  Incorporating the Hamiltonian structure of physical dynamics into deep
learning models provides a powerful way to improve the interpretability and
prediction accuracy. While previous works are mostly limited to the Euclidean
spaces, their extension to the Lie group manifold is needed when rotations form
a key component of the dynamics, such as the higher-order physics beyond simple
point-mass dynamics for N-body celestial interactions. Moreover, the multiscale
nature of these processes presents a challenge to existing methods as a long
time horizon is required. By leveraging a symplectic Lie-group manifold
preserving integrator, we present a method for data-driven discovery of
non-Newtonian astronomy. Preliminary results show the importance of both these
properties in training stability and prediction accuracy.
