Machine Learning Of Parity-conserving Universality Class

Machine learning is widely used in the field of artificial intelligence,including natural language processing,big data processing,image recognition and so on.Based on the understanding of equilibrium phase transition and non-equilibrium phase transition theory,using machine learning method to study phase transition has gradually become a field that can be deeply studied.Using the complex data processing method of machine learning to identify and predict the structural characteristics of the evolution process of phase transition model is one of the basic methods of applying machine learning to phase transition research.Based on this idea,this paper studies the machine learning training of phase transition models including directed percolation(DP)universality class and parity-conserving(PC)universality class.For the paper,the research on surprise learning includes:a cluster graph generation program designed based on the evolution rules of one-dimensional directed percolation model,selecting the specific training data and testing data for supervised learning,and getting the identification of the critical point of the(1+1)dimensional bond directed percolation model(bDP)system and the prediction of the critical point under the infinite size limit.The prediction result of the critical point under the infinite size limit is p_c=0.6432.It is consistent with the theoretical prediction p_c=0.6447,At the same time,the characteristic time step is identified to determine the dynamic exponent z,and the identification of the dynamic exponent is z=1.5808(0).Based on the evolution rules of(1+1)dimensional branching and annihilating random walks model(BAW),we designed the cluster generation program.The different cluster structure characteristics under the condition of parity-seed are compared.The smaller size training data and testing data are selected for supervised learning training,and the result is p_c=0.491(4)The result is very close to the result of large-scale Monte Carlo simulation which is p_c=0.4946(2).Then we compare the effects of different sizes on the training accuracy to improve the direction of method improvement.We also calculate the critical exponents of spatial correlation length according to the finite-size scaling low which is v_⊥=1.83.The research of unsupervised learning includes:Using the autoencoder method to extract the structural features of DP cluster graphs and fitting the one-dimensional output data to determine the critical point.After training the bDP model data for many times,we get p_c=0.6472(8)The result is also very close to the theoretical prediction.Furthermore,accurate results can be obtain when the system size is compressed.We use unsupervised learning analyse the phase classification effect of PC autoencoder two-dimensional coding results,and use cross prediction of autoencoder one-dimensional encoder results to identify critical point.The critical point is p_c=0.492(2).We also compare the particle number density of the system with the one-dimensional coding outputs of autoencoder.The Pearson correlation coefficient is 0.9979.