Explainable AI for analyzing the decision of GNNs at predicting dynamic stability of complex oscillator networks

Understanding the synchronization of complex oscillator networks is a central question in complex systems research. Recent studies have shown that graph neural networks (GNNs) outperform a wide range of traditional network measures in predicting probabilistic stability in synthetic power grids based on the Kuramoto model. This suggests that analyzing GNN decisions could enhance our understanding of synchronization patterns. We use explainable artificial intelligence (XAI), specifically Layer-wise Relevance Propagation (LRP) and its adaptation for GNNs (GNN-LRP) to analyze these decision processes. Our results indicate that larger neighborhoods beyond direct nodes strongly influence the dynamic behavior, with slightly different patterns for nodes with low stability compared to stable nodes. Aggregating LRP scores provides a nodal measure of stability contribution, correlating with some network measures and suggesting pathways to more stable power grids. However, GNN decision processes appear to be more complex and not only influenced by established node metrics. Our study highlights the potential of GNNs and XAI in understanding synchronization patterns of oscillator networks and emphasizes the need for new XAI methods tailored to this domain.