Predicting Network Controllability Robustness: A Convolutional Neural Network Approach
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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 paper, a method to predict the controllability robustness based on machine learning using a convolutional neural network 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 gray-scale image, and 3) the convolutional neural network 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 convolutional neural network 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.