Reconstruction of a random phase dynamics network from observations

TL;DR

This paper presents a method for reconstructing various types of phase oscillator networks, including complex and experimental data-driven networks, from observed phase dynamics using error minimization techniques.

Contribution

It introduces a unified approach for network and coupling function reconstruction applicable to diverse phase oscillator models and experimental data.

Findings

Effective reconstruction of random networks with disordered connections and couplings.

Applicable to asynchronous and synchronized phase dynamics with phase resettings.

Demonstrated on electrochemical oscillator data.

Abstract

We consider networks of coupled phase oscillators of different complexity: Kuramoto-Daido-type networks, generalized Winfree networks, and hypernetworks with triple interactions. For these setups an inverse problem of reconstruction of the network connections and of the coupling function from the observations of the phase dynamics is addressed. We show how a reconstruction based on the minimization of the squared error can be implemented in all these cases. Examples include random networks with full disorder both in the connections and in the coupling functions, as well as networks where the coupling functions are taken from experimental data of electrochemical oscillators. The method can be directly applied to asynchronous dynamics of units, while in the case of synchrony, additional phase resettings are necessary for reconstruction.