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Complex network robustness prediction using attention-augmented CNN

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Abstract

Assessing the strength of complex networks is crucial for evaluating their functionality and monitoring system security. Two primary perspectives for measuring network robustness are connectivity and controllability, which quantify how well a network maintains connectivity and controllability after experiencing complete attacks. However, conventional robustness calculation methods that use simulation attacks can be impractical for large-scale networks. Recent research has explored the use of deep learning methods for network robustness prediction, including PCR (short for predictor of controllability robustness), which uses a VGG (short for visual geometry group)-based convolutional neural network (CNN) and a linear filter. However, PCR has limitations, including inaccurate edge importance differentiation and fluctuating output curves. This paper presents ATTRP, an attention-based robustness predictor, which addresses these limitations. ATTRP uses a novel convolutional neural network with channel and spatial attention mechanisms to improve prediction accuracy and a robustness filter based on Savitzky–Golay smoothing to rectify the robustness curve. Experimental studies demonstrate that ATTRP outperforms other predictors, with much lower errors, while its computational speed is far superior to that of traditional attacking simulation. Overall, our research provides a more effective and efficient means of predicting network robustness, with potential applications in monitoring system security.

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Data Availability

The synthetic networks utilized in experiments 5.1, 5.2, 5.3, 5.4, and 5.6 were generated based on three network generating models (ER, SF, SW) using a MATLAB program, according to their specific parameter settings such as the number of nodes and node degree. The source code utilized for generating these networks is available upon request from the authors. The real-world networks used in experiment 5.5 are publicly available in the [networkrepository] at [https://networkrepository.com]. Details on the specific datasets used in this study are provided in the manuscript.

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Funding

This work was supported by the National Natural Science Foundation of China under grant number 62002249, entitled ‘Optimization and Application of Controllability Robustness of Complex Networks Based on Computational Intelligence.’

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Authors and Affiliations

  1. College of Computer Science, Sichuan Normal University, Chenglong Avenue, Chengdu, 610101, Sichuan, China

    Jie Huang & Junli Li

  2. Institution of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Xiyuan Avenue, Chengdu, 611731, Sichuan, China

    Ruizi Wu

  3. Key Laboratory of Land Resources Evaluation and Monitoring in Southwest (Sichuan Normal University), Ministry of Education, Chengdu, 610068, Sichuan, China

    Junli Li

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  1. Jie Huang
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Correspondence to Junli Li.

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Huang, J., Wu, R. & Li, J. Complex network robustness prediction using attention-augmented CNN. Neural Comput & Applic 36, 7279–7294 (2024). https://doi.org/10.1007/s00521-024-09460-0

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