Neural network learning of multi-scale and discrete temporal features in directed percolation
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909534159634432 |
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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 |