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

2025/06/15 by Koichiro Yawata, Ryo Sakuma, Yawata, Koichiro +7 · 4 citations
Computer Science · #Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences #Neural Networks and Applications #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.2506.12777

openalex publication_date 2025/06/15 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/29

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.

Citations

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Cited by

• Extreme Aerodynamics: A Data-Driven Perspective
• Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators
• Data-driven phase control for limit-cycle oscillators under partial observation
• Phase reduction analysis of traveling breathers in reaction--diffusion systems

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• Prediction and control of spatiotemporal chaos by learning conjugate tubular neighborhoods