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Phase transitions, percolation, fracture of materials, and deep learning

Serveh Kamrava, Pejman Tahmasebi, Muhammad Sahimi, and Sepehr Arbabi
Phys. Rev. E 102, 011001(R) – Published 14 July 2020; Retraction Phys. Rev. E 104, 049901 (2021)

Abstract

This article has been retracted: see Phys. Rev. E 104, 049901 (2021)

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 pc 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 pc 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 pc, the elastic moduli, and the universal Poisson ratio at pc. All the predictions are in excellent agreement with the data. In particular, the DNN predicts correctly pc, even though the training data were for the state of the systems far from pc. 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.

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  • Received 5 May 2020
  • Accepted 24 June 2020

DOI:https://doi.org/10.1103/PhysRevE.102.011001

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Erratum

Retraction: Phase transitions, percolation, fracture of materials, and deep learning [Phys. Rev. E 102, 011001(R) (2020)]

Serveh Kamrava, Pejman Tahmasebi, Muhammad Sahimi, and Sepehr Arbabi
Phys. Rev. E 104, 049901 (2021)

Authors & Affiliations

Serveh Kamrava1, Pejman Tahmasebi2, Muhammad Sahimi1,*, and Sepehr Arbabi3

  • 1Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
  • 2Department of Petroleum Engineering, University of Wyoming, Laramie, Wyoming 82071, USA
  • 3Department of Chemical Engineering, University of Texas of the Permian Basin, Odessa, Texas 79762, USA

  • *moe@usc.edu

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Issue

Vol. 102, Iss. 1 — July 2020

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