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.

Related papers

• Coding schemes in neural networks learning classification tasks [52.22978725954347]
  We investigate fully-connected, wide neural networks learning classification tasks. We show that the networks acquire strong, data-dependent features. Surprisingly, the nature of the internal representations depends crucially on the neuronal nonlinearity.
  arXiv  Detail & Related papers  (2024-06-24T14:50:05Z)
• Quantum-Inspired Analysis of Neural Network Vulnerabilities: The Role of Conjugate Variables in System Attacks [54.565579874913816]
  Neural networks demonstrate inherent vulnerability to small, non-random perturbations, emerging as adversarial attacks. A mathematical congruence manifests between this mechanism and the quantum physics' uncertainty principle, casting light on a hitherto unanticipated interdisciplinarity.
  arXiv  Detail & Related papers  (2024-02-16T02:11:27Z)
• How neural networks learn to classify chaotic time series [77.34726150561087]
  We study the inner workings of neural networks trained to classify regular-versus-chaotic time series. We find that the relation between input periodicity and activation periodicity is key for the performance of LKCNN models.
  arXiv  Detail & Related papers  (2023-06-04T08:53:27Z)
• Certified Invertibility in Neural Networks via Mixed-Integer Programming [16.64960701212292]
  Neural networks are known to be vulnerable to adversarial attacks. There may exist large, meaningful perturbations that do not affect the network's decision. We discuss how our findings can be useful for invertibility certification in transformations between neural networks.
  arXiv  Detail & Related papers  (2023-01-27T15:40:38Z)
• Uncovering the Origins of Instability in Dynamical Systems: How Attention Mechanism Can Help? [0.0]
  We show that attention should be directed toward the collective behaviour of imbalanced structures and polarity-driven structural instabilities within the network. Our study provides a proof of concept to understand why perturbing some nodes of a network may cause dramatic changes in the network dynamics.
  arXiv  Detail & Related papers  (2022-12-19T17:16:41Z)
• Vanilla Feedforward Neural Networks as a Discretization of Dynamical Systems [9.382423715831687]
  In this paper, we back to the classical network structure and prove that the vanilla feedforward networks could also be a numerical discretization of dynamic systems. Our results could provide a new perspective for understanding the approximation properties of feedforward neural networks.
  arXiv  Detail & Related papers  (2022-09-22T10:32:08Z)
• A Learning Convolutional Neural Network Approach for Network Robustness Prediction [13.742495880357493]
  Network robustness is critical for various societal and industrial networks again malicious attacks. In this paper, an improved method for network robustness prediction is developed based on learning feature representation using convolutional neural network (LFR-CNN) In this scheme, higher-dimensional network data are compressed to lower-dimensional representations, and then passed to a CNN to perform robustness prediction.
  arXiv  Detail & Related papers  (2022-03-20T13:45:55Z)
• Stability of Neural Networks on Manifolds to Relative Perturbations [118.84154142918214]
  Graph Neural Networks (GNNs) show impressive performance in many practical scenarios. GNNs can scale well on large size graphs, but this is contradicted by the fact that existing stability bounds grow with the number of nodes.
  arXiv  Detail & Related papers  (2021-10-10T04:37:19Z)
• Learning Autonomy in Management of Wireless Random Networks [102.02142856863563]
  This paper presents a machine learning strategy that tackles a distributed optimization task in a wireless network with an arbitrary number of randomly interconnected nodes. We develop a flexible deep neural network formalism termed distributed message-passing neural network (DMPNN) with forward and backward computations independent of the network topology.
  arXiv  Detail & Related papers  (2021-06-15T09:03:28Z)
• A Probabilistic Approach to Neural Network Pruning [20.001091112545065]
  We theoretically study the performance of two pruning techniques (random and magnitude-based) on FCNs and CNNs. The results establish that there exist pruned networks with expressive power within any specified bound from the target network.
  arXiv  Detail & Related papers  (2021-05-20T23:19:43Z)
• Decentralized Control with Graph Neural Networks [147.84766857793247]
  We propose a novel framework using graph neural networks (GNNs) to learn decentralized controllers. GNNs are well-suited for the task since they are naturally distributed architectures and exhibit good scalability and transferability properties. The problems of flocking and multi-agent path planning are explored to illustrate the potential of GNNs in learning decentralized controllers.
  arXiv  Detail & Related papers  (2020-12-29T18:59:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.