  As powerful as machine learning (ML) techniques are in solving problems
involving data with large dimensionality, explaining the results from the
fitted parameters remains a challenging task of utmost importance, especially
in physics applications. This work shows how this can be accomplished for the
ferromagnetic Ising model, the main target of several ML studies in statistical
physics. Here it is demonstrated that the successful unsupervised
identification of the phases and order parameter by principal component
analysis, a common method in those studies, detects that the magnetization per
spin has its greatest variation with the temperature, the actual control
parameter of the phase transition. Then, by using a neural network (NN) without
hidden layers (the simplest possible) and informed by the symmetry of the
Hamiltonian, an explanation is provided for the strategy used in finding the
supervised learning solution for the critical temperature of the model's
continuous phase transition. This allows the prediction of the minimal
extension of the NN to solve the problem when the symmetry is not known, which
becomes also explainable. These results pave the way to a physics-informed
explainable generalized framework, enabling the extraction of physical laws and
principles from the parameters of the models.
