Unsupervised Learning Phase Transition Of Epidemic Dynamics On Complex Networks

In the field of complex networks,threshold identification of epidemic spreading dynamics is a hot issue.The outbreak threshold plays an important role in guiding the assessment,early warning,and prevention and control of epidemics.For different types of dynamic processes and networks of different structures,the identification results of epidemic outbreak thresholds often vary greatly.The traditional methods of identifying the outbreak threshold of epidemics,such as theoretical analysis and numerical simulation,have some limitations.This thesis mainly uses machine learning theories and methods to conduct in-depth research on the threshold identification problem of epidemic spread on complex networks,and explores the identification method of disease spread threshold through the classic Susceptible-Infected-Susceptible(SIS)and Susceptible-Infected-Removed(SIR)models and their spread dynamics configuration information,and mainly completed the following two aspects of research:1.Threshold identification of SIS propagation model.First,this thesis proposes a method based on the feedforward neural network prediction model.Through the training of feedforward neural network,the configuration information of epidemic spreading dynamics is linked with the effective spread rate.Therefore,the accuracy of the effective propagation rate predicted by the feedforward neural network can be used as a measure for identifying phase transition,and accurate phase transition predictions can be made without any prior knowledge.Then,considering that the feedforward neural network simply uses the dynamics information of the nodes,and completely ignores the network structure information.This thesis proposes a prediction model based on a convolutional neural network.This method combines the network topology and dynamics information into a multi-channel picture;by training the convolutional neural network,the network structure and dynamics information can be learned at the same time.Although the predictive model method does not require phase information when identifying the threshold,it still requires a supervised subroutine.Therefore,a completely unsupervised threshold identification method based on variational autoencoder is proposed.These three models were tested on a large number of synthetic networks and real networks respectively,and relatively accurate outbreak thresholds were obtained.2.Threshold identification of SIR propagation model.First of all,this thesis extends the prediction model method to the SIR propagation model.Since it is impossible to extract enough information from the single simulation data of the SIR model to identify the phase transition,the effect of the predictive model method in identifying the threshold is not ideal.This paper adopts the critical variability feature extraction method,introduces the average infection probability of the node,and preprocesses the data set,so that the processed dynamic information can well reflect the critical behavior characteristics of propagation.Secondly,this thesis uses the lowdimensional latent space of the variational autoencoder to interpret the changes in the propagation dynamics data after feature extraction,and uses the phase transition features found in the low-dimensional space as an indicator of phase transition.In this thesis,the prediction model and the variational autoencoder were tested on a large number of synthetic networks and real networks,and good threshold recognition results were obtained.