Predicting Instability in Complex Oscillator Networks: Limitations and Potentials of Network Measures and Machine Learning
This addresses the problem of predicting functional stability from network structure for researchers in network science and engineering, particularly for power grid applications, but is incremental as it builds on existing GNN methods.
The study investigated the ability of network measures and Graph Neural Networks (GNNs) to predict stability in complex oscillator networks, finding that no small subset of 46 network measures reliably predicts stability, and while combining all measures with machine learning matches GNN performance, it fails to extrapolate to real power grids, unlike GNNs.
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.