Stochastic dynamics generation of directed percolation using a two-channel convolutional neural network
Abstract
Neural networks provide a promising approach to learning and generating the stochastic dynamics of nonequilibrium systems. In this study, we propose a stochastic dynamics generative method based on a two-channel convolutional neural network, using the (1+1)-dimensional directed bond percolation model to investigate its ability to learn local stochastic transition rules and reproduce stochastic dynamics across different system sizes. The proposed method takes the current particle configuration and the control parameter as inputs, learns the conditional activation probabilities at the next time step through local convolutions, and generates stochastic temporal evolution through iterative Bernoulli sampling. The results show that the network-generated dynamics agree well with Monte Carlo simulations across different control parameters. Furthermore, applying the trained network to a substantially larger system with L=10000 yields an estimated critical probability of pc=0.643 and an effective density decay exponent of δ≈0.1592, close to the established theoretical values. These findings demonstrate that the proposed method can reproduce the stochastic dynamics of directed percolation and capture its macroscopic dynamical and statistical properties across different spatial sizes.
Related
- Invariance in half-space last passage percolation and directed polymers
- Conditional Flat Exponential Directed Last Passage Percolation under a One-Point Upper Large Deviation Event
- Directed fractal percolation and non-Lipschitz variants
- Percolation in the Stochastic Block Model
- Noise-Robust Distributed Optimization Over Directed Graphs With Row Stochastic Matrices
BibTeX
@misc{gao2026stochastic,
title = {{Stochastic dynamics generation of directed percolation using a two-channel convolutional neural network}},
author = {Feng Gao and Jianmin Shen and Wei Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41299},
eprint = {2610.41299},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41299},
}
RIS
TY - UNPB
TI - Stochastic dynamics generation of directed percolation using a two-channel convolutional neural network
AU - Feng Gao
AU - Jianmin Shen
AU - Wei Li
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41299
UR - https://arxiv.org/abs/2610.41299
AB - Neural networks provide a promising approach to learning and generating the stochastic dynamics of nonequilibrium systems. In this study, we propose a stochastic dynamics generative method based on a two-channel convolutional neural network, using the (1+1)-dimensional directed bond percolation model to investigate its ability to learn local stochastic transition rules and reproduce stochastic dynamics across different system sizes. The proposed method takes the current particle configuration and the control parameter as inputs, learns the conditional activation probabilities at the next time step through local convolutions, and generates stochastic temporal evolution through iterative Bernoulli sampling. The results show that the network-generated dynamics agree well with Monte Carlo simulations across different control parameters. Furthermore, applying the trained network to a substantially larger system with L=10000 yields an estimated critical probability of p_c=0.643 and an effective density decay exponent of δ≈0.1592, close to the established theoretical values. These findings demonstrate that the proposed method can reproduce the stochastic dynamics of directed percolation and capture its macroscopic dynamical and statistical properties across different spatial sizes.
ER -