论文标题
基于群集的网络建模 - 复杂动力学系统的自动鲁棒建模
Cluster-based network modeling -- automated robust modeling of complex dynamical systems
论文作者
论文摘要
我们提出了一种通用方法，用于在没有时间分辨的快照数据的情况下对复杂非线性动力学进行数据驱动的建模。复杂的非线性动力学控制了许多科学和工程领域。数据驱动的动态建模通常假定状态的低维子空间或歧管。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来使自己摆脱这一假设。 CNM仅假定状态空间中动力学的平滑度，可鲁棒地描述短期和长期行为，并且完全可自动化，因为它不依赖于应用程序特定的知识。证明了CNM的Lorenz吸引子，ECG心跳信号，Kolmogorov流量和高维驱动的湍流边界层。即使是臭名昭著的罕见事件在Kolmogorov流中的建模基准也可以解决。这种复杂非线性动力学的自动通用数据驱动的表示，并扩展了网络连接科学，并承诺在所有科学领域中了解，估算，预测，预测和控制复杂系统的新快速途径。
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 only assumes smoothness of the dynamics in the state space, robustly 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.
