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arXiv · 2607.28046

Inferring Coupling Strength from the Kuramoto Order Parameter

Gug Young Kim·Hoseok Sul·Jee Woong Choi·Seung-Woo Son
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Abstract

Accurately estimating the coupling strength in oscillator networks from macroscopic observations is essential for predicting synchronization transitions. We consider the inverse problem of reconstructing the unknown coupling strength $K$ in the globally coupled Kuramoto model from scalar observations of the macroscopic order parameter $R(t)$, assuming that the natural frequencies and the initial phase configuration are known. After initialization, individual phase trajectories are treated as hidden, and only the scalar order parameter is observed. We employ an extended Kalman filter with an augmented state representation that recursively estimates the coupling strength from observations of $R(t)$. By exploiting the mean-field structure of the globally coupled Kuramoto model, the covariance prediction step can be computed efficiently, substantially reducing the computational cost. Numerical simulations demonstrate that the proposed estimator accurately reconstructs the coupling strength and remains stable even when $R(t)$ is small and strongly fluctuating.

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Gug Young Kim, Hoseok Sul, Jee Woong Choi, Seung-Woo Son. 2026-09-14. Inferring Coupling Strength from the Kuramoto Order Parameter. https://arxiv.org/abs/2607.28046

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