Dong Chenyu, Faranda Davide, Gualandi Adriano, Lucarini Valerio, Mengaldo Gianmarco
Department of Mechanical Engineering, National University of Singapore, Singapore 117575, Singapore.
Laboratoire des Sciences du Climat et de l'Environnement, Commissariat á l'énergie atomique et aux énergies alternatives Saclay l'Orme des Merisiers Unité Mixte de Recherche 8212 CEA-Centre National de la Recherche Scientifique-Université de Versailles - Saint-Quentin-en-Yvelines, Université Paris-Saclay & Institut Pierre Simon Laplace, 91191, Gif-sur-Yvette, France.
Proc Natl Acad Sci U S A. 2025 May 20;122(20):e2420252122. doi: 10.1073/pnas.2420252122. Epub 2025 May 16.
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 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 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.
非线性动力系统在自然界中无处不在，且难以预测。它们不仅可能对初始条件中的小扰动敏感，而且通常由多个尺度上的过程组成。基于李雅普诺夫谱的经典方法依赖于动态正向算子的知识，或者其数据衍生近似。这个算子通常是未知的，或者数据噪声太大，无法得到其可靠的表示。在这里，我们提出一种数据驱动的方法来分析动力系统的局部可预测性。这种基于递归概念的方法与成熟的局部动力学指标框架密切相关。当应用于理想化系统和来自大规模大气场的实际数据集时，我们的方法证明了其在估计局部可预测性方面的有效性。此外，我们讨论了它与其他局部动力学指标的关系，以及它如何揭示可预测性的尺度依赖性本质。此外，我们探索了它与信息论的联系、其包含加权策略的扩展以及其实时应用。我们相信这些方面共同证明了它作为复杂系统强大诊断工具的潜力。
