# Inverse problems for dynamic patterns in coupled oscillator networks: when larger networks are simpler

## TL;DR

This paper introduces a method to infer model parameters in large networks of oscillators by analyzing their synchronized dynamics.

## Contribution

The paper derives statistical equilibrium relations for large oscillator networks and uses them for parameter reconstruction.

## Key findings

- Statistical equilibrium relations can be derived for partially synchronized patterns in large oscillator networks.
- The method is effective for large networks, noisy data, and partial observations.
- The approach is demonstrated on chimera states and extended to other network topologies.

## Abstract

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially synchronized dynamic patterns, which in the case of large networks can be analysed using a variant of the mean-field approach. This method allows to predict what type of network dynamics can be observed for different system parameters. But it is less known that for different partially synchronized patterns it also allows to obtain statistical equilibrium relations that express the dependence of some time-averaged observable quantities of individual oscillators on the internal parameters of these oscillators and the interaction functions between them. In this paper, we show how such relations can be derived, what their typical accuracy is for finite-size networks, and how they can be used to reconstruct the parameters of the corresponding model. The proposed method is particularly effective for large networks, for unevenly sampled or noisy observables, and for partial observations. Its possibilities are demonstrated by application to chimera states in networks of phase oscillator with nonlocal coupling. The extension of the method to other systems with all-to-all and random network topologies is also described.

Inferring model parameters from partially synchronized dynamics is a major challenge in networks of coupled oscillators. Here, the author derives statistical equilibrium relations valid for large networks and uses them to reconstruct system parameters from time-averaged observables.