  We propose Symplectic Recurrent Neural Networks (SRNNs) as learning
algorithms that capture the dynamics of physical systems from observed
trajectories. An SRNN models the Hamiltonian function of the system by a neural
network and furthermore leverages symplectic integration, multiple-step
training and initial state optimization to address the challenging numerical
issues associated with Hamiltonian systems. We show that SRNNs succeed reliably
on complex and noisy Hamiltonian systems. We also show how to augment the SRNN
integration scheme in order to handle stiff dynamical systems such as bouncing
billiards.
