Statistical characterization and reconstruction of heterogeneous microstructures using deep neural network

Abstract Heterogeneous materials, whether natural or artificial, are usually composed of distinct constituents present in complex microstructures with discontinuous, irregular and hierarchical characteristics. For many heterogeneous materials, such as porous media and composites, the microstructural features are of fundamental importance for their macroscopic properties. This paper presents a novel method to statistically characterize and reconstruct random microstructures through a deep neural network (DNN) model, which can be used to study the microstructure–property relationships. In our method, the digital microstructure image is assumed to be a stationary Markov random field (MRF), and local patterns covering the basic morphological features are collected to train a DNN model, after which statistically equivalent samples can be generated through a DNN-guided reconstruction procedure. Furthermore, to overcome the short-distance limitation associated with the MRF assumption, a multi-level approach is developed to preserve the long-distance morphological features of heterogeneous microstructures. A large number of tests have been conducted to compare the reconstructed and target microstructures in both morphological characteristics and physical properties, and good agreements are observed in all test cases. The proposed method is efficient, accurate, versatile, and especially beneficial to the statistical reconstruction of 2D/3D microstructures with long-distance correlations.

[1]  I. Tiselj,et al.  Lattice Boltzmann Method , 2022, Advanced Computational Techniques for Heat and Mass Transfer in Food Processing.

[2]  Wei Chen,et al.  A Transfer Learning Approach for Microstructure Reconstruction and Structure-property Predictions , 2018, Scientific Reports.

[3]  Dorthe Wildenschild,et al.  Image processing of multiphase images obtained via X‐ray microtomography: A review , 2014 .

[4]  Erlend Magnus Viggen,et al.  The Lattice Boltzmann Method , 2017 .

[5]  Orestis Malaspinas,et al.  Synchrotron X-ray microtomography and lattice Boltzmann simulations of gas flow through volcanic pumices , 2010 .

[6]  D. Owen,et al.  Statistical reconstruction and Karhunen–Loève expansion for multiphase random media , 2016 .

[7]  Martin J. Blunt,et al.  Reconstruction of three-dimensional porous media using generative adversarial neural networks , 2017, Physical review. E.

[8]  Hans-Jörg Vogel,et al.  Quantification of soil structure based on Minkowski functions , 2010, Comput. Geosci..

[9]  P. Corson,et al.  Correlation functions for predicting properties of heterogeneous materials. II. Empirical construction of spatial correlation functions for two‐phase solids , 1974 .

[10]  Hongxun Yao,et al.  Auto-encoder based dimensionality reduction , 2016, Neurocomputing.

[11]  Geoffrey E. Hinton,et al.  Reducing the Dimensionality of Data with Neural Networks , 2006, Science.

[12]  Chiho Kim,et al.  Machine learning in materials informatics: recent applications and prospects , 2017, npj Computational Materials.

[13]  W Chen,et al.  Characterization and reconstruction of 3D stochastic microstructures via supervised learning , 2016, Journal of microscopy.

[14]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[15]  Nigel P. Brandon,et al.  TauFactor: An open-source application for calculating tortuosity factors from tomographic data , 2016, SoftwareX.

[16]  Christoph H. Arns,et al.  Porous Structure Reconstruction Using Convolutional Neural Networks , 2018, Mathematical Geosciences.

[17]  M. Blunt,et al.  Pore space reconstruction using multiple-point statistics , 2005 .

[18]  Jürgen Schmidhuber,et al.  Deep learning in neural networks: An overview , 2014, Neural Networks.

[19]  S. Torquato,et al.  Random Heterogeneous Materials: Microstructure and Macroscopic Properties , 2005 .

[20]  Stan Z. Li,et al.  Markov Random Field Modeling in Image Analysis , 2001, Computer Science Workbench.

[21]  Wei Chen,et al.  Stochastic microstructure characterization and reconstruction via supervised learning , 2016 .

[22]  Bao-Lian Su,et al.  Hierarchically porous materials: synthesis strategies and structure design. , 2017, Chemical Society reviews.

[23]  Marc Levoy,et al.  Fast texture synthesis using tree-structured vector quantization , 2000, SIGGRAPH.

[24]  S. Torquato,et al.  Reconstructing random media , 1998 .

[25]  Kenneth Stuart Sorbie,et al.  3D Stochastic Modelling of Heterogeneous Porous Media – Applications to Reservoir Rocks , 2006 .

[26]  Pejman Tahmasebi,et al.  Reconstruction of three-dimensional porous media using a single thin section. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Randall J. LeVeque,et al.  Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems , 2007 .

[28]  C. Berg.  Permeability Description by Characteristic Length, Tortuosity, Constriction and Porosity , 2014, Transport in Porous Media.

[29]  Surya R. Kalidindi,et al.  Structure–property linkages using a data science approach: Application to a non-metallic inclusion/steel composite system , 2015 .

[30]  D. Owen,et al.  Resolution Effect: An Error Correction Model for Intrinsic Permeability of Porous Media Estimated from Lattice Boltzmann Method , 2020, Transport in Porous Media.

[31]  Paul E. Stutzman,et al.  Scanning electron microscopy imaging of hydraulic cement microstructure , 2004 .

[32]  W. B. Lindquist,et al.  Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontaineble , 2000 .

[33]  Jianzhong Wu,et al.  Stacked Sparse Autoencoder (SSAE) for Nuclei Detection on Breast Cancer Histopathology Images , 2016, IEEE Transactions on Medical Imaging.

[34]  S. Bakke,et al.  Process Based Reconstruction of Sandstones and Prediction of Transport Properties , 2002 .

[35]  Nicholas Zabaras,et al.  Classification and reconstruction of three-dimensional microstructures using support vector machines , 2005 .

[36]  David Brandon,et al.  Microstructural Characterization of Materials , 1999 .

[37]  D. Owen,et al.  Statistical reconstruction of two-phase random media , 2014 .

[38]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[39]  Yang Ju,et al.  3D numerical reconstruction of well-connected porous structure of rock using fractal algorithms , 2014 .

[40]  A. Choudhary,et al.  Deep materials informatics: Applications of deep learning in materials science , 2019, MRS Communications.

[41]  Ming Yang,et al.  New algorithms for virtual reconstruction of heterogeneous microstructures , 2018, Computer Methods in Applied Mechanics and Engineering.

[42]  Peter Grathwohl,et al.  Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics , 1998 .

[43]  Max Yi Ren,et al.  Microstructure Representation and Reconstruction of Heterogeneous Materials via Deep Belief Network for Computational Material Design , 2016, ArXiv.

[44]  Jef Caers,et al.  Geostatistical Reservoir Modelling using Statistical Pattern Recognition , 2001 .

[45]  Xingchen Liu,et al.  Random heterogeneous materials via texture synthesis , 2015 .

[46]  J. Quiblier.  A new three-dimensional modeling technique for studying porous media , 1984 .