Data-driven Chaos Indicator for Nonlinear Dynamics and Applications on Storage Ring Lattice Design

TL;DR

This paper introduces a data-driven chaos indicator based on surrogate model prediction accuracy to characterize chaos in nonlinear dynamical systems, aiding in beam dynamics optimization and resonance identification.

Contribution

The paper presents a novel chaos indicator derived from surrogate model accuracy, enabling direct assessment of nonlinearity and chaos in storage ring lattice design.

Findings

Prediction accuracy decreases with increased chaos in particle motion.

The indicator effectively identifies resonances and stop-band widths.

Application to storage rings improves nonlinear lattice optimization.

Abstract

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 Henon 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.