Speaker
Jian-Min SHEN
Description
In this paper, we apply the supervised learning method in deep learning to study the critical threshold, the spatial and temporal correlation exponent, and also the characteristic times of directed percolation(DP) in both (1+1) and (2+1) dimensions. DP is a classic type of absorbing phase transition in non-equilibrium phase transitions. The previous machine learning method mainly focuses on the equilibrium phase transition such as Ising model, Potts model, XY model. However, studying the non-equilibrium phase transition with a time dimension, we find that the neural network can successfully predict the spatial and temporal correlation exponent of DP model. With the supervised learning method, it is possible to learn and predict the time step t experienced by different size models from the active phase to the absorbing one, and the test accuracy is above 0.9. We also find that (2+1)-dimensional DP can obtain higher test accuracy. This explains the influence of fluctuations in low-dimensional condition on simulation results of the underlying system, which will be weakened by the configurations generated by higher-dimensional models. Furthermore, in the (1+1)-dimensional DP, We can combine configurations of different time steps t into a 2-dimensional image. And the neural network can identify the trend very well. In the case of (2+1) dimensions, the processing method of this work is to flatten $lx * lx$ and then combine it with configurations of different time steps t into a 2-dimensional image. The underlying results suggest that the neural network can still detect its trend and identify the complex pattern.
| Publications | unpublished |
|---|---|
| Master Student, PhD Student or Postdoc | PhD Student |
| Presenter | 申建民 |
Primary authors
Jianmin Shen
(CCNU)
Prof.
Wei Li
(CCNU)
