1
|
Sahimi M. Physics-informed and data-driven discovery of governing equations for complex phenomena in heterogeneous media. Phys Rev E 2024; 109:041001. [PMID: 38755895 DOI: 10.1103/physreve.109.041001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Indexed: 05/18/2024]
Abstract
Rapid evolution of sensor technology, advances in instrumentation, and progress in devising data-acquisition software and hardware are providing vast amounts of data for various complex phenomena that occur in heterogeneous media, ranging from those in atmospheric environment, to large-scale porous formations, and biological systems. The tremendous increase in the speed of scientific computing has also made it possible to emulate diverse multiscale and multiphysics phenomena that contain elements of stochasticity or heterogeneity, and to generate large volumes of numerical data for them. Thus, given a heterogeneous system with annealed or quenched disorder in which a complex phenomenon occurs, how should one analyze and model the system and phenomenon, explain the data, and make predictions for length and time scales much larger than those over which the data were collected? We divide such systems into three distinct classes. (i) Those for which the governing equations for the physical phenomena of interest, as well as data, are known, but solving the equations over large length scales and long times is very difficult. (ii) Those for which data are available, but the governing equations are only partially known, in the sense that they either contain various coefficients that must be evaluated based on the data, or that the number of degrees of freedom of the system is so large that deriving the complete equations is very difficult, if not impossible, as a result of which one must develop the governing equations with reduced dimensionality. (iii) In the third class are systems for which large amounts of data are available, but the governing equations for the phenomena of interest are not known. Several classes of physics-informed and data-driven approaches for analyzing and modeling of the three classes of systems have been emerging, which are based on machine learning, symbolic regression, the Koopman operator, the Mori-Zwanzig projection operator formulation, sparse identification of nonlinear dynamics, data assimilation combined with a neural network, and stochastic optimization and analysis. This perspective describes such methods and the latest developments in this highly important and rapidly expanding area and discusses possible future directions.
Collapse
Affiliation(s)
- Muhammad Sahimi
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
| |
Collapse
|
2
|
Lavrukhin EV, Karsanina MV, Gerke KM. Measuring structural nonstationarity: The use of imaging information to quantify homogeneity and inhomogeneity. Phys Rev E 2023; 108:064128. [PMID: 38243461 DOI: 10.1103/physreve.108.064128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2023] [Accepted: 11/20/2023] [Indexed: 01/21/2024]
Abstract
Heterogeneity is the concept we encounter in numerous research areas and everyday life. While "not mixing apples and oranges" is easy to grasp, a more quantitative approach to such segregation is not always readily available. Consider the problem from a different angle: To what extent does one have to make apples more orange and oranges more "apple-shaped" to put them into the same basket (according to their appearance alone)? This question highlights the central problem of the blurred interface between heterogeneous and homogeneous, which also depends on the metrics used for its identification. This work uncovers the physics of structural stationarity quantification, based on correlation functions (CFs) and clustering based on CFs different between image subregions. By applying the methodology to a wide variety of synthetic and real images of binary porous media, we confirmed computationally that only periodically unit-celled structures and images produced by stationary processes with resolutions close to infinity are strictly stationary. Natural structures without recurring unit cells are only weakly stationary. We established a physically meaningful definition for these stationarity types and their distinction from nonstationarity. In addition, the importance of information content of the chosen metrics is highlighted and discussed. We believe the methodology as proposed in this contribution will find its way into numerous research areas dealing with materials, structures, and measurements and modeling based on structural imaging information.
Collapse
Affiliation(s)
- Efim V Lavrukhin
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, Moscow 123242, Russia; Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, Russia; and Dokuchaev Soil Science Institute, Moscow 119017, Russia
| | - Marina V Karsanina
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, Moscow 123242, Russia
| | - Kirill M Gerke
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, Moscow 123242, Russia
| |
Collapse
|
3
|
Kalule R, Abderrahmane HA, Alameri W, Sassi M. Stacked ensemble machine learning for porosity and absolute permeability prediction of carbonate rock plugs. Sci Rep 2023; 13:9855. [PMID: 37330558 DOI: 10.1038/s41598-023-36096-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 05/29/2023] [Indexed: 06/19/2023] Open
Abstract
This study employs a stacked ensemble machine learning approach to predict carbonate rocks' porosity and absolute permeability with various pore-throat distributions and heterogeneity. Our dataset consists of 2D slices from 3D micro-CT images of four carbonate core samples. The stacking ensemble learning approach integrates predictions from several machine learning-based models into a single meta-learner model to accelerate the prediction and improve the model's generalizability. We used the randomized search algorithm to attain optimal hyperparameters for each model by scanning over a vast hyperparameter space. To extract features from the 2D image slices, we applied the watershed-scikit-image technique. We showed that the stacked model algorithm effectively predicts the rock's porosity and absolute permeability.
Collapse
Affiliation(s)
- Ramanzani Kalule
- Department of Mechanical Engineering, Khalifa University, Abu Dhabi, UAE.
| | | | - Waleed Alameri
- Department of Petroleum Engineering, Khalifa University, Abu Dhabi, UAE
| | - Mohamed Sassi
- Department of Mechanical Engineering, Khalifa University, Abu Dhabi, UAE
| |
Collapse
|
4
|
Graczyk KM, Strzelczyk D, Matyka M. Deep learning for diffusion in porous media. Sci Rep 2023; 13:9769. [PMID: 37328555 DOI: 10.1038/s41598-023-36466-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 06/04/2023] [Indexed: 06/18/2023] Open
Abstract
We adopt convolutional neural networks (CNN) to predict the basic properties of the porous media. Two different media types are considered: one mimics the sand packings, and the other mimics the systems derived from the extracellular space of biological tissues. The Lattice Boltzmann Method is used to obtain the labeled data necessary for performing supervised learning. We distinguish two tasks. In the first, networks based on the analysis of the system's geometry predict porosity and effective diffusion coefficient. In the second, networks reconstruct the concentration map. In the first task, we propose two types of CNN models: the C-Net and the encoder part of the U-Net. Both networks are modified by adding a self-normalization module [Graczyk et al. in Sci Rep 12, 10583 (2022)]. The models predict with reasonable accuracy but only within the data type, they are trained on. For instance, the model trained on sand packings-like samples overshoots or undershoots for biological-like samples. In the second task, we propose the usage of the U-Net architecture. It accurately reconstructs the concentration fields. In contrast to the first task, the network trained on one data type works well for the other. For instance, the model trained on sand packings-like samples works perfectly on biological-like samples. Eventually, for both types of the data, we fit exponents in the Archie's law to find tortuosity that is used to describe the dependence of the effective diffusion on porosity.
Collapse
Affiliation(s)
- Krzysztof M Graczyk
- Faculty of Physics and Astronomy, Institute of Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50-204, Wrocław, Poland.
| | - Dawid Strzelczyk
- Faculty of Physics and Astronomy, Institute of Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50-204, Wrocław, Poland
| | - Maciej Matyka
- Faculty of Physics and Astronomy, Institute of Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50-204, Wrocław, Poland
| |
Collapse
|
5
|
Samarin A, Postnicov V, Karsanina MV, Lavrukhin EV, Gafurova D, Evstigneev NM, Khlyupin A, Gerke KM. Robust surface-correlation-function evaluation from experimental discrete digital images. Phys Rev E 2023; 107:065306. [PMID: 37464648 DOI: 10.1103/physreve.107.065306] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Accepted: 04/18/2023] [Indexed: 07/20/2023]
Abstract
Correlation functions (CFs) are universal structural descriptors; surface-surface F_{ss} and surface-void F_{sv} CFs are a subset containing additional information about the interface between the phases. The description of the interface between pores and solids in porous media is of particular importance and recently Ma and Torquato [Phys. Rev. E 98, 013307 (2018)2470-004510.1103/PhysRevE.98.013307] proposed an elegant way to compute these functions for a wide variety of cases. However, their "continuous" approach is not always applicable to digital experimental 2D and 3D images of porous media as obtained using x-ray tomography or scanning electron microscopy due to nonsingularities in chemical composition or local solid material's density and partial volume effects. In this paper we propose to use edge-detecting filters to compute surface CFs in the "digital" fashion directly in the images. Computed this way, surface correlation functions are the same as analytically known for Poisson disks in case the resolution of the image is adequate. Based on the multiscale image analysis we developed a C_{0.5} criterion that can predict if the imaging resolution is enough to make an accurate evaluation of the surface CFs. We also showed that in cases when the input image contains all major features, but do not pass the C_{0.5} criterion, it is possible with the help of image magnification to sample CFs almost similar to those obtained for high-resolution image of the same structure with high C_{0.5}. The computational framework as developed here is open source and available within the CorrelationFunctions.jl package developed by our group. Our "digital" approach was applied to a wide variety of real porous media images of different quality. We discuss critical aspects of surface correlation functions computations as related to different applications. The developed methodology allows applying surface CFs to describe the structure of porous materials based on their experimental images and enhance stochastic reconstructions or super-resolution procedures, or serve as an efficient metrics in machine learning applications due to computationally effective GPU implementation.
Collapse
Affiliation(s)
- Aleksei Samarin
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, Moscow 107031, Russia
- Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, Russia
| | - Vasily Postnicov
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, Moscow 107031, Russia
| | - Marina V Karsanina
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, Moscow 107031, Russia
| | - Efim V Lavrukhin
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, Moscow 107031, Russia
- Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, Russia
| | - Dina Gafurova
- Oil and Gas Research Institute Russian Academy of Sciences (OGRI RAS) 3, Gubkina Street, Moscow 119333, Russian Federation
| | - Nikolay M Evstigneev
- Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, Moscow 117312, Russia
| | - Aleksey Khlyupin
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, Moscow 107031, Russia
| | - Kirill M Gerke
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, Moscow 107031, Russia
| |
Collapse
|
6
|
Fu J, Wang M, Chen B, Wang J, Xiao D, Luo M, Evans B. A data-driven framework for permeability prediction of natural porous rocks via microstructural characterization and pore-scale simulation. ENGINEERING WITH COMPUTERS 2023:1-32. [PMID: 37362240 PMCID: PMC10198039 DOI: 10.1007/s00366-023-01841-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 05/03/2023] [Indexed: 06/28/2023]
Abstract
Understanding the microstructure-property relationships of porous media is of great practical significance, based on which macroscopic physical properties can be directly derived from measurable microstructural informatics. However, establishing reliable microstructure-property mappings in an explicit manner is difficult, due to the intricacy, stochasticity, and heterogeneity of porous microstructures. In this paper, a data-driven computational framework is presented to investigate the inherent microstructure-permeability linkage for natural porous rocks, where multiple techniques are integrated together, including microscopy imaging, stochastic reconstruction, microstructural characterization, pore-scale simulation, feature selection, and data-driven modeling. A large number of 3D digital rocks with a wide porosity range are acquired from microscopy imaging and stochastic reconstruction techniques. A broad variety of morphological descriptors are used to quantitatively characterize pore microstructures from different perspectives, and they compose the raw feature pool for feature selection. High-fidelity lattice Boltzmann simulations are conducted to resolve fluid flow passing through porous media, from which reliable permeability references are obtained. The optimal feature set that best represents permeability is identified through a performance-oriented feature selection process, upon which a cost-effective surrogate model is rapidly fitted to approximate the microstructure-permeability mapping via data-driven modeling. This surrogate model exhibits great advantages over empirical/analytical formulas in terms of prediction accuracy and generalization capacity, which can predict reliable permeability values spanning four orders of magnitude. Besides, feature selection also greatly enhances the interpretability of the data-driven prediction model, from which new insights into the mechanism of how microstructural characteristics determine intrinsic permeability are obtained.
Collapse
Affiliation(s)
- Jinlong Fu
- Zienkiewicz Institute for Modelling, Data and AI, Faculty of Science and Engineering, Swansea University, Swansea, SA1 8EN UK
| | - Min Wang
- Fluid Dynamics and Solid Mechanics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA
| | - Bin Chen
- College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210098 China
| | - Jinsheng Wang
- School of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031 China
| | - Dunhui Xiao
- School of Mathematical Sciences, Tongji University, Shanghai, 200092 China
| | - Min Luo
- Ocean College, Zhejiang University, Zhoushan, 316021 Zhejiang China
| | - Ben Evans
- Zienkiewicz Institute for Modelling, Data and AI, Faculty of Science and Engineering, Swansea University, Swansea, SA1 8EN UK
| |
Collapse
|
7
|
Liu S, Barati R, Zhang C, Kazemi M. Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport. ACS OMEGA 2023; 8:13649-13669. [PMID: 37091418 PMCID: PMC10116521 DOI: 10.1021/acsomega.2c07643] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 03/13/2023] [Indexed: 05/03/2023]
Abstract
In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge.
Collapse
Affiliation(s)
- Siyan Liu
- Department
of Chemical & Petroleum Engineering, University of Kansas, Lawrence, Kansas 66045, United States
- Computational
Sciences and Engineering Division, Oak Ridge
National Laboratory, Oak Ridge, Tennessee 37830, United States
| | - Reza Barati
- Department
of Chemical & Petroleum Engineering, University of Kansas, Lawrence, Kansas 66045, United States
| | - Chi Zhang
- Department
of Meteorology and Geophysics, Institute of Meteorology and Geophysics, University of Vienna, Universität Wien, UZA II, Josef-Holaubek-Platz
2, Wien 1090, Austria
| | - Mohammad Kazemi
- Department
of Physics and Engineering, Slippery Rock
University, Slippery Rock, Pennsylvania 16057, United States
| |
Collapse
|
8
|
Mohyeddini A, Rasaei MR. Calculating porosity and permeability from synthetic micro‐
CT
scan images based on a hybrid artificial intelligence. CAN J CHEM ENG 2023. [DOI: 10.1002/cjce.24901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/31/2023]
|
9
|
Homogenization-Informed Convolutional Neural Networks for Estimation of Li-ion Battery Effective Properties. Transp Porous Media 2022. [DOI: 10.1007/s11242-022-01862-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/10/2022]
|
10
|
Machine learning to predict effective reaction rates in 3D porous media from pore structural features. Sci Rep 2022; 12:5486. [PMID: 35361834 PMCID: PMC8971379 DOI: 10.1038/s41598-022-09495-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 03/24/2022] [Indexed: 12/03/2022] Open
Abstract
Large discrepancies between well-mixed reaction rates and effective reactions rates estimated under fluid flow conditions have been a major issue for predicting reactive transport in porous media systems. In this study, we introduce a framework that accurately predicts effective reaction rates directly from pore structural features by combining 3D pore-scale numerical simulations with machine learning (ML). We first perform pore-scale reactive transport simulations with fluid–solid reactions in hundreds of porous media and calculate effective reaction rates from pore-scale concentration fields. We then train a Random Forests model with 11 pore structural features and effective reaction rates to quantify the importance of structural features in determining effective reaction rates. Based on the importance information, we train artificial neural networks with varying number of features and demonstrate that effective reaction rates can be accurately predicted with only three pore structural features, which are specific surface, pore sphericity, and coordination number. Finally, global sensitivity analyses using the ML model elucidates how the three structural features affect effective reaction rates. The proposed framework enables accurate predictions of effective reaction rates directly from a few measurable pore structural features, and the framework is readily applicable to a wide range of applications involving porous media flows.
Collapse
|
11
|
Aslannejad H, Samari-Kermani M, Nezami H, Jafari S, Raoof A. Application of machine learning in colloids transport in porous media studies: Lattice Boltzmann simulation results as training data. Chem Eng Sci 2022. [DOI: 10.1016/j.ces.2022.117548] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
|
12
|
González Tejada I, Antolin P. Use of machine learning for unraveling hidden correlations between particle size distributions and the mechanical behavior of granular materials. ACTA GEOTECHNICA 2022; 17:1443-1461. [PMID: 35535303 PMCID: PMC9050806 DOI: 10.1007/s11440-021-01420-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2020] [Accepted: 11/09/2021] [Indexed: 05/05/2023]
Abstract
A data-driven framework was used to predict the macroscopic mechanical behavior of dense packings of polydisperse granular materials. The discrete element method, DEM, was used to generate 92,378 sphere packings that covered many different kinds of particle size distributions, PSD, lying within 2 particle sizes. These packings were subjected to triaxial compression and the corresponding stress-strain curves were fitted to Duncan-Chang hyperbolic models. An artificial neural network (NN) scheme was able to anticipate the value of the model parameters for all these PSDs, with an accuracy similar to the precision of the experiment and even when the NN was trained with a few hundred DEM simulations. The estimations were indeed more accurate than those given by multiple linear regressions (MLR) between the model parameters and common geotechnical and statistical descriptors derived from the PSD. This was achieved in spite of the presence of noise in the training data. Although the results of this massive simulation are limited to specific systems, ways of packing and testing conditions, the NN revealed the existence of hidden correlations between PSD of the macroscopic mechanical behavior.
Collapse
Affiliation(s)
- Ignacio González Tejada
- ETSI de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, C/ Profesor Aranguren S/N, 28040 Madrid, Spain
| | - P. Antolin
- Institute of Mathematics, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| |
Collapse
|
13
|
Bai T, Jiang Z, Tahmasebi P. Debris flow prediction with machine learning: smart management of urban systems and infrastructures. Neural Comput Appl 2021. [DOI: 10.1007/s00521-021-06197-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
14
|
Terry N, Johnson CD, Day-Lewis FD, Parker B, Slater L. Beware of Spatial Autocorrelation When Applying Machine Learning Algorithms to Borehole Geophysical Logs. GROUND WATER 2021; 59:315-319. [PMID: 33521933 DOI: 10.1111/gwat.13081] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Revised: 01/26/2021] [Accepted: 01/28/2021] [Indexed: 06/12/2023]
Affiliation(s)
| | - Carole D Johnson
- U.S. Geological Survey, Earth System Processes Division, Hydrogeophysics Branch, 425 Jordan Road, Troy, NY, 12180, USA
| | - Frederick D Day-Lewis
- U.S. Geological Survey, Earth System Processes Division, Hydrogeophysics Branch, 425 Jordan Road, Troy, NY, 12180, USA
| | - Beth Parker
- G360 Institute for Groundwater Research, University of Guelph, Guelph, ON, Canada
| | - Lee Slater
- Department of Earth and Environmental Sciences, Rutgers University Newark, New Brunswick, NJ, USA
| |
Collapse
|
15
|
Wang YD, Chung T, Armstrong RT, Mostaghimi P. ML-LBM: Predicting and Accelerating Steady State Flow Simulation in Porous Media with Convolutional Neural Networks. Transp Porous Media 2021. [DOI: 10.1007/s11242-021-01590-6] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
16
|
Kamrava S, Tahmasebi P, Sahimi M. Physics- and image-based prediction of fluid flow and transport in complex porous membranes and materials by deep learning. J Memb Sci 2021. [DOI: 10.1016/j.memsci.2021.119050] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
17
|
Rock Porous Structure Characterization: A Critical Assessment of Various State-of-the-Art Techniques. Transp Porous Media 2021. [DOI: 10.1007/s11242-020-01518-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
18
|
Röding M, Ma Z, Torquato S. Predicting permeability via statistical learning on higher-order microstructural information. Sci Rep 2020; 10:15239. [PMID: 32943677 PMCID: PMC7498464 DOI: 10.1038/s41598-020-72085-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2020] [Accepted: 08/25/2020] [Indexed: 11/08/2022] Open
Abstract
Quantitative structure-property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure facilitates prediction of permeability, a key property that has been extensively studied in material science, geophysics and chemical engineering. In this work, we study the predictability of different structural descriptors via both linear regressions and neural networks. A large data set of 30,000 virtual, porous microstructures of different types, including both granular and continuous solid phases, is created for this end. We compute permeabilities of these structures using the lattice Boltzmann method, and characterize the pore space geometry using one-point correlation functions (porosity, specific surface), two-point surface-surface, surface-void, and void-void correlation functions, as well as the geodesic tortuosity as an implicit descriptor. Then, we study the prediction of the permeability using different combinations of these descriptors. We obtain significant improvements of performance when compared to a Kozeny-Carman regression with only lowest-order descriptors (porosity and specific surface). We find that combining all three two-point correlation functions and tortuosity provides the best prediction of permeability, with the void-void correlation function being the most informative individual descriptor. Moreover, the combination of porosity, specific surface, and geodesic tortuosity provides very good predictive performance. This shows that higher-order correlation functions are extremely useful for forming a general model for predicting physical properties of complex materials. Additionally, our results suggest that artificial neural networks are superior to the more conventional regression methods for establishing quantitative structure-property relationships. We make the data and code used publicly available to facilitate further development of permeability prediction methods.
Collapse
Affiliation(s)
- Magnus Röding
- RISE Research Institutes of Sweden, 41276, Göteborg, Sweden.
- Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 41296, Göteborg, Sweden.
| | - Zheng Ma
- Department of Physics, Princeton University, Princeton, NJ, 08544, USA
| | - Salvatore Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA
| |
Collapse
|
19
|
CNN-PFVS: Integrating Neural Network and Finite Volume Models to Accelerate Flow Simulation on Pore Space Images. Transp Porous Media 2020. [DOI: 10.1007/s11242-020-01466-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
|
20
|
Kamrava S, Tahmasebi P, Sahimi M, Arbabi S. Phase transitions, percolation, fracture of materials, and deep learning. Phys Rev E 2020; 102:011001. [PMID: 32794896 DOI: 10.1103/physreve.102.011001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 06/24/2020] [Indexed: 11/07/2022]
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 p_{c} 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 p_{c} 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 p_{c}, the elastic moduli, and the universal Poisson ratio at p_{c}. All the predictions are in excellent agreement with the data. In particular, the DNN predicts correctly p_{c}, even though the training data were for the state of the systems far from p_{c}. 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.
Collapse
Affiliation(s)
- Serveh Kamrava
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
| | - Pejman Tahmasebi
- Department of Petroleum Engineering, University of Wyoming, Laramie, Wyoming 82071, USA
| | - Muhammad Sahimi
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
| | - Sepehr Arbabi
- Department of Chemical Engineering, University of Texas of the Permian Basin, Odessa, Texas 79762, USA
| |
Collapse
|
21
|
Chen PE, Xu W, Ren Y, Jiao Y. Probing information content of hierarchical n-point polytope functions for quantifying and reconstructing disordered systems. Phys Rev E 2020; 102:013305. [PMID: 32794921 DOI: 10.1103/physreve.102.013305] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Accepted: 06/16/2020] [Indexed: 11/07/2022]
Abstract
Disordered systems are ubiquitous in physical, biological, and material sciences. Examples include liquid and glassy states of condensed matter, colloids, granular materials, porous media, composites, alloys, packings of cells in avian retina, and tumor spheroids, to name but a few. A comprehensive understanding of such disordered systems requires, as the first step, systematic quantification, modeling, and representation of the underlying complex configurations and microstructure, which is generally very challenging to achieve. Recently, we introduced a set of hierarchical statistical microstructural descriptors, i.e., the "n-point polytope functions" P_{n}, which are derived from the standard n-point correlation functions S_{n}, and successively included higher-order n-point statistics of the morphological features of interest in a concise, explainable, and expressive manner. Here we investigate the information content of the P_{n} functions via optimization-based realization rendering. This is achieved by successively incorporating higher-order P_{n} functions up to n=8 and quantitatively assessing the accuracy of the reconstructed systems via unconstrained statistical morphological descriptors (e.g., the lineal-path function). We examine a wide spectrum of representative random systems with distinct geometrical and topological features. We find that, generally, successively incorporating higher-order P_{n} functions and, thus, the higher-order morphological information encoded in these descriptors leads to superior accuracy of the reconstructions. However, incorporating more P_{n} functions into the reconstruction also significantly increases the complexity and roughness of the associated energy landscape for the underlying stochastic optimization, making it difficult to convergence numerically.
Collapse
Affiliation(s)
- Pei-En Chen
- Department of Mechanical Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Wenxiang Xu
- College of Mechanics and Materials, Hohai University, Nanjing 211100, People's Republic of China
| | - Yi Ren
- Department of Mechanical Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Yang Jiao
- Department of Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA.,Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
| |
Collapse
|
22
|
Lubbers N, Agarwal A, Chen Y, Son S, Mehana M, Kang Q, Karra S, Junghans C, Germann TC, Viswanathan HS. Modeling and scale-bridging using machine learning: nanoconfinement effects in porous media. Sci Rep 2020; 10:13312. [PMID: 32770012 PMCID: PMC7414857 DOI: 10.1038/s41598-020-69661-0] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Accepted: 07/14/2020] [Indexed: 11/09/2022] Open
Abstract
Fine-scale models that represent first-principles physics are challenging to represent at larger scales of interest in many application areas. In nanoporous media such as tight-shale formations, where the typical pore size is less than 50 nm, confinement effects play a significant role in how fluids behave. At these scales, fluids are under confinement, affecting key properties such as density, viscosity, adsorption, etc. Pore-scale Lattice Boltzmann Methods (LBM) can simulate flow in complex pore structures relevant to predicting hydrocarbon production, but must be corrected to account for confinement effects. Molecular dynamics (MD) can model confinement effects but is computationally expensive in comparison. The hurdle to bridging MD with LBM is the computational expense of MD simulations needed to perform this correction. Here, we build a Machine Learning (ML) surrogate model that captures adsorption effects across a wide range of parameter space and bridges the MD and LBM scales using a relatively small number of MD calculations. The model computes upscaled adsorption parameters across varying density, temperature, and pore width. The ML model is 7 orders of magnitude faster than brute force MD. This workflow is agnostic to the physical system and could be generalized to further scale-bridging applications.
Collapse
Affiliation(s)
- Nicholas Lubbers
- Information Sciences Group, Computer, Computational and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| | - Animesh Agarwal
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Yu Chen
- Computational Earth Science Group, Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Soyoun Son
- Institut des Sciences de la Terre, Université Grenoble Alpes, Grenoble, France.,Geophysics Group, Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Mohamed Mehana
- Computational Earth Science Group, Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Qinjun Kang
- Computational Earth Science Group, Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Satish Karra
- Computational Earth Science Group, Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Christoph Junghans
- Applied Computer Science Group, Computer, Computational and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Timothy C Germann
- Physics and Chemistry of Materials Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Hari S Viswanathan
- Computational Earth Science Group, Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| |
Collapse
|
23
|
Piasecki R, Olchawa W, Frączek D, Bartecka A. A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions. MATERIALS (BASEL, SWITZERLAND) 2020; 13:E2748. [PMID: 32560404 PMCID: PMC7345931 DOI: 10.3390/ma13122748] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Revised: 05/29/2020] [Accepted: 06/13/2020] [Indexed: 01/29/2023]
Abstract
The main goal of our research is to develop an effective method with a wide range of applications for the statistical reconstruction of heterogeneous microstructures with compact inclusions of any shape, such as highly irregular grains. The devised approach uses multi-scale extended entropic descriptors (ED) that quantify the degree of spatial non-uniformity of configurations of finite-sized objects. This technique is an innovative development of previously elaborated entropy methods for statistical reconstruction. Here, we discuss the two-dimensional case, but this method can be generalized into three dimensions. At the first stage, the developed procedure creates a set of black synthetic clusters that serve as surrogate inclusions. The clusters have the same individual areas and interfaces as their target counterparts, but random shapes. Then, from a given number of easy-to-generate synthetic cluster configurations, we choose the one with the lowest value of the cost function defined by us using extended ED. At the second stage, we make a significant change in the standard technique of simulated annealing (SA). Instead of swapping pixels of different phases, we randomly move each of the selected synthetic clusters. To demonstrate the accuracy of the method, we reconstruct and analyze two-phase microstructures with irregular inclusions of silica in rubber matrix as well as stones in cement paste. The results show that the two-stage reconstruction (TSR) method provides convincing realizations for these complex microstructures. The advantages of TSR include the ease of obtaining synthetic microstructures, very low computational costs, and satisfactory mapping in the statistical context of inclusion shapes. Finally, its simplicity should greatly facilitate independent applications.
Collapse
Affiliation(s)
- Ryszard Piasecki
- Institute of Physics, University of Opole, Oleska 48, 45-052 Opole, Poland; (W.O.); (A.B.)
| | - Wiesław Olchawa
- Institute of Physics, University of Opole, Oleska 48, 45-052 Opole, Poland; (W.O.); (A.B.)
| | - Daniel Frączek
- Department of Materials Physics, Opole University of Technology, Katowicka 48, 45-061 Opole, Poland;
| | - Agnieszka Bartecka
- Institute of Physics, University of Opole, Oleska 48, 45-052 Opole, Poland; (W.O.); (A.B.)
| |
Collapse
|