  Recent advances in machine learning have become increasingly popular in the
applications of phase transitions and critical phenomena. By machine learning
approaches, we try to identify the physical characteristics in the
two-dimensional percolation model. To achieve this, we adopt Monte Carlo
simulation to generate dataset at first, and then we employ several approaches
to analyze the dataset. Four kinds of convolutional neural networks (CNNs), one
variational autoencoder (VAE), one convolutional VAE (cVAE), one principal
component analysis (PCA), and one $k$-means are used for identifying order
parameter, the permeability, and the critical transition point. The former
three kinds of CNNs can simulate the two order parameters and the permeability
with high accuracy, and good extrapolating performance. The former two kinds of
CNNs have high anti-noise ability. To validate the robustness of the former
three kinds of CNNs, we also use the VAE and the cVAE to generate new
percolating configurations to add perturbations into the raw configurations. We
find that there is no difference by using the raw or the perturbed
configurations to identify the physical characteristics, under the prerequisite
of corresponding labels. In the case of lacking labels, we use unsupervised
learning to detect the physical characteristics. The PCA, a classical
unsupervised learning, performs well when identifying the permeability but
fails to deduce order parameter. Hence, we apply the fourth kinds of CNNs with
different preset thresholds, and identify a new order parameter and the
critical transition point. Our findings indicate that the effectiveness of
machine learning still needs to be evaluated in the applications of phase
transitions and critical phenomena.
