  A universal (supervised) neural network (NN), which is only trained once on a
one-dimensional lattice of 200 sites, is employed to study the phase transition
of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square
lattice. In particular, the NN is obtained by using merely two artificially
made configurations as the training set. Due to the elegant features of the
considered NN, results associated with systems consisting of over 4000000 spins
can be obtained with ease, and convincing evidence showing the investigated
phase transition is weakly first order is reached. The outcomes demonstrated
here can hardly be achieved with the standard NNs that are commonly used in the
literature.
