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

• URL: http://arxiv.org/abs/2402.17500v1
• Date: Tue, 27 Feb 2024 13:34:08 GMT
• Title: Predicting Instability in Complex Oscillator Networks: Limitations and Potentials of Network Measures and Machine Learning
• Authors: Christian Nauck, Michael Lindner, Nora Molkenthin, J\"urgen Kurths, Eckehard Sch\"oll, J\"org Raisch and Frank Hellmann
• Abstract summary: 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. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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