Deep learning in phase transition prediction of disordered materials

Percolation and fracture propagation in disordered solids represent an important problems in science and engineering that is characterized by phase transitions: loss of macroscopic connectivity at the percolation threshold p_c. An important unsolved problem is accurate prediction of physical properties of systems undergoing such transitions, given limited data far from the transition point. There is currently no theoretical method that can use limited data for a region far from a transition point p_c and predict the physical properties all the way to that point, including their location. We present a deep neural network (DNN) for predicting such properties of two- and three-dimensional systems and in particular their percolation probability, the threshold p_c. All the predictions are in excellent agreement with the data. This opens up the possibility of using the DNN for predicting physical properties of many types of disordered materials that undergo phase transformation, for which limited data are available for only far from the transition point.