Phase autoencoder for rapid data-driven synchronization of rhythmic spatiotemporal patterns.

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Computational Physics

Background:

• Reaction-diffusion systems exhibit complex rhythmic spatiotemporal patterns.
• Controlling these dynamics, especially synchronization, is challenging due to high dimensionality.
• Existing methods often struggle with precise phase control without affecting amplitude.

Purpose of the Study:

• To develop a data-driven machine-learning method for synchronizing rhythmic spatiotemporal patterns in reaction-diffusion systems.
• To extend the phase autoencoder framework for high-dimensional field variables.
• To enable precise phase control of spatiotemporal dynamics.

Main Methods:

• Developed a framework to map high-dimensional field variables to low-dimensional latent variables using a phase autoencoder.
• Characterized asymptotic phase and amplitudes of the system's dynamics.
• Proposed a method to drive the system along the limit cycle's tangential direction for phase control.

Main Results:

• Achieved data-driven phase description of limit cycle dynamics.
• Demonstrated successful rapid synchronization of 1D oscillating spots and 2D spiral waves in the FitzHugh-Nagumo system.
• Showcased phase control without inducing amplitude deviations in reference-based and coupling-based settings.

Conclusions:

• The phase autoencoder provides a powerful tool for data-driven phase description of complex spatiotemporal dynamics.
• The proposed method enables effective synchronization of reaction-diffusion systems.
• This approach holds significant potential for controlling high-dimensional spatiotemporal patterns.