  In this paper, we present neural networks learning mechanical systems that
are both symplectic (for instance particle mechanics) and non-symplectic (for
instance rotating rigid body). Mechanical systems have Hamiltonian evolution,
which consists of two building blocks: a Poisson bracket and an energy
functional. We feed a set of snapshots of a Hamiltonian system to our neural
network models which then find both the two building blocks. In particular, the
models distinguish between symplectic systems (with non-degenerate Poisson
brackets) and non-symplectic systems (degenerate brackets). In contrast with
earlier works, our approach does not assume any further a priori information
about the dynamics except its Hamiltonianity, and it returns Poisson brackets
that satisfy Jacobi identity. Finally, the models indicate whether a system of
equations is Hamiltonian or not.
