Symplectic Recurrent Neural Networks

TL;DR

Symplectic Recurrent Neural Networks (SRNNs) are designed to learn and simulate the dynamics of physical Hamiltonian systems, effectively handling complex, noisy, and stiff systems through specialized training and integration techniques.

Contribution

This paper introduces SRNNs that incorporate symplectic integration and Hamiltonian modeling, advancing neural network methods for physical system dynamics.

Findings

SRNNs reliably model complex Hamiltonian systems

SRNNs effectively handle noisy data

SRNNs can simulate stiff dynamical systems like bouncing billiards

Abstract

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.