https://doi.org/10.1140/epjp/s13360-024-05707-w
Regular Article
Machine learning of (1+1)-dimensional directed percolation based on raw and shuffled configurations
1
College of Engineering and Technology, Baoshan University, 678000, Baoshan, China
2
Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, 430079, Wuhan, China
3
École Supérieure d’Informatique Électronique Automatique, 94200, Ivry-sur-Seine, France
4
Research Center of Applied Mathematics and Interdisciplinary Science, Wuhan Textile University, 430073, Wuhan, China
b
liw@mail.ccnu.edu.cn
c
xudian.work@mails.ccnu.edu.cn
Received:
13
August
2024
Accepted:
1
October
2024
Published online:
28
October
2024
Machine learning (ML) can process large sets of data generated from complex systems, which is ideal for classification tasks as often appeared in critical phenomena. Meanwhile ML techniques have been found effective in detecting critical points, or in a broader sense phase separation, and extracting critical exponents. But there are still many unsolved issues with the ML, one of which is the meaning of hidden variables of unsupervised learning. Some say that the hidden variables and the principal component may contain basic information regarding the order parameter of the system of interest, which sounds plausible but lacks evidence. Based on the non-equilibrium directed percolation (DP) model, this paper demonstrates through random shuffling that the single latent variable from autoencoder and the first principal component from PCA both represent the particle density, which is also the order parameter of the DP model. This study further shows that random shuffling can alter the system’s correlations, the larger the shuffle ratio, the smaller the spatial correlation length of the system.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.