Neural network learning of multi-scale and discrete temporal features in directed percolation

Fuente: arXiv
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Main Authors: Gao, Feng, Shen, Jianmin, Wang, Shanshan, Li, Wei, Xu, Dian
Format: Preprint
Published: 2025
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author Gao, Feng
Shen, Jianmin
Wang, Shanshan
Li, Wei
Xu, Dian
author_facet Gao, Feng
Shen, Jianmin
Wang, Shanshan
Li, Wei
Xu, Dian
contents Neural network methods are increasingly applied to solve phase transition problems, particularly in identifying critical points in non-equilibrium phase transitions, offering more convenience compared to traditional methods. In this paper, we analyze the (1+1)-dimensional and (2+1)-dimensional directed percolation models using an autoencoder network. We demonstrate that single-step configurations after reaching steady state can replace traditional full configurations for learning purposes. This approach significantly reduces data size and accelerates training time.Furthermore, we introduce a multi-input branch autoencoder network to extract shared features from systems of different sizes. The neural network is capable of learning results from finite-size scaling. By modifying the network input to include configurations at discrete time steps, the network can also capture temporal information, enabling dynamic analysis of non-equilibrium phase boundaries. Our proposed method allows for high-precision identification of critical points using both spatial and temporal features.
format Preprint
id arxiv_https___arxiv_org_abs_2503_08278
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Neural network learning of multi-scale and discrete temporal features in directed percolation
Gao, Feng
Shen, Jianmin
Wang, Shanshan
Li, Wei
Xu, Dian
Statistical Mechanics
Neural network methods are increasingly applied to solve phase transition problems, particularly in identifying critical points in non-equilibrium phase transitions, offering more convenience compared to traditional methods. In this paper, we analyze the (1+1)-dimensional and (2+1)-dimensional directed percolation models using an autoencoder network. We demonstrate that single-step configurations after reaching steady state can replace traditional full configurations for learning purposes. This approach significantly reduces data size and accelerates training time.Furthermore, we introduce a multi-input branch autoencoder network to extract shared features from systems of different sizes. The neural network is capable of learning results from finite-size scaling. By modifying the network input to include configurations at discrete time steps, the network can also capture temporal information, enabling dynamic analysis of non-equilibrium phase boundaries. Our proposed method allows for high-precision identification of critical points using both spatial and temporal features.
title Neural network learning of multi-scale and discrete temporal features in directed percolation
topic Statistical Mechanics
url https://arxiv.org/abs/2503.08278