Network controllability measures how well a networked system can be controlled to a target state, and its robustness reflects how well the system can maintain the controllability against malicious attacks by means of node removals or edge removals. The measure of network controllability is quantified by the number of external control inputs needed to recover or to retain the controllability after the occurrence of an unexpected attack. The measure of the network controllability robustness, on the other hand, is quantified by a sequence of values that record the remaining controllability of the network after a sequence of attacks. Traditionally, the controllability robustness is determined by attack simulations, which is computationally time consuming. In this article, a method to predict the controllability robustness based on machine learning using a convolutional neural network (CNN) is proposed, motivated by the observations that: 1) there is no clear correlation between the topological features and the controllability robustness of a general network; 2) the adjacency matrix of a network can be regarded as a grayscale image; and 3) the CNN technique has proved successful in image processing without human intervention. Under the new framework, a fairly large number of training data generated by simulations are used to train a CNN for predicting the controllability robustness according to the input network-adjacency matrices, without performing conventional attack simulations. Extensive experimental studies were carried out, which demonstrate that the proposed framework for predicting controllability robustness of different network configurations is accurate and reliable with very low overheads.

中文翻译：

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预测网络可控性鲁棒性：一种卷积神经网络方法

网络可控性衡量一个网络化系统可以控制到目标状态的程度，其鲁棒性反映了系统通过节点去除或边缘去除来保持对恶意攻击的可控性。网络可控性的度量是通过在发生意外攻击后恢复或保持可控性所需的外部控制输入的数量来量化的。另一方面，网络可控性鲁棒性的度量是通过一系列值来量化的，这些值记录了在一系列攻击之后网络的剩余可控性。传统上，可控性鲁棒性由攻击模拟确定，这在计算上非常耗时。在本文中，提出了一种基于使用卷积神经网络 (CNN) 的机器学习来预测可控性鲁棒性的方法，其动机是观察到：1) 拓扑特征与一般网络的可控性鲁棒性之间没有明显的相关性；2）一个网络的邻接矩阵可以看成一幅灰度图；3) CNN 技术已被证明在无需人工干预的情况下进行图像处理是成功的。在新框架下，使用大量模拟生成的训练数据来训练CNN，根据输入的网络邻接矩阵预测可控性鲁棒性，而无需执行传统的攻击模拟。进行了广泛的实验研究，