The calculation of the entropy of a physical system constitutes a critical stage in analyzing its thermodynamic properties. Much research has been carried out, endeavoring a general scheme for this calculation, yet current methods suffer from a high computational cost and inability to work on complex systems or apply to only specific systems. In our research, we developed a method based on a neural network estimator, which obtains the entropy of the physical system by an iterative calculation of the mutual information between its sub-systems. We tested our method on both discrete and continuous systems and showed that it allows for a precise calculation of the entropy with – at most - logarithmic running time. Compared to other methods, our method obtains high precision in calculating the entropy of the standard and the antiferromagnetic Ising models and the XY model with and without an external field. Last, our network studies the physical characteristics of the system and successfully uses the knowledge gained from one system for a fast entropy calculation of supplementary systems, of various temperatures and sizes.