  Quantum many-body methods provide a systematic route to computing electronic
properties of molecules and materials, but high computational costs restrict
their use in large-scale applications. Due to the complexity in many-electron
wavefunctions, machine learning models capable of capturing fundamental
many-body physics remain limited. Here, we present a deep learning framework
targeting the many-body Green's function, which unifies predictions of
electronic properties in ground and excited states, while offering deep
physical insights into electron correlation effects. By learning the $GW$ or
coupled-cluster self-energy from mean-field features, our graph neural network
achieves competitive performance in predicting one- and two-particle
excitations and quantities derivable from one-particle density matrix. We
demonstrate its high data efficiency and good transferability across chemical
species, system sizes, molecular conformations, and correlation strengths in
bond breaking, through multiple molecular and nanomaterial benchmarks. This
work opens up new opportunities for utilizing machine learning to solve
many-electron problems.
