A semi-supervised method for fast prediction of chaotic motions in nonintegrable systems

We propose to use a semi-supervised learning technique to quickly estimate the stability of chaotic dynamical systems by utilizing longand short-term numerical integrations jointly. To determine the stability of a chaotic Hamiltonian system, pure long-term numerical integration is the most reliable method, which is however computationally expensive. When applying to the dynamic aperture (DA) evaluation of a diffraction-limited synchrotron light source and a lepton collider, this semi-supervised method can approximately distinguish the regular and chaotic trajectories of particles from their one-turn trajectories with up to 90% accuracy. We demonstrate that the needed computation time can be reduced by an order of magnitude when applying this method to the DA optimization of a diffraction-limited synchrotron light source. This model-independent method is not limited to a particular physical model such as a storage ring beam dynamics, thus are directly transferable to other chaotic dynamical systems.