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Cluster-based network modeling-From snapshots to complex dynamical systems.

Daniel Fernex1, Bernd R Noack2,3, Richard Semaan4

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We introduce cluster-based network modeling (CNM), a universal method for data-driven modeling of complex nonlinear dynamics. This automatable approach accurately captures system behavior without prior knowledge, advancing scientific understanding and control.

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Area of Science:

  • Complex systems analysis
  • Data-driven modeling
  • Network science

Background:

  • Complex nonlinear dynamics are prevalent across science and engineering.
  • Existing data-driven methods often require assumptions about low-dimensional state spaces.
  • Modeling rare events in complex systems remains a significant challenge.

Purpose of the Study:

  • To develop a universal, automatable data-driven method for modeling complex nonlinear dynamics.
  • To overcome the limitations of state-space assumptions in dynamic modeling.
  • To provide a robust framework for analyzing diverse complex systems.

Main Methods:

  • Propose cluster-based network modeling (CNM), integrating machine learning, network science, and statistical physics.
  • CNM models system dynamics using time-resolved snapshot data without prior knowledge.
  • Demonstrate CNM's applicability across various complex systems.

Main Results:

  • CNM accurately models both short- and long-term behaviors of complex nonlinear dynamics.
  • The method successfully models the Lorenz attractor, ECG signals, Kolmogorov flow, and turbulent boundary layers.
  • CNM effectively addresses the challenge of modeling rare events, as shown in Kolmogorov flow.

Conclusions:

  • CNM offers a universal, automatable approach to data-driven dynamic modeling.
  • This method expands network connectivity science and provides new tools for complex system analysis.
  • CNM facilitates understanding, estimation, prediction, and control of complex systems across scientific disciplines.