Shanshan Wang

Dian Xu, Shanshan Wang, Weibing Deng et al.

The application of machine learning in the study of phase transitions has achieved remarkable success in both equilibrium and non-equilibrium systems. It is widely recognized that unsupervised learning can retrieve phase transition information through hidden variables. However, using unsupervised methods to identify the critical point of percolation models has remained an intriguing challenge. This paper suggests that, by inputting the largest cluster rather than the original configuration into the learning model, unsupervised learning can indeed predict the critical point of the percolation model. Furthermore, we observe that when the largest cluster configuration is randomly shuffled-altering the positions of occupied sites or bonds-there is no significant difference in the output compared to learning the largest cluster configuration directly. This finding suggests a more general principle: unsupervised learning primarily captures particle density, or more specifically, occupied site density. However, shuffling does impact the formation of the largest cluster, which is directly related to phase transitions. As randomness increases, we observe that the correlation length tends to decrease, providing direct evidence of this relationship. We also propose a method called Fake Finite Size Scaling (FFSS) to calculate the critical value, which improves the accuracy of fitting to a great extent.

Dian Xu, Shanshan Wang, Wei Li et al.

Modern machine learning, grounded in the Universal Approximation Theorem, has achieved significant success in the study of phase transitions in both equilibrium and non-equilibrium systems. However, identifying the critical points of percolation models using raw configurations remains a challenging and intriguing problem. This paper proposes the use of the Kolmogorov-Arnold Network, which is based on the Kolmogorov-Arnold Representation Theorem, to input raw configurations into a learning model. The results demonstrate that the KAN can indeed predict the critical points of percolation models. Further observation reveals that, apart from models associated with the density of occupied points, KAN is also capable of effectively achieving phase classification for models where the sole alteration pertains to the orientation of spins, resulting in an order parameter that manifests as an external magnetic flux, such as the Ising model.

Shanshan Wang, Michael Schreckenberg, Thomas Guhr

In a motorway network, correlations between parts or, more precisely, between the sections of (different) motorways, are of considerable interest. Knowledge of flows and velocities on individual motorways is not sufficient, rather, their correlations determine or reflect, respectively, the functionality of and the dynamics on the network. These correlations are time-dependent as the dynamics on the network is highly non-stationary. Apart from the conceptual importance, correlations are also indispensable to detect risks of failure in a traffic network. Here, we proceed with revealing a certain hierarchy of correlations in traffic networks that is due to the presence and to the extent of collectivity. In a previous study, we focused on the collectivity motion present in the entire traffic network, i.e. the collectivity of the system as a whole. Here, we manage to subtract this dominant effect from the data and identify the subdominant collectivities which affect different, large parts of the traffic network. To this end, we employ a spectral analysis of the correlation matrix for the whole system. We thereby extract information from the virtual network induced by the correlations and map it on the true topology, i.e. on the real motorway network. The uncovered subdominant collectivities provide a new characterization of the traffic network. We carry out our study for the large motorway network of North Rhine-Westphalia (NRW), Germany.