A method for predicting controllability and robustness of complex networks based on targeted attacks

Abstract

The present invention belongs to the technical field of complex network controllability, specifically a method for predicting the controllability robustness of a complex network under targeted attacks. The method comprises: constructing a convolutional neural network; generating a complex network and obtaining its controllability robustness under targeted attacks as training data; training the convolutional neural network; and predicting the controllability robustness of the complex network under targeted attacks. By predicting the controllability robustness of a network through a convolutional neural network, the present invention overcomes the high computational cost and slow speed of existing attack simulation methods.

Description

Technical Field

[0001] The present invention belongs to the technical field of complex network controllability, and in particular relates to a method for predicting controllability robustness under complex network target attacks. Background Art

[0002] Complex networks are ubiquitous in the real world, such as transportation networks, the Internet, the Internet of Things, social networks, neural networks in the human body, and brain networks. Network science has emerged to explore complex networks. Controlling complex networks is a crucial issue in network science: driving them to a desired state to achieve specific functions. This presupposes network controllability. Given the complexity of networks, controlling a few key nodes is often unnecessary; controlling the entire network is sufficient. This is known as targeted controllability. Similarly, in reality, attackers often focus on a few key nodes, aiming to disrupt the controllability of the target node. This is known as a targeted attack. Whether or not a target node can be controlled is the question of targeted controllability in complex networks. When attacking a complex network, the ability to maintain target controllability is the question of controllability robustness under targeted attacks.

[0003] Existing literature often focuses on the robustness of controllability of the overall network. Research on the robustness of controllability of complex networks under targeted attacks is relatively lacking. Furthermore, the computational cost of robustness of controllability of complex networks under targeted attacks is extremely high. In particular, changes in target nodes require re-simulation even for the same network. This makes it difficult to use simulation attacks to calculate robustness of controllability under targeted attacks. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the controllability robustness of complex networks based on target attack with fast prediction speed, low computational cost, accurate and reliable prediction results, so as to overcome the problems of high computational cost and long time consumption of existing methods.

[0005] The method for predicting the controllability and robustness of complex networks based on targeted attacks provided by the present invention comprises the following specific steps:

[0006] Step 1. Construct a convolutional neural network: specifically an 18-layer neural network, including convolutional layers, maximum pooling layers, ReLU activation layers and fully connected layers. Its structure is as follows: 5 groups of three-layer neural network structures consisting of convolutional layers, maximum pooling layers and ReLU activation layers, fully connected layers, ReLU activation layers, and fully connected layers.

[0007] Step 2: Generate a complex network and calculate its controllability robustness under target attack as training data: Specifically, generate complex networks with the same number of nodes, different network models, and different average degrees. Randomly scatter the node numbers, fix the target node ratio to f, select the target nodes using different selection strategies, and use attack simulation to calculate the controllability robustness under target attack for different attack strategies. For a network with N nodes and a target node ratio of f, the controllability robustness of the network under target attack is defined as follows based on the node removal method:

[0008]

[0009] Among them, N D (i) is the number of target controllable driver nodes in the remaining network after the i-th node attack, and fN is the number of target nodes.

[0010] Step 3: Train the convolutional neural network: The complex network adjacency matrix is recorded as The target node set is denoted as The target matrix is denoted as embedding matrix is a random matrix; is the adjacency matrix of the network composed of target nodes after the attack is completed; the neural network input is a tensor of size (batch_size,3,fN,N), with 3 channels, channel 1 is Channel 2 is Channel three is Normalize the tensor preprocessing; the neural network output is The sequence is recorded as the predicted value vector pv (predicted value); the true value vector corresponding to the predicted value is recorded as tv (true value); the loss function uses the mean square error:

[0011]

[0012] Train the model; PV i , TV i The th predicted value vector pv and the true value vector tv respectively.

[0013] Step 4: Predict the controllability and robustness of the complex network under target attack: convert the complex network to be predicted into the tensor described in step 3, input the trained neural network model, and the output result is the predicted value.

[0014] Compared with existing methods, the controllability robustness prediction method under complex network target attack proposed in the present invention has the following characteristics and advantages: fast prediction speed, low calculation cost, and accurate and reliable prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a flow chart of the controllability robustness prediction method under complex network target attack of the present invention.

[0016] Figure 2 Schematic diagram of the neural network model in the controllability robustness prediction method under complex network target attack of the present invention.

[0017] Figure 3 Schematic diagram of predicted and actual values of an ER random graph network with an average degree of 8 based on betweenness attack in the embodiment. DETAILED DESCRIPTION

[0018] The present invention will be further described below with reference to the embodiments and accompanying drawings to provide a clearer understanding of the essence of the present invention, as well as the effectiveness and advantages of the present invention. However, it should be understood that the specific embodiments described herein are not intended to limit the present invention.

[0019] like Figure 1 As shown, a controllability robustness prediction method under complex network target attack includes the following steps:

[0020] Step 1: Construct a convolutional neural network: In this embodiment, Figure 2 As shown in the figure, an 18-layer neural network is constructed. Its structure is as follows: five groups of three-layer neural network structures consisting of convolutional layers, maximum pooling layers, and ReLU activation layers → fully connected layers → ReLU activation layers → fully connected layers. The convolution kernel sizes of the first to fifth three-layer neural network structures are 5×5, 7×7, 5×5, 4×4, and 3×4, respectively. The pooling kernel size of the first to second groups is 2×2, and the pooling kernel size of the third to fifth groups is 3×3.

[0021] Step 2: Generate a complex network and evaluate its controllability robustness under targeted attacks as training data: Generate a random graph network, a scale-free network, a Q-loop network, and a small-world model network with 1000 nodes and average degrees of 4, 8, and 12, respectively. Node numbers are randomly scattered, and the target node ratio is fixed at f = 10%. Target nodes are selected using a random scheme and a local scheme, respectively. Attack simulations are used to evaluate the controllability robustness under targeted attacks for random attacks, betweenness-based attacks, and degree-based attacks. For a network with N nodes and a target node ratio of f, the controllability robustness of the network under targeted attacks is defined as follows based on the node removal method:

[0022]

[0023] Among them, N D (i) is the number of target controllable driver nodes in the remaining network after the i-th node attack, and fN is the number of target nodes.

[0024] Step 3: Train the convolutional neural network: The complex network adjacency matrix is recorded as The target node set is denoted as The target matrix is denoted as embedding matrix is a random matrix; is the adjacency matrix of the network composed of target nodes after the attack is completed; the neural network input is a tensor of size (batch_size,3,fN,N), with 3 channels, channel 1 is Channel 2 is Channel three is Normalize the tensor preprocessing; the neural network output is The sequence is recorded as the predicted value vector pv (predicted value); the true value vector corresponding to the predicted value is recorded as tv (true value); the loss function uses the mean square error: Train the model.

[0025] Step 4: Predict the controllability and robustness of the complex network under target attack: convert the complex network to be predicted into the tensor described in step 3, input the trained neural network model, and the output result is the predicted value.

[0026] In the embodiment, the network with an average degree of 12 is simulated using the existing attack simulation method and the method based on the present invention. The time consumption results are shown in the following table:

[0027]

[0028]

[0029] It can be seen from the above table that compared with the existing methods, the method of the present invention has a fast prediction speed and low calculation cost.

[0030] Figure 3 Schematic diagram of predicted and actual values of an ER random graph network with an average degree of 8 based on betweenness attack in the embodiment. Figure 3 As shown, the prediction results of the prediction method of the present invention are accurate and reliable.

Claims

1. A method for predicting the controllability and robustness of complex networks based on targeted attacks, characterized in that: The specific steps are: Step 1: Build a convolutional neural network; Step 2: Generate a complex network and obtain its controllability and robustness under target attacks as training data; Step 3: train the convolutional neural network; Step 4: predict the controllability and robustness of the complex network under target attacks; The convolutional neural network constructed in step 1 is an 18-layer neural network, including a convolution layer, a maximum pooling layer, a ReLU activation layer, and a fully connected layer. Its structure is as follows: 5 groups of three-layer neural network structures consisting of a convolution layer, a maximum pooling layer, and a ReLU activation layer, a fully connected layer, a ReLU activation layer, and a fully connected layer; the convolution kernel sizes of the first to fifth groups of three-layer neural network structures are 5×5, 7×7, 5×5, 4×4, and 3×4, respectively, the pooling kernel size of the first to second groups is 2×2, and the pooling kernel size of the third to fifth groups is 3×3; Generating a complex network and obtaining its controllability robustness under target attack as training data as described in step 2 specifically includes: generating complex networks with the same number of nodes, different network models, and different average degrees, randomly scattering the node numbers, fixing the target node ratio to f, selecting target nodes using different selection strategies, and using attack simulation for different attack strategies to obtain their controllability robustness under target attack; For a network with N nodes and target nodes accounting for f, the controllability and robustness of the network under targeted attack based on the node removal method is defined as follows: Among them, N D (i) is the number of target controllable driver nodes in the remaining network after the i-th node attack, and fN is the number of target nodes; The training convolutional neural network described in step 4 is as follows: The complex network adjacency matrix is recorded as The target node set is denoted as The target matrix is denoted as embedding matrix is a random matrix; is the adjacency matrix of the network composed of target nodes after the attack is completed; the neural network input is a tensor of size (batch_size,3,fN,N), with 3 channels, channel 1 is Channel 2 is Channel three is Normalize the tensor preprocessing; the neural network output is The sequence is recorded as the predicted value vector pv; the true value vector corresponding to the predicted value is recorded as tv; the loss function uses the mean square error: Train the model; PV i , TV i The th predicted value vector pv and the true value vector tv respectively.

2. The method for predicting controllability and robustness of complex networks based on targeted attacks according to claim 1, characterized in that: The controllability and robustness of the complex network under the predicted target attack described in step 4 is specifically as follows: the complex network to be predicted is converted into a tensor of the size of (batch_size, 3, fN, N), the trained neural network model is input, and the output result is the predicted value.

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