Identifiability and amortized inference limitations in Kuramoto models

TL;DR

This paper introduces an amortized Bayesian inference method for Kuramoto models, enabling fast, scalable, and uncertainty-aware parameter estimation in complex oscillator networks, overcoming computational challenges of traditional techniques.

Contribution

The paper presents a novel neural network-based amortized inference approach tailored for Kuramoto models, improving efficiency and scalability in Bayesian analysis of oscillator networks.

Findings

Effective approximation of posterior distributions in synthetic Kuramoto networks

Significant computational savings over traditional Bayesian methods

Demonstrated flexibility and practicality for uncertainty quantification

Abstract

Bayesian inference is a powerful tool for parameter estimation and uncertainty quantification in dynamical systems. However, for nonlinear oscillator networks such as Kuramoto models, widely used to study synchronization phenomena in physics, biology, and engineering, inference is often computationally prohibitive due to high-dimensional state spaces and intractable likelihood functions. We present an amortized Bayesian inference approach that learns a neural approximation of the posterior from simulated phase dynamics, enabling fast, scalable inference without repeated sampling or optimization. Applied to synthetic Kuramoto networks, the method shows promising results in approximating posterior distributions and capturing uncertainty, with computational savings compared to traditional Bayesian techniques. These findings suggest that amortized inference is a practical and flexible framework for uncertainty-aware analysis of oscillator networks.