时间滞后复发：一种数据驱动的方法，用于估计动力系统可预测性
Time-Lagged Recurrence: a data-driven method to estimate the predictability of dynamical systems
AI总结：
本文提出了一种基于复发的概念的数据驱动方法，用于估计动力系统的局部可预测性，该方法在理想系统和真实世界数据集上均显示出有效性，并探讨了其与局部动力学指数的关系及信息理论的联系。
摘要：
非线性动力系统在自然界中普遍存在，但难以预测。它们不仅可能对初始条件的小扰动敏感，而且通常由多个尺度的过程组成。基于李雅普诺夫谱的经典方法依赖于动态前向算子或数据推导的近似值。此算子通常未知，或数据太噪杂无法准确表示。本文提出了一种新的数据驱动方法，用于分析动力系统的局部可预测性。该方法基于复发的概念，与已建立的局部动力学指数框架密切相关。当应用于理想系统和大规模大气场数据集时，该方法在估计局部可预测性方面证明了其有效性。此外，我们讨论了其与其他局部动力学指数的关系，以及它揭示可预测性的尺度依赖性。此外，我们探讨了其与信息理论的联系，其扩展方法包括加权策略，并探讨了其实时应用。我们相信这些方面共同展示了其作为复杂系统强大诊断工具的潜力。
英文摘要：
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales. Classical approaches based on the Lyapunov spectrum rely on the knowledge of the dynamic forward operator, or of a data-derived approximation of it. This operator is typically unknown, or the data are too noisy to derive its faithful representation. Here we propose a new data-driven approach to analyze the local predictability of dynamical systems. This method, based on the concept of recurrence, is closely linked to the well-established framework of local dynamical indices. When applied to both idealized systems and real-world datasets arising from large-scale atmospheric fields, our new approach proves its effectiveness in estimating local predictability. Additionally, we discuss its relationship with other local dynamical indices, and how it reveals the scale-dependent nature of predictability. Furthermore, we explore its link to information theory, its extension that includes a weighting strategy, and its real-time application. We believe these aspects collectively demonstrate its potential as a powerful diagnostic tool for complex systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
