Unpacking the black box of deep learning for identifying El Nino-Southern oscillation

By training a convolutional neural network(CNN) model, we successfully recognize different phases of the El Nino-Southern oscillation. Our model achieves high recognition performance,with accuracy rates of 89.4% for the training dataset and 86.4% for the validation dataset.Through statistical analysis of the weight parameter distribution and activation output in the CNN, we find that most of the convolution kernels and hidden layer neurons remain inactive,while only two convolution kernels and two hidden layer neurons play active roles. By examining the weight parameters of connections between the active convolution kernels and the active hidden neurons, we can automatically differentiate various types of El Nino and La Nina,thereby identifying the specific functions of each part of the CNN. We anticipate that this progress will be helpful for future studies on both climate prediction and a deeper understanding of artificial neural networks.

Universality class of machine learning for critical phenomena

Herein,percolation phase transitions on a two-dimensional lattice were studied using machine learning techniques.Results reveal that different phase transitions belonging to the same universality class can be identified using the same neural networks(NNs),whereas phase transitions of different universality classes require different NNs.Based on this finding,we proposed the universality class of machine learning for critical phenomena.Furthermore,we investigated and discussed the NNs of different universality classes.Our research contributes to machine learning by relating the NNs with the universality class.

Eigen microstates and their evolutions in complex systems

Emergence refers to the existence or formation of collective behaviors in complex systems.Here,we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system.In this framework,the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N×M matrix A,whose columns represent microstates and order of row is consist with the time.The ensemble matrix A can be decomposed as■,where r=min(N,M),eigenvalueσIbehaves as the probability amplitude of the eigen microstate U_I so that■and U_I evolves following V_I.In a disorder complex system,there is no dominant eigenvalue and eigen microstate.When a probability amplitudeσIbecomes finite in the thermodynamic limit,there is a condensation of the eigen microstate UIin analogy to the Bose–Einstein condensation of Bose gases.This indicates the emergence of U_I and a phase transition in complex system.Our framework has been applied successfully to equilibrium threedimensional Ising model,climate system and stock markets.We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown orderparameters,such as phase transitions of collective motion and tipping points in climate systems and ecosystems.

Condensation of eigen microstate in statistical ensemble and phase transition

In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. Eigen microstates of ensemble can be defined using eigenvectors of the correlation matrix. The eigenvalue normalized by M represents weight factor in the ensemble of the corresponding eigen microstate. In the limit M →∞, weight factors drop to zero in the ensemble without localization of the microstate. The finite limit of the weight factor when M →∞ indicates a condensation of the corresponding eigen microstate. This finding indicates a transition into a new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors are confirmed using Monte Carlo data of one-dimensional and two-dimensional Ising models.

Study of the shear-rate dependence of granular friction based on community detection

In this study, computer simulations are performed on three-dimensional granular systems under shear conditions. The system comprises granular particles that are confined between two rigid plates. The top plate is subjected to a normal force and driven by a shearing velocity. A positive shear-rate dependence of granular friction, known as velocity-strengthening, exists between the granular and shearing plate. To understand the origin of the dependence of frictional sliding, we treat the granular system as a complex network, where granular particles are nodes and normal contact forces are weighted edges used to obtain insight into the interiors of granular matter. Community structures within granular property networks are detected under different shearing velocities in the steady state. Community parameters, such as the size of the largest cluster and average size of clusters, show significant monotonous trends in shearing velocity associated with the shear-rate dependence of granular friction. Then, we apply an instantaneous change in shearing velocity. A dramatic increase in friction is observed with a change in shearing velocity in the non-steady state. The community structures in the non-steady state are different from those in the steady state. Results indicate that the largest cluster is a key factor affecting the friction between the granular and shearing plate.

Finite-size scaling of correlation functions in finite systems

We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|^(-(d-2+η))and a finite-size scaling function of the variables r/L and tL^(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.