We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM describes short- and long-term behavior and is fully automatable, as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict, and control complex systems in all scientific fields.

我们提出了一种通用方法，用于在没有先验知识的情况下从时间分辨快照数据对复杂非线性动力学进行数据驱动建模。复杂的非线性动力学支配着科学和工程的许多领域。数据驱动的动态建模通常为状态假设一个低维子空间或流形。我们通过提出基于集群的网络建模 (CNM) 桥接机器学习、网络科学和统计物理学，将自己从这种假设中解放出来。CNM 描述短期和长期行为，并且完全可以自动化，因为它不依赖于特定于应用程序的知识。CNM 用于洛伦兹吸引子、ECG 心跳信号、Kolmogorov 流和高维驱动湍流边界层。即使是众所周知的 Kolmogorov 流中罕见事件的建模基准也得到了解决。