用神经网络加速相位振子模型的贝叶斯推断，实现快速不确定性分析。
Identifiability and amortized inference limitations in Kuramoto models
- 用神经网络学习后验分布，避免重复采样与优化
- 在合成网络上准确捕捉参数后验与不确定性
- 适合需要快速分析同步系统的科研与工程人员
贝叶斯推断是动态系统中参数估计与不确定性量化的重要工具。然而，对于如库朗莫模型这类广泛用于物理、生物和工程中同步现象研究的非线性振子网络，由于状态空间维度高且似然函数不可解析，传统推断常计算成本过高。本文提出一种摊销贝叶斯推断方法，通过模拟相位动力学学习后验的神经近似，实现无需重复采样或优化的快速、可扩展推断。应用于合成库朗莫网络时，该方法在近似后验分布和捕捉不确定性方面表现良好，相较传统贝叶斯技术显著降低计算开销。结果表明，摊销推断是进行振子网络不确定性分析的一种实用且灵活的框架。
原文摘要 · Abstract (English)
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.
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