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<p>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.</p>

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Design of robust networks via reinforcement learning prompts the emergence of multi-backbones

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月20日

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  • Bingyu Zhu,
  • Tianchen Zhu,
  • Jianxi Gao,
  • Shlomo Havlin,
  • Daqing Li

摘要

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.