Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise

TL;DR

Inferring the dynamics of interacting oscillators from their signals remains an inverse problem, especially when noise and time-varying dynamics are present. This paper uses Bayesian inference of phase dynamics to track parameters and coupling functions; simulations and cardio-respiratory data show that synchronization, directionality, and interaction functions can vary over time.

• Problem

  How to infer interacting oscillators’ dynamics from their signals remains an open inverse problem, while earlier phase-model techniques did not infer noise dynamics or noise parameters.

  Source: p. 1

• Method

  The method infers phase dynamics with Bayesian updating, diffusing the parameter prior over time and evaluating whether inferred dynamics are synchronized.

  Source: pp. 1–2

• Results

  In simulations, varying parameters were accurately traced during unsynchronized intervals but diverged from their true values during synchronized intervals; cardio-respiratory analysis found time-varying directionality and coupling functions.

  Source: pp. 3–4

• Takeaways & Limitations

  The method tracks evolving phase dynamics and interaction functions, including their changing forms in the analyzed cardio-respiratory data.

  Source: p. 4

  The method assumes a finite Fourier basis and, in the considered diffusion example, uncorrelated parameter changes with known fractional standard deviations.

  Source: pp. 1–2