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

TL;DR

This paper introduces a machine-learning approach using a phase autoencoder to achieve rapid data-driven synchronization of complex rhythmic patterns in reaction-diffusion systems, enabling efficient phase control without amplitude disturbances.

Contribution

The paper develops a novel data-driven phase autoencoder method that enables rapid synchronization of high-dimensional spatiotemporal patterns in reaction-diffusion systems.

Findings

Achieves rapid synchronization of 1D and 2D patterns

Enables phase control without amplitude deviations

Demonstrates effectiveness in FitzHugh-Nagumo systems

Abstract

We present a machine-learning method for data-driven synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems. Based on the phase autoencoder [Yawata {\it et al.}, Chaos {\bf 34}, 063111 (2024)], we map high-dimensional field variables of the reaction-diffusion system to low-dimensional latent variables characterizing the asymptotic phase and amplitudes of the field variables. This yields a reduced phase description of the limit cycle underlying the rhythmic spatiotemporal dynamics in a data-driven manner. We propose a method to drive the system along the tangential direction of the limit cycle, enabling phase control without inducing amplitude deviations. With examples of 1D oscillating spots and 2D spiral waves in the FitzHugh-Nagumo reaction-diffusion system, we show that the method achieves rapid synchronization in both reference-based and coupling-based settings. These results demonstrate the potential of data-driven phase description based on the phase autoencoder for synchronization of high-dimensional spatiotemporal dynamics.