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.

网络科学的一个核心问题是系统的功能特性如何从其结构中产生。将网络测量与振动系统的稳定性等功能特性相结合的图神经网络 (GNNs) 在预测这种稳定性方面表现出色，而网络测量则难以清晰地描述。

复杂振荡器网络的不稳定性预测：网络度量和机器学习的局限性和潜力