Transfer learning of phase transitions in percolation and directed percolation

TL;DR

This paper demonstrates that transfer learning with domain adversarial neural networks can efficiently identify phase transitions in percolation models, reducing labeled data requirements while maintaining high accuracy.

Contribution

The study introduces a transfer learning approach using DANN for phase transition detection in percolation models, requiring minimal labeled data and refining critical point estimation.

Findings

DANN accurately identifies critical points in percolation models.

The method achieves high accuracy with significantly less labeled data.

Results are comparable to traditional Monte Carlo simulations.

Abstract

The latest advances of statistical physics have shown remarkable performance of machine learning in identifying phase transitions. In this paper, we apply domain adversarial neural network (DANN) based on transfer learning to studying non-equilibrium and equilibrium phase transition models, which are percolation model and directed percolation (DP) model, respectively. With the DANN, only a small fraction of input configurations (2d images) needs to be labeled, which is automatically chosen, in order to capture the critical point. To learn the DP model, the method is refined by an iterative procedure in determining the critical point, which is a prerequisite for the data collapse in calculating the critical exponent $\nu_{\perp}$. We then apply the DANN to a two-dimensional site percolation with configurations filtered to include only the largest cluster which may contain the information related to the order parameter. The DANN learning of both models yields reliable results which are comparable to the ones from Monte Carlo simulations. Our study also shows that the DANN can achieve quite high accuracy at much lower cost, compared to the supervised learning.