  Electron-phonon coupling (EPC) plays an important role in many fundamental
physical phenomena, but the high computational cost of the EPC matrix hinders
the theoretical research on them. In this paper, an analytical formula is
derived to calculate the EPC matrix in terms of the Hamiltonian and its
gradient in the nonorthogonal atomic orbital bases. The recently-developed E(3)
equivariant neural network is used to directly predict the Hamiltonian and its
gradient needed by the formula, thus bypassing the expensive self-consistent
iterations in DFT. The correctness of the proposed EPC calculation formula and
the accuracy of the predicted EPC values of the network are illustrated by the
tests on a water molecule and a MoS2 crystal.
