  A universal supervised neural network (NN) relevant to compute the associated
criticalities of real experiments studying phase transitions is constructed.
The validity of the built NN is examined by applying it to calculate the
criticalities of several three-dimensional (3D) models on the cubic lattice,
including the classical $O(3)$ model, the 5-state ferromagnetic Potts model,
and a dimerized quantum antiferromagnetic Heisenberg model. Particularly,
although the considered NN is only trained one time on a one-dimensional (1D)
lattice with 120 sites, yet it has successfully determined the related critical
points of the studied 3D systems. Moreover, real configurations of states are
not used in the testing stage. Instead, the employed configurations for the
prediction are constructed on a 1D lattice of 120 sites and are based on the
bulk quantities or the microscopic states of the considered models. As a
result, our calculations are ultimately efficient in computation and the
applications of the built NN is extremely broaden. Considering the fact that
the investigated systems vary dramatically from each other, it is amazing that
the combination of these two strategies in the training and the testing stages
lead to a highly universal supervised neural network for learning phases and
criticalities of 3D models. Based on the outcomes presented in this study, it
is favorably probable that much simpler but yet elegant machine learning
techniques can be constructed for fields of many-body systems other than the
critical phenomena.
