  The combination of numerical integration and deep learning, i.e., ODE-net,
has been successfully employed in a variety of applications. In this work, we
introduce inverse modified differential equations (IMDE) to contribute to the
behaviour and error analysis of discovery of dynamics using ODE-net. It is
shown that the difference between the learned ODE and the truncated IMDE is
bounded by the sum of learning loss and a discrepancy which can be made sub
exponentially small. In addition, we deduce that the total error of ODE-net is
bounded by the sum of discrete error and learning loss. Furthermore, with the
help of IMDE, theoretical results on learning Hamiltonian system are derived.
Several experiments are performed to numerically verify our theoretical
results.
