  Machine learning has become increasingly popular for efficiently modelling
the dynamics of complex physical systems, demonstrating a capability to learn
effective models for dynamics which ignore redundant degrees of freedom.
Learned simulators typically predict the evolution of the system in a
step-by-step manner with numerical integration techniques. However, such models
often suffer from instability over long roll-outs due to the accumulation of
both estimation and integration error at each prediction step. Here, we propose
an alternative construction for learned physical simulators that are inspired
by the concept of action-angle coordinates from classical mechanics for
describing integrable systems. We propose Action-Angle Networks, which learn a
nonlinear transformation from input coordinates to the action-angle space,
where evolution of the system is linear. Unlike traditional learned simulators,
Action-Angle Networks do not employ any higher-order numerical integration
methods, making them extremely efficient at modelling the dynamics of
integrable physical systems.
