Parameter inference in nonlinear dynamical systems via recurrence plots and convolutional neural networks

Area of Science:

• Nonlinear Dynamics
• Machine Learning
• Chaos Theory

Background:

• Inferring control parameters in nonlinear dynamical systems is crucial for understanding their behavior, especially with deterministic chaos.
• Traditional methods often require system-specific models and complex parameterizations, limiting their broad application.

Purpose of the Study:

• To develop and validate a novel methodology for inferring control parameters in nonlinear dynamical systems.
• To demonstrate the effectiveness of using recurrence plots and convolutional neural networks for this task.

Main Methods:

• Recurrence plots were used to represent nonlinear trajectories.
• Convolutional neural networks were trained on these recurrence plots to infer control parameters.
• The methodology was tested on the logistic map and the standard map.

Main Results:

• The proposed approach accurately estimated control parameters for the tested nonlinear systems.
• Recurrence plot-based methods showed significantly more robust results compared to direct time-series regression models.
• Accurate parameter inference, combined with initial conditions, allows for deterministic system reconstruction.

Conclusions:

• Recurrence-based learning frameworks offer a powerful tool for automated identification and characterization of nonlinear dynamical systems.
• This methodology provides a generalizable and robust approach to parameter inference in nonlinear dynamics.
• The findings advance the understanding and analysis of complex systems exhibiting chaotic behavior.