Learning Hamiltonians of constrained mechanical systems

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian are elegant compact formalism classical mechanics, where the dynamics is fully determined by one scalar function, Hamiltonian. The solution trajectories often constrained to evolve on a submanifold linear vector space. In this work, we propose new approaches for accurate approximation function mechanical given sample data information their solutions. We focus importance preservation constraints learning strategy using both explicit Lie group integrators other schemes.