数据驱动的非线性动力学混沌指示器及其在储存环晶格设计中的应用
Data-driven Chaos Indicator for Nonlinear Dynamics and Applications on Storage Ring Lattice Design
摘要：
引入数据驱动混沌指标的概念来表征非线性动力系统的混沌程度。该指标由纯粹根据数据建立的替代模型的预测准确性表示。它为给定系统中非线性运动的可预测性提供了一个度量。当使用指示器来实现二次Henon映射的调谐扫描时，可以识别主谐振及其不对称阻带宽度。应用于储存环中的粒子输运时，随着粒子运动的混沌化，代理模型的预测精度相应降低。因此，预测精度作为混沌指标，可以直接作为非线性束流动力学优化的目标。该方法为非线性梁动力学研究提供了一个新的视角，也为非线性格点优化提供了一种有效的方法。在动态孔径优化的应用程序被证明是现实世界的例子。
英文摘要：
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.
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