Symplectic Recurrent Neural Networks
This work addresses the challenge of modeling physical system dynamics for applications in physics and engineering, representing an incremental improvement by combining existing techniques like symplectic integration with neural networks.
The authors tackled the problem of learning dynamics of physical systems from observed trajectories by proposing Symplectic Recurrent Neural Networks (SRNNs), which reliably succeeded on complex and noisy Hamiltonian systems and were extended to handle stiff dynamical systems like bouncing billiards.
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.