Abstract
Percolation and fracture propagation in disordered solids represent two important problems in science and engineering that are characterized by phase transitions: loss of macroscopic connectivity at the percolation threshold and formation of a macroscopic fracture network at the incipient fracture point (IFP). Percolation also represents the fracture problem in the limit of very strong disorder. 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 or the IFP 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 , the elastic moduli, and the universal Poisson ratio at . All the predictions are in excellent agreement with the data. In particular, the DNN predicts correctly , even though the training data were for the state of the systems far from . 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.
- Received 5 May 2020
- Accepted 24 June 2020
DOI:https://doi.org/10.1103/PhysRevE.102.011001
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