Data-driven chaos indicator for nonlinear dynamics and applications on storage ring lattice design

A data-driven chaos indicator concept is introduced to characterize the degree of chaos for nonlinear dynamical systems. The indicator is represented by the prediction accuracy of surrogate models established purely from data. It provides a metric for the predictability of nonlinear motions in a given system. When using the indicator to implement a tune-scan for a quadratic Hénon map, the main resonances and their asymmetric stop-band widths can be identified. When applied to particle transportation in a storage ring, as particle motion becomes more chaotic, its surrogate model prediction accuracy decreases correspondingly. Therefore, the prediction accuracy, acting as a chaos indicator, can be used directly as the objective for nonlinear beam dynamics optimization. This method provides a different perspective on nonlinear beam dynamics and an efficient method for nonlinear lattice optimization. Applications in dynamic aperture optimization are demonstrated as real world examples.