标题： 复杂振荡器网络中的不稳定性预测：网络度量和机器学习的局限性与潜力 显示英文标题

标题： Predicting Instability in Complex Oscillator Networks: Limitations and Potentials of Network Measures and Machine Learning

摘要： 网络科学的一个核心问题是系统功能属性如何从其结构中产生。 对于网络动力系统，结构通常通过网络度量来量化。 对于振荡系统来说，同步性对局部扰动的稳定性是一个理论和实践上都感兴趣的功能属性。 最近，图神经网络（GNNs）已被证明可以成功预测这种稳定性；同时，网络度量在描绘清晰图景方面遇到了困难。 在这里，我们收集了46个相关的网络度量，并发现没有一个小的子集能够可靠地预测稳定性。 GNNs 的性能只能通过结合所有网络度量和节点级机器学习来达到。 然而，与 GNNs 不同，这种方法无法从网络集合外推到几种实际的电力网拓扑结构。 这表明网络度量和功能之间的相关性可能是有误导性的，而 GNNs 在捕捉结构与稳定性之间的因果关系方面要显著更好。 显示英文摘要

摘要： A central question of network science is how functional properties of systems arise from their structure. For networked dynamical systems, structure is typically quantified with network measures. A functional property that is of theoretical and practical interest for oscillatory systems is the stability of synchrony to localized perturbations. Recently, Graph Neural Networks (GNNs) have been shown to predict this stability successfully; at the same time, network measures have struggled to paint a clear picture. Here we collect 46 relevant network measures and find that no small subset can reliably predict stability. The performance of GNNs can only be matched by combining all network measures and nodewise machine learning. However, unlike GNNs, this approach fails to extrapolate from network ensembles to several real power grid topologies. This suggests that correlations of network measures and function may be misleading, and that GNNs capture the causal relationship between structure and stability substantially better.