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A universal supervised neural network (NN) relevant to compute the associatedcriticalities of real experiments studying phase transitions is constructed.The validity of the built NN is examined by applying it to calculate thecriticalities 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 criticalpoints of the studied 3D systems. Moreover, real configurations of states arenot used in the testing stage. Instead, the employed configurations for theprediction are constructed on a 1D lattice of 120 sites and are based on thebulk quantities or the microscopic states of the considered models. As aresult, our calculations are ultimately efficient in computation and theapplications of the built NN is extremely broaden. Considering the fact thatthe investigated systems vary dramatically from each other, it is amazing thatthe combination of these two strategies in the training and the testing stageslead to a highly universal supervised neural network for learning phases andcriticalities of 3D models. Based on the outcomes presented in this study, itis favorably probable that much simpler but yet elegant machine learningtechniques can be constructed for fields of many-body systems other than thecritical phenomena.

A universal neural network for learning phases and criticalities