Abstract
Network robustness design is a significant engineering task in complex systems including urban planning, communication programming, and chip designing. With the embedded vulnerability of complex networks, the relationship between network topology and its robustness remains unknown, presenting a significant challenge in designing robust networks. Existing approaches—ranging from empirical manual designs, statistically-driven rules to optimization via Monte Carlo simulations, struggle to meet the design demands of robust networks under multidimensional attacks. Here, we introduce a general framework for designing robust networks based on AI reinforcement learning. This framework establishes an interactive environment between network attack strategies and design models, enabling the learning of effective robustness design strategies against attacks. Our framework enables effective design of robust networks, for a given cost, surpassing existing methods. Notably, we find that during the design process, the network may develop suitable multi-backbones that mitigate its current vulnerability, offering insight into higher-order relations in real-world networks. Our approach can be adopted to various network design scenarios, which provides an integrative intelligent solution for designing robust complex systems.
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Data availability
The data used for training and testing the RL agent, the trained neural network parameters, the real networks data, the designed networks data, and corresponding source code are available at https://github.com/Zhu-BY/Design_Robust_Network.
Code availability
All codes used for training, network design based on the trained model, and backbone structure analysis in this research can be freely accessed at: https://github.com/Zhu-BY/Design_Robust_Network.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grants 72225012, D.L.; 72288101, D.L.; and 71822101, D.L.), the National Key Research and Development Program of China (2023YFB4302901, D.L.), the Fundamental Research Funds for the Central Universities (D.L.).
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B.Z. and D.L. designed the main idea of the research; B.Z. and T.Z. designed the RL framework; B.Z. performed the experiments; B.Z., J.G., S.H. and D.L. conducted the theoretical analysis. All authors contributed to discussing the results and writing the manuscript.
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Zhu, B., Zhu, T., Gao, J. et al. Design of robust networks via reinforcement learning prompts the emergence of multi-backbones. Nat Commun (2026). https://doi.org/10.1038/s41467-026-70745-0
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DOI: https://doi.org/10.1038/s41467-026-70745-0
