论文标题
数据驱动方法的指南研究多尺度系统中的过渡：Lyapunov向量的情况
Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors
论文作者
论文摘要
我们详细研究了协方差lyapunov载体及其各自的角度在动态系统中检测亚稳态状态之间的过渡的角度，如最近在几种大气科学应用中所讨论的那样。基础模型是通过动态聚类方法（称为fem-bv-var的数据）构建的，lyapunov矢量是根据这些模型近似的。我们在三个井井有条的示例系统的手中测试了这种基于数据的数值方法，这些系统具有增加的动态复杂性，确定了允许成功应用该方法的关键属性：特别是，事实证明，该方法需要清晰的多个时间尺度结构，并在慢速子系统之间进行快速过渡，从而可以通过线性近似模型的不变性中性方向进行动态表征。
We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric science applications. The underlying models are built from data by the dynamical clustering method, called FEM-BV-VAR, and the Lyapunov vectors are approximated based on these models. We test this data-based numerical approach at the hand of three well-understood example systems with increasing dynamical complexity, identifying crucial properties that allow for a successful application of the method: in particular, it turns out that the method requires a clear multiple time scale structure with fast transitions between slow subsystems which can be dynamically characterized by invariant neutral directions of the linear approximation model.
