Bayesian estimation of coupling strength and heterogeneity in a coupled oscillator model from macroscopic quantities

TL;DR

This paper introduces a Bayesian method to estimate parameters of coupled oscillator models using only macroscopic data, specifically the Kuramoto order parameter, enhancing understanding of synchronization mechanisms.

Contribution

It presents a novel Bayesian framework utilizing the exchange Monte Carlo method for parameter estimation from macroscopic quantities, which is a departure from traditional methods relying on individual oscillator data.

Findings

The method accurately estimates parameters under various noise conditions.

Estimation error depends on observational noise and system size.

Numerical experiments validate the approach's effectiveness.

Abstract

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.