Reconstructing resonant phase oscillator interactions from noisy time series

TL;DR

This paper introduces a method to reconstruct resonant interactions in weakly coupled phase oscillator systems from noisy data, focusing on normal form terms rather than full phase equations.

Contribution

The authors develop first- and second-order reconstruction procedures using Fourier modes and least-squares estimation, with proven error bounds under noise.

Findings

Successfully reconstructs resonant subnetworks from noisy data

Detects higher-order interactions through second-order methods

Numerical examples validate the approach

Abstract

We present a method for reconstructing resonant interactions in weakly coupled phase oscillator systems from noisy time series. Instead of attempting to recover the full phase equations, which may be non-identifiable in the presence of bounded observational uncertainty, the method reconstructs the resonant normal form terms that determine the leading-order drift dynamics. We develop first-order and second-order reconstruction procedures based on finite libraries of resonant Fourier modes and least-squares estimation. We prove error bounds for the reconstructed coefficients under natural assumptions on the observation noise and the distribution of initial conditions. The second-order method detects effective resonant interactions generated by the interplay of nonresonant first-order couplings. Numerical examples illustrate the reconstruction of resonant subnetworks and emergent higher-order interactions.