  Recently, Hamiltonian neural networks (HNN) have been introduced to
incorporate prior physical knowledge when learning the dynamical equations of
Hamiltonian systems. Hereby, the symplectic system structure is preserved
despite the data-driven modeling approach. However, preserving symmetries
requires additional attention. In this research, we enhance HNN with a Lie
algebra framework to detect and embed symmetries in the neural network. This
approach allows to simultaneously learn the symmetry group action and the total
energy of the system. As illustrating examples, a pendulum on a cart and a
two-body problem from astrodynamics are considered.
