  Unsupervised machine learning applied to the study of phase transitions is an
ongoing and interesting research direction. The active contour model, also
called the snake model, was initially proposed for target contour extraction in
two-dimensional images. In order to obtain a physical phase diagram, the snake
model with an artificial neural network is applied in an unsupervised learning
way by the authors of [Phys.Rev.Lett. 120, 176401(2018)]. It guesses the phase
boundary as an initial snake and then drives the snake to convergence with
forces estimated by the artificial neural network. In this paper, we extend
this unsupervised learning method with one contour to a snake net with multiple
contours for the purpose of obtaining several phase boundaries in a phase
diagram. For the classical Blume-Capel model, the phase diagram containing
three and four phases is obtained. Moreover, to overcome the limitations of the
initial position and speed up the movement of the snake, the balloon force
decaying with the iteration steps is introduced and applied to the snake net
structure. Our method is helpful in determining the phase diagram with multiple
phases, using just snapshots of configurations from cold atoms or other
experiments without knowledge of the phases.
