发表机构
Hanyang University（汉阳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对无法获取单个振荡器相位的场景，采用增广状态的扩展卡尔曼滤波，仅从宏观序参量演化准确推断全局耦合Kuramoto模型的耦合强度，计算高效且在R(t)波动时仍稳定。
AI 中文摘要
仅从宏观观测准确估计振荡器网络中的耦合强度，对于预测同步跃迁至关重要。我们考虑从宏观序参量R(t)的标量观测值中，重构全局耦合Kuramoto模型中未知耦合强度K的逆问题，假设自然频率和初始相位构型已知。该问题源于实际场景：无法获取单个振荡器相位，却可连续测量粗粒度的集体信号。我们的方法不依赖微观状态观测，仅从宏观序参量R(t)的演化推断耦合强度。采用增广状态表示的扩展卡尔曼滤波，通过R(t)的观测值递归估计耦合强度；利用全局耦合Kuramoto模型的平均场结构，可高效计算协方差预测步骤，大幅降低计算成本。数值模拟表明，所提估计器能准确重构耦合强度，且在R(t)较小且波动剧烈时仍保持稳定。
英文摘要
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.
Comments12 pages, 6 figures. Submitted to the Journal of the Korean Physical Society
