Identifiability and amortized inference limitations in Kuramoto models

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.

Figures (7)

• Figure 1: Illustration of training and inference phases in amortized Bayesian inference.
• Figure 2: Three simulations from the Kuramoto system with $N=100$ oscillators with given initial values and frequencies, randomized by $\zeta \sim \mathcal{N}(0,10^{-2})$. The system is simulated for the duration of 1000 time steps.
• Figure 3: Example of a three-node closed network connectivity graph and its adjacency matrix.
• Figure 4: Estimated vs true $\kappa$ values with $n_d$ samples from $n_v$ simulations.
• Figure 5: Posterior distribution for $\kappa$ with $n_d$ samples.