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Data-driven ordinary-differential-equation modeling of high-frequency complex dynamics via a low-frequency dynamics
Natsuki Tsutsumi1, Kengo Nakai2, Yoshitaka Saiki3
1Hitotsubashi University, Faculty of Commerce and Management, Tokyo 186-8601, Japan.
Physical Review. E
|February 20, 2025
Summary
This study introduces an improved method for modeling complex chaotic dynamics, like fluid flow, by using a joint model with a simpler base variable. This approach enhances the reconstruction of chaotic sets and statistical properties from time series data.
Area of Science:
- Nonlinear dynamics
- Fluid mechanics
- Time series analysis
Background:
- Previous radial function-based regression (RfR) method struggles with complex, intermittent time series data.
- Modeling chaotic behavior from observable data is crucial for understanding complex systems.
Purpose of the Study:
- To develop a robust method for modeling complex chaotic dynamics, including intermittent fluid flow behavior.
- To construct an autonomous joint model that overcomes limitations of direct RfR application.
Main Methods:
- Proposed a novel joint modeling approach using a base variable with simpler dynamics.
- Developed a two-part autonomous model: one for the base variable, another for the targeted variable influenced by the base variable.
- Applied the model to reconstruct chaotic sets and statistical properties from time series data.
Main Results:
- The joint model successfully inferred short trajectories.
- Reconstructed chaotic sets and statistical properties, including density distributions, from long trajectories.
- Demonstrated effectiveness in modeling high-frequency intermittent behavior in fluid flow dynamics.
Conclusions:
- The proposed joint modeling method enhances the analysis of complex chaotic systems.
- This approach provides a more accurate reconstruction of dynamics compared to direct RfR.
- The method is effective for inferring dynamics from observable deterministic time series, even with intermittent behavior.
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