an equivariant message passing neural
network, our method respects its analytical property and the $E(3)$
equivariance. The Green's function is obtained from the predicted self-energy
through Dyson equation with target total number of electrons. We present
proof-of-concept benchmark results for both molecules and simple periodic
systems, showing that our method is able to provide accurate estimate of
physical observables such as energy and density of states based on the
predicted Green's function.
