Connectivity robustness, a crucial aspect for understanding, optimizing, and repairing complex networks, has traditionally been evaluated through time-consuming and often impractical simulations. Fortunately, machine learning provides a new avenue for addressing this challenge. However, several key issues remain unresolved, including the performance in more general edge removal scenarios, capturing robustness through attack curves instead of directly training for robustness, scalability of predictive tasks, and transferability of predictive capabilities. In this paper, we address these challenges by designing a convolutional neural networks (CNN) model with spatial pyramid pooling networks (SPP-net), adapting existing evaluation metrics, redesigning the attack modes, introducing appropriate filtering rules, and incorporating the value of robustness as training data. The results demonstrate the thoroughness of the proposed CNN framework in addressing the challenges of high computational time across various network types, failure component types and failure scenarios. However, the performance of the proposed CNN model varies: for evaluation tasks that are consistent with the trained network type, the proposed CNN model consistently achieves accurate evaluations of both attack curves and robustness values across all removal scenarios. When the predicted network type differs from the trained network, the CNN model still demonstrates favorable performance in the scenario of random node failure, showcasing its scalability and performance transferability. Nevertheless, the performance falls short of expectations in other removal scenarios. This observed scenario-sensitivity in the evaluation of network features has been overlooked in previous studies and necessitates further attention and optimization. Lastly, we discuss important unresolved questions and further investigation.

翻译：连通鲁棒性是理解、优化和修复复杂网络的关键方面，传统上通过耗时且通常不切实际的模拟进行评估。幸运的是，机器学习为解决这一挑战提供了新途径。然而，几个关键问题仍未解决，包括在更通用的边移除场景中的性能、通过攻击曲线而非直接训练鲁棒性来捕获鲁棒性、预测任务的可扩展性以及预测能力的可迁移性。本文通过设计具有空间金字塔池化网络（SPP-net）的卷积神经网络（CNN）模型、调整现有评估指标、重新设计攻击模式、引入合适的过滤规则以及将鲁棒性值作为训练数据来解决这些挑战。结果表明，所提出的CNN框架在解决各种网络类型、故障组件类型和故障场景下的高计算时间挑战方面具有全面性。然而，所提出CNN模型的性能存在差异：对于与训练网络类型一致的评估任务，所提出的CNN模型在所有移除场景下均能准确评估攻击曲线和鲁棒性值。当预测的网络类型与训练网络不同时，CNN模型在随机节点故障场景中仍表现出良好性能，展示了其可扩展性和性能可迁移性。然而，在其他移除场景中，性能未能达到预期。这种在网络特征评估中观察到的场景敏感性在以往研究中被忽视，需要进一步关注和优化。最后，我们讨论了未解决的关键问题和未来研究方向。