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.

翻译：贝叶斯推断是动力系统中参数估计与不确定性量化的强大工具。然而，对于非线性振荡器网络（如广泛用于研究物理、生物学和工程学中同步现象的Kuramoto模型），由于高维状态空间和难以处理的似然函数，推断过程在计算上往往难以实现。本文提出一种摊销贝叶斯推断方法，该方法通过从模拟的相位动力学中学习后验的神经近似，无需重复采样或优化即可实现快速、可扩展的推断。在合成Kuramoto网络上的应用表明，该方法在近似后验分布和捕获不确定性方面取得了良好结果，相较于传统贝叶斯技术显著节省了计算成本。这些发现表明，摊销推断是面向振荡器网络进行不确定性感知分析的实用且灵活的框架。