Inferring Coupling Strength from the Kuramoto Order Parameter
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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BibTeX
@misc{kim2026inferring,
title = {{Inferring Coupling Strength from the Kuramoto Order Parameter}},
author = {Gug Young Kim and Hoseok Sul and Jee Woong Choi and Seung-Woo Son},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.28046},
eprint = {2607.28046},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.28046},
}
RIS
TY - UNPB
TI - Inferring Coupling Strength from the Kuramoto Order Parameter
AU - Gug Young Kim
AU - Hoseok Sul
AU - Jee Woong Choi
AU - Seung-Woo Son
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2607.28046
UR - https://arxiv.org/abs/2607.28046
AB - 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.
ER -