Robustness is pivotal for comprehending, designing, optimizing, and rehabilitating networks, with simulation attacks being the prevailing evaluation method. Simulation attacks are often time-consuming or even impractical, however, a more crucial yet persistently overlooked drawback is that any attack strategy merely provides a potential paradigm of disintegration. The key concern is: in the worst-case scenario or facing the most severe attacks, what is the limit of robustness, referred to as ``Worst Robustness'', for a given system? Understanding a system's worst robustness is imperative for grasping its reliability limits, accurately evaluating protective capabilities, and determining associated design and security maintenance costs. To address these challenges, we introduce the concept of Most Destruction Attack (MDA) based on the idea of knowledge stacking. MDA is employed to assess the worst robustness of networks, followed by the application of an adapted CNN algorithm for rapid worst robustness prediction. We establish the logical validity of MDA and highlight the exceptional performance of the adapted CNN algorithm in predicting the worst robustness across diverse network topologies, encompassing both model and empirical networks.

翻译：鲁棒性对于理解、设计、优化和修复网络至关重要，模拟攻击是当前主流的评估方法。然而，模拟攻击往往耗时甚至不切实际，更为关键但长期被忽视的缺陷在于：任何攻击策略仅提供了一种潜在的瓦解范式。核心问题在于：给定系统在遭遇最坏情形或面对最严重攻击时，其鲁棒性的极限——即“最差鲁棒性”——究竟为何？理解系统的最差鲁棒性对于把握其可靠性极限、准确评估防护能力以及确定相关设计与安全维护成本具有重要意义。为解决这些挑战，我们基于知识堆叠的思想提出了“最大破坏攻击”（MDA）概念。利用MDA评估网络的最差鲁棒性，随后采用改进型CNN算法进行快速最差鲁棒性预测。我们验证了MDA的逻辑有效性，并凸显了改进型CNN算法在预测多种网络拓扑（包括模型网络与实证网络）最差鲁棒性方面的卓越性能。