  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.
