Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning
Abstract
Fractured systems are ubiquitous in natural and engineered applications as diverse as hydraulic fracturing, underground nuclear test detection, corrosive damage in materials and brittle failure of metals and ceramics. Microstructural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for these systems but can only be known statistically. Current models either ignore or idealize microscale information at these larger scales because we lack a framework that efficiently utilizes it in its entirety to predict macroscale behavior in brittle materials. Here, we propose a method that integrates computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive high-fidelity models to coarse-scale graphs without loss of critical structural information. We exploit the underlying discrete structure of fracture networks in systems considering flow through fractures and fracture propagation. We demonstrate that compact graph representations require significantly fewer degrees of freedom (dof) to capture micro-fracture information and further accelerate these models with Machine Learning. Our method has been shown to improve accuracy of predictions with up to four orders of magnitude speedup.
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1462126
- Alternate Identifier(s):
- OSTI ID: 1467273
- Report Number(s):
- LA-UR-17-29575
Journal ID: ISSN 2045-2322; 11665; PII: 30117
- Grant/Contract Number:
- AC52-06NA25396; 20170103DR; 20150693ECR
- Resource Type:
- Published Article
- Journal Name:
- Scientific Reports
- Additional Journal Information:
- Journal Name: Scientific Reports Journal Volume: 8 Journal Issue: 1; Journal ID: ISSN 2045-2322
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING
Citation Formats
Srinivasan, Gowri, Hyman, Jeffrey D., Osthus, David A., Moore, Bryan A., O’Malley, Daniel, Karra, Satish, Rougier, Esteban, Hagberg, Aric A., Hunter, Abigail, and Viswanathan, Hari S. Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning. United Kingdom: N. p., 2018.
Web. doi:10.1038/s41598-018-30117-1.
Srinivasan, Gowri, Hyman, Jeffrey D., Osthus, David A., Moore, Bryan A., O’Malley, Daniel, Karra, Satish, Rougier, Esteban, Hagberg, Aric A., Hunter, Abigail, & Viswanathan, Hari S. Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning. United Kingdom. https://doi.org/10.1038/s41598-018-30117-1
Srinivasan, Gowri, Hyman, Jeffrey D., Osthus, David A., Moore, Bryan A., O’Malley, Daniel, Karra, Satish, Rougier, Esteban, Hagberg, Aric A., Hunter, Abigail, and Viswanathan, Hari S. Fri .
"Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning". United Kingdom. https://doi.org/10.1038/s41598-018-30117-1.
@article{osti_1462126,
title = {Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning},
author = {Srinivasan, Gowri and Hyman, Jeffrey D. and Osthus, David A. and Moore, Bryan A. and O’Malley, Daniel and Karra, Satish and Rougier, Esteban and Hagberg, Aric A. and Hunter, Abigail and Viswanathan, Hari S.},
abstractNote = {Fractured systems are ubiquitous in natural and engineered applications as diverse as hydraulic fracturing, underground nuclear test detection, corrosive damage in materials and brittle failure of metals and ceramics. Microstructural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for these systems but can only be known statistically. Current models either ignore or idealize microscale information at these larger scales because we lack a framework that efficiently utilizes it in its entirety to predict macroscale behavior in brittle materials. Here, we propose a method that integrates computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive high-fidelity models to coarse-scale graphs without loss of critical structural information. We exploit the underlying discrete structure of fracture networks in systems considering flow through fractures and fracture propagation. We demonstrate that compact graph representations require significantly fewer degrees of freedom (dof) to capture micro-fracture information and further accelerate these models with Machine Learning. Our method has been shown to improve accuracy of predictions with up to four orders of magnitude speedup.},
doi = {10.1038/s41598-018-30117-1},
journal = {Scientific Reports},
number = 1,
volume = 8,
place = {United Kingdom},
year = {Fri Aug 03 00:00:00 EDT 2018},
month = {Fri Aug 03 00:00:00 EDT 2018}
}
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https://doi.org/10.1038/s41598-018-30117-1
https://doi.org/10.1038/s41598-018-30117-1
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Cited by: 35 works
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Figures / Tables:
Figure 1: A modest sized fracture network with 459 fractures. (a) The original Discrete Fracture Network (DFN) model; (b) the 2-core representation of the DFN and (c) the graph corresponding to the shortest path between inflow and outflow boundaries. Insets show the DFN models corresponding to the reduced graph representations.
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Works referenced in this record:
Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 2. Permeability of networks based on lognormal distribution of apertures
journal, August 2001
- de Dreuzy, Jean-Raynald; Davy, Philippe; Bour, Olivier
- Water Resources Research, Vol. 37, Issue 8
Effective permeability of fractured porous media with power-law distribution of fracture sizes
journal, September 2007
- Bogdanov, I. I.; Mourzenko, V. V.; Thovert, J. -F.
- Physical Review E, Vol. 76, Issue 3
Curve Fitting and Optimal Design for Prediction
journal, September 1978
- O'Hagan, A.
- Journal of the Royal Statistical Society: Series B (Methodological), Vol. 40, Issue 1
Computer Model Calibration Using High-Dimensional Output
journal, June 2008
- Higdon, Dave; Gattiker, James; Williams, Brian
- Journal of the American Statistical Association, Vol. 103, Issue 482
Machine learning for graph-based representations of three-dimensional discrete fracture networks
journal, January 2018
- Valera, Manuel; Guo, Zhengyang; Kelly, Priscilla
- Computational Geosciences, Vol. 22, Issue 3
PFLOTRAN User Manual: A Massively Parallel Reactive Flow and Transport Model for Describing Surface and Subsurface Processes
report, January 2015
- Lichtner, Peter; Hammond, Glenn; Lu, Chuan
Bayesian calibration of computer models
journal, August 2001
- Kennedy, Marc C.; O'Hagan, Anthony
- Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 63, Issue 3
A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks
journal, January 2012
- Nœtinger, B.; Jarrige, N.
- Journal of Computational Physics, Vol. 231, Issue 1
Learning on Graphs for Predictions of Fracture Propagation, Flow and Transport
conference, May 2017
- Djidjev, Hristo; O'Malley, Daniel; Viswanathan, Hari
- 2017 IEEE International Parallel and Distributed Processing Symposium: Workshops (IPDPSW), 2017 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)
Evaluating the effect of internal aperture variability on transport in kilometer scale discrete fracture networks
journal, August 2016
- Makedonska, Nataliia; Hyman, Jeffrey D.; Karra, Satish
- Advances in Water Resources, Vol. 94
Data Analysis Using Regression and Multilevel/Hierarchical Models
book, January 2006
- Gelman, Andrew; Hill, Jennifer
Predictions of first passage times in sparse discrete fracture networks using graph-based reductions
journal, July 2017
- Hyman, Jeffrey D.; Hagberg, Aric; Srinivasan, Gowri
- Physical Review E, Vol. 96, Issue 1
Fracture size and transmissivity correlations: Implications for transport simulations in sparse three-dimensional discrete fracture networks following a truncated power law distribution of fracture size: FRACTURE SIZE AND TRANSMISSIVITY CORRELATIONS
journal, August 2016
- Hyman, J. D.; Aldrich, G.; Viswanathan, H.
- Water Resources Research, Vol. 52, Issue 8
Shale gas and non-aqueous fracturing fluids: Opportunities and challenges for supercritical CO2
journal, June 2015
- Middleton, Richard S.; Carey, J. William; Currier, Robert P.
- Applied Energy, Vol. 147
dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport
journal, November 2015
- Hyman, Jeffrey D.; Karra, Satish; Makedonska, Nataliia
- Computers & Geosciences, Vol. 84
Trends, prospects and challenges in quantifying flow and transport through fractured rocks
journal, February 2005
- Neuman, Shlomo P.
- Hydrogeology Journal, Vol. 13, Issue 1
Trace gas emissions on geological faults as indicators of underground nuclear testing
journal, August 1996
- Carrigan, C. R.; Heinle, R. A.; Hudson, G. B.
- Nature, Vol. 382, Issue 6591
Conforming Delaunay Triangulation of Stochastically Generated Three Dimensional Discrete Fracture Networks: A Feature Rejection Algorithm for Meshing Strategy
journal, January 2014
- Hyman, Jeffrey D.; Gable, Carl W.; Painter, Scott L.
- SIAM Journal on Scientific Computing, Vol. 36, Issue 4
Understanding hydraulic fracturing: a multi-scale problem
journal, October 2016
- Hyman, J. D.; Jiménez-Martínez, J.; Viswanathan, H. S.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 374, Issue 2078
Design and Analysis of Computer Experiments
journal, November 1989
- Sacks, Jerome; Welch, William J.; Mitchell, Toby J.
- Statistical Science, Vol. 4, Issue 4
Scaling of fracture systems in geological media
journal, August 2001
- Bonnet, E.; Bour, O.; Odling, N. E.
- Reviews of Geophysics, Vol. 39, Issue 3
Ranking in interconnected multilayer networks reveals versatile nodes
journal, April 2015
- De Domenico, Manlio; Solé-Ribalta, Albert; Omodei, Elisa
- Nature Communications, Vol. 6, Issue 1
Approaching a universal scaling relationship between fracture stiffness and fluid flow
journal, February 2016
- Pyrak-Nolte, Laura J.; Nolte, David D.
- Nature Communications, Vol. 7, Issue 1
Where Does Water Go During Hydraulic Fracturing?: D. O'Malley et al. Groundwater xx, no. x: xx-xx
journal, October 2015
- O'Malley, D.; Karra, S.; Currier, R. P.
- Groundwater, Vol. 54, Issue 4
Modeling flow and transport in fracture networks using graphs
journal, March 2018
- Karra, S.; O'Malley, D.; Hyman, J. D.
- Physical Review E, Vol. 97, Issue 3
Computational Mechanics of Discontinua
book, January 2011
- Munjiza, Antonio A.; Knight, Earl E.; Rougier, Esteban
- John Wiley & Sons, Ltd
Figures / Tables found in this record:
Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.