Identifiability and amortized inference limitations in Kuramoto models

2026-03-23

AI Summary

This work addresses the challenge of Bayesian inference in Kuramoto oscillator networks, where high-dimensional state spaces and intractable likelihood functions hinder conventional approaches. To overcome this, the study introduces an amortized Bayesian inference framework that leverages neural networks to learn an approximation of the posterior distribution directly from simulated phase dynamics. By bypassing repeated sampling or iterative optimization, the method substantially enhances computational efficiency and enables practical uncertainty quantification. Experiments on synthetic Kuramoto networks demonstrate that the proposed approach accurately recovers the true posterior, effectively captures parameter uncertainty, and significantly reduces computational cost. This establishes a scalable, data-driven paradigm for Bayesian inference in complex dynamical systems.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

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.

Problem

• Kuramoto models
• Bayesian inference
• identifiability
• amortized inference
• oscillator networks

Innovation

• amortized inference
• Kuramoto model
• Bayesian inference
• neural posterior approximation
• synchronization