从宏观量估计耦合振子模型中的耦合强度与异质性的贝叶斯方法
Bayesian estimation of coupling strength and heterogeneity in a coupled oscillator model from macroscopic quantities
AI总结：
本研究提出了一个基于序贯蒙特卡罗方法的贝叶斯框架，利用宏观量（如 Kuramoto 序参数）来估计耦合振子模型的参数，并通过数值实验验证了该方法的有效性及其对观测噪声和系统规模的依赖性。
摘要：
心跳和萤火虫闪烁等多种宏观振荡是由振荡单元（oscillators）同步产生的。为了阐明同步机制，人们设计并广泛分析了几种耦合振子模型。尽管这些模型的参数估计已被积极研究，但现有方法大多基于来自单个振子的数据，而非宏观量。在本研究中，我们提出了一个贝叶斯框架，利用 Kuramoto 序参数等宏观量来估计耦合振子模型的参数。我们采用序贯蒙特卡罗方法来有效估计后验分布。进行了数值实验以验证我们方法的有效性，并考察了估计误差对观测噪声和系统规模的依赖性。
英文摘要：
Various macroscopic oscillations, such as the heartbeat and the flashing of fireflies, are created by synchronizing oscillatory units (oscillators). To elucidate the mechanism of synchronization, several coupled oscillator models have been devised and extensively analyzed. Although parameter estimation of these models has also been actively investigated, most of the proposed methods are based on the data from individual oscillators, not from macroscopic quantities. In the present study, we propose a Bayesian framework to estimate the model parameters of coupled oscillator models, using the time series data of the Kuramoto order parameter as the only given data. We adopt the exchange Monte Carlo method for the efficient estimation of the posterior distribution and marginal likelihood. Numerical experiments are performed to confirm the validity of our method and examine the dependence of the estimation error on the observational noise and system size.
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