Deep Hamiltonian networks based on symplectic integrators

Understand

HNets is a class of neural networks on grounds of physical prior for learning Hamiltonian systems.

• This paper explains the influences of different integrators as hyper-parameters on the HNets through error analysis.
• If we define the network target as the map with zero empirical loss on arbitrary training data, then the non-symplectic integrators cannot guarantee the existence of the network targets of HNets.
• We introduce the inverse modified equations for HNets and prove that the HNets based on symplectic integrators possess network targets and the differences between the network targets and the original Hamiltonians depend on the accuracy orders of the integrators.