Identifying percolation phase transitions with unsupervised learning based on largest clusters

Fuente: arXiv
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Main Authors: Xu, Dian, Wang, Shanshan, Deng, Weibing, Gao, Feng, Li, Wei, Shen, Jianmin
Format: Preprint
Published: 2023
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author Xu, Dian
Wang, Shanshan
Deng, Weibing
Gao, Feng
Li, Wei
Shen, Jianmin
author_facet Xu, Dian
Wang, Shanshan
Deng, Weibing
Gao, Feng
Li, Wei
Shen, Jianmin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2311_14725
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Identifying percolation phase transitions with unsupervised learning based on largest clusters
Xu, Dian
Wang, Shanshan
Deng, Weibing
Gao, Feng
Li, Wei
Shen, Jianmin
Statistical Mechanics
Machine Learning
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.
title Identifying percolation phase transitions with unsupervised learning based on largest clusters
topic Statistical Mechanics
Machine Learning
url https://arxiv.org/abs/2311.14725