Today, there is an increasing concern about malicious attacks on various networks in society and industry, against which the network robustness is critical. Network connectivity robustness, in particular, is of fundamental importance, which is generally measured by a sequence of calculated values that indicate the connectedness of the remaining network after a sequence of attacks by means of node- or edge-removal. It is computationally time-consuming, however, to measure and evaluate the network connectivity robustness using the conventional attack simulations, especially for large-scale networked systems. In the present paper, an efficient robustness predictor based on multiple convolutional neural networks (mCNN-RP) is proposed for predicting the network connectivity robustness, which is an natural extension of the single CNN-based predictor. In mCNN-RP, one CNN works as the classifier, while each of the rest CNNs works as an estimator for predicting the connectivity robustness of every classified network category. The network categories are classified according to the available prior knowledge. A data-based filter is installed for predictive data refinement. Extensive experimental studies on both synthetic and real-world networks, including directed and undirected as well as weighted and unweighted topologies, verify the effectiveness of mCNN-RP. The results demonstrate that the average prediction error is lower than the standard deviation of the tested data, which outperforms the single CNN-based framework. The runtime in assessing network connectivity robustness is significantly reduced by using the CNN-based technique. The proposed mCNN-RP not only can accurately predict the connectivity robustness of various complex networks, but also provides an excellent indicator for the connectivity robustness, better than other existing prediction measures.

如今，社会和工业界对各种网络的恶意攻击越来越受到关注，网络的健壮性对此至关重要。尤其是网络连接稳健性具有根本重要性，通常通过一系列计算值来衡量，这些计算值指示在通过节点或边缘删除进行一系列攻击后剩余网络的连接性。然而，使用传统的攻击模拟来测量和评估网络连接的鲁棒性在计算上非常耗时，尤其是对于大型网络系统。在本论文中，提出了一种基于多个卷积神经网络 (mCNN-RP) 的高效鲁棒性预测器来预测网络连接鲁棒性，这是基于单一 CNN 的预测器的自然扩展。在 mCNN-RP 中，一个 CNN 用作分类器，而其余每个 CNN 用作估计器，用于预测每个分类网络类别的连接稳健性。网络类别根据可用的先验知识进行分类。安装基于数据的过滤器用于预测数据细化。对合成网络和真实网络的广泛实验研究，包括有向和无向以及加权和未加权拓扑，验证了 mCNN-RP 的有效性。结果表明，平均预测误差低于测试数据的标准偏差，优于单一的基于 CNN 的框架。通过使用基于 CNN 的技术，评估网络连接稳健性的运行时间显着减少。