Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
169 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Prediction of Effective Elastic Moduli of Rocks using Graph Neural Networks (2310.19274v3)

Published 30 Oct 2023 in cs.LG, physics.comp-ph, and physics.geo-ph

Abstract: This study presents a Graph Neural Networks (GNNs)-based approach for predicting the effective elastic moduli of rocks from their digital CT-scan images. We use the Mapper algorithm to transform 3D digital rock images into graph datasets, encapsulating essential geometrical information. These graphs, after training, prove effective in predicting elastic moduli. Our GNN model shows robust predictive capabilities across various graph sizes derived from various subcube dimensions. Not only does it perform well on the test dataset, but it also maintains high prediction accuracy for unseen rocks and unexplored subcube sizes. Comparative analysis with Convolutional Neural Networks (CNNs) reveals the superior performance of GNNs in predicting unseen rock properties. Moreover, the graph representation of microstructures significantly reduces GPU memory requirements (compared to the grid representation for CNNs), enabling greater flexibility in the batch size selection. This work demonstrates the potential of GNN models in enhancing the prediction accuracy of rock properties and boosting the efficiency of digital rock analysis.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (62)
  1. Computation of effective elastic moduli of rocks using hierarchical homogenization. Journal of the Mechanics and Physics of Solids 174, 105268.
  2. Homogenizing elastic properties of large digital rock images by combining CNN with hierarchical homogenization method. arXiv preprint arXiv:2305.06519 .
  3. Understanding of a convolutional neural network, in: 2017 International Conference on Engineering and Technology (ICET), IEEE. pp. 1–6.
  4. Pore-GNN: A graph neural network-based framework for predicting flow properties of porous media from micro-CT images. Advances in Geo-Energy Research 10, 39–55.
  5. Digital rock physics benchmarks—part I: Imaging and segmentation. Computers & Geosciences 50, 25–32.
  6. Digital rock physics benchmarks—part II: Computing effective properties. Computers & Geosciences 50, 33–43.
  7. Long-wavelength propagation in composite elastic media i. spherical inclusions. The Journal of the Acoustical Society of America 68, 1809–1819.
  8. Mixture theories for rock properties. Rock physics and phase relations: A handbook of physical constants 3, 205–228.
  9. Pore-scale imaging and modelling. Advances in Water resources 51, 197–216.
  10. Some unique properties of eigenvector centrality. Social networks 29, 555–564.
  11. Geometric deep learning: going beyond Euclidean data. IEEE Signal Processing Magazine 34, 18–42.
  12. Stick slip, stable sliding, and earthquakes—effect of rock type, pressure, strain rate, and stiffness. Journal of Geophysical Research 73, 6031–6037.
  13. An introduction to topological data analysis: fundamental and practical aspects for data scientists. Frontiers in artificial intelligence 4, 667963.
  14. Neural message passing for quantum chemistry, in: International conference on machine learning, PMLR. pp. 1263–1272.
  15. Laboratory measurements of porosity, permeability, resistivity, and velocity on Fontainebleau sandstones. Geophysics 75, E191–E204.
  16. Variable importance assessment in regression: linear regression versus random forest. The American Statistician 63, 308–319.
  17. Evaluating variability with atomistic simulations: the effect of potential and calculation methodology on the modeling of lattice and elastic constants. Modelling and Simulation in Materials Science and Engineering 26, 055003.
  18. Graph representation learning. Synthesis Lectures on Artifical Intelligence and Machine Learning 14, 1–159.
  19. Effects of porosity and clay content on wave velocities in sandstones. Geophysics 51, 2093–2107.
  20. A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids 11, 127–140.
  21. Control batch size and learning rate to generalize well: Theoretical and empirical evidence. Advances in Neural Information Processing Systems 32.
  22. The elastic behaviour of a crystalline aggregate. Proceedings of the Physical Society. Section A 65, 349.
  23. A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids 13, 213–222.
  24. Rapid estimation of permeability from digital rock using 3D convolutional neural network. Computational Geosciences 24, 1523–1539.
  25. The effect of batch size on the generalizability of the convolutional neural networks on a histopathology dataset. ICT express 6, 312–315.
  26. Stochastic geomodeling of karst morphology by dynamic graph dissolution. Mathematical Geosciences , 1–25.
  27. Point-cloud deep learning of porous media for permeability prediction. Physics of Fluids 33, 097109.
  28. Deep learning without poor local minima. Advances in neural information processing systems 29.
  29. Computational rock physics: Transport properties in porous media and applications. PhD dissertation, Stanford University.
  30. Deeper inside pagerank. Internet Mathematics 1, 335–380.
  31. Introduction to micromechanics and nanomechanics. World Scientific Publishing Company.
  32. tmap: an integrative framework based on topological data analysis for population-scale microbiome stratification and association studies. Genome biology 20, 1–19.
  33. Hierarchical homogenization with deep-learning-based surrogate model for rapid estimation of effective permeability from digital rocks. Journal of Geophysical Research: Solid Earth 128, e2022JB025378.
  34. Prediction of compressive strength and elastic modulus of carbonate rocks. Measurement 88, 202–213.
  35. Revisiting small batch training for deep neural networks. arXiv preprint arXiv:1804.07612 .
  36. Math2Market GmbH, 2023. GeoDict Simulation Software Release 2023. https://doi.org/10.30423/release.geodict2023.
  37. The rock physics handbook. Cambridge university press.
  38. Compliance of elastic bodies in contact. Journal of Applied Mechanics 16.
  39. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta metallurgica 21, 571–574.
  40. Micromechanics of defects in solids. Springer Science & Business Media.
  41. Building informative priors for the subsurface with generative adversarial networks and graphs. PhD Dissertation, Stanford University.
  42. Deep neural networks are easily fooled: High confidence predictions for unrecognizable images, in: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 427–436.
  43. Effective-medium theories for two-phase dielectric media. Journal of Applied Physics 57, 1990–1996.
  44. PointNet: Deep learning on point sets for 3d classification and segmentation, in: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 652–660.
  45. Berechnung der fließgrenze von mischkristallen auf grund der plastizitätsbedingung für einkristalle. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 9, 49–58.
  46. Numerical tests of nucleation theories for the Ising models. Physical Review E 82, 011603.
  47. Characterization of pore and grain size distributions in porous geological samples–an image processing workflow. Computers & Geosciences 156, 104895.
  48. Rock compressibility from microcomputed tomography images: Controls on digital rock simulations. Geophysics 84, WA127–WA139.
  49. The graph neural network model. IEEE transactions on neural networks 20, 61–80.
  50. Topological methods for the analysis of high dimensional data sets and 3d object recognition. PBG@ Eurographics 2, 091–100.
  51. Don’t decay the learning rate, increase the batch size. arXiv preprint arXiv:1711.00489 .
  52. Mechanical properties of shale-gas reservoir rocks—part 1: Static and dynamic elastic properties and anisotropy. Geophysics 78, D381–D392.
  53. Depth-first search and linear graph algorithms. SIAM journal on computing 1, 146–160.
  54. A deep learning perspective on predicting permeability in porous media from network modeling to direct simulation. Computational Geosciences 24, 1541–1556.
  55. Deep learning for computer vision: A brief review. Computational intelligence and neuroscience 2018.
  56. Predicting effective diffusivity of porous media from images by deep learning. Scientific reports 9, 20387.
  57. Seeing permeability from images: fast prediction with convolutional neural networks. Science bulletin 63, 1215–1222.
  58. A comprehensive survey on graph neural networks. IEEE transactions on neural networks and learning systems 32, 4–24.
  59. How powerful are graph neural networks? arXiv preprint arXiv:1810.00826 .
  60. Effect of spatial variability of the elastic modulus in composite ground on the structural performance of large-diameter tunnels, in: IOP Conference Series: Earth and Environmental Science, IOP Publishing. p. 072010.
  61. An end-to-end deep learning architecture for graph classification, in: Proceedings of the AAAI conference on artificial intelligence.
  62. Graph convolutional networks: a comprehensive review. Computational Social Networks 6, 1–23.
Citations (5)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now