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Quantifying complex microstructures of earth materials: Reconstructing higher-order spatial correlations using deep generative adversarial networks
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  • Hamed Amiri,
  • Ivan Vasconcelos,
  • Yang Jiao,
  • Pei-En Chen,
  • Oliver Plümper
Hamed Amiri
Utrecht University

Corresponding Author:[email protected]

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Ivan Vasconcelos
Utrecth Univeristy
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Yang Jiao
Arizona State University
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Pei-En Chen
Arizona state university
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Oliver Plümper
Utrecht University
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Key to most subsurface processes is to determine how structural and topological features at small length scales, i.e., the microstructure, control the effective and macroscopic properties of earth materials. Recent progress in imaging technology has enabled us to visualise and characterise microstructures at different length scales and dimensions. An approach to characterisation is the sampling of n-point correlation functions - known as statistical microstructural descriptors (SMDs) - from images. SMDs can then be used to generate statistically equivalent structures having larger sizes and additional dimensions – this process is known as $reconstruction$. We show that a deep-convolutional generative adversarial network trained with Wasserstein-loss and gradient penalty (WGAN-GP) results in a stable training and high-quality reconstructions of two-dimensional electron microscopy images of complex rock samples. To evaluate reconstruction performance, n-point polytope functions are calculated in both reconstructed and original microstructures and mean square error between them is used as a quality metric. These n-point polytope functions provide statistical information about symmetric, user-oriented higher-order geometrical patterns in microstructures. Our results show that GANs can naturally capture these higher-order statistics at short and long ranges. Furthermore, we compare our model with a benchmark stochastic reconstruction method based solely on two-point correlation. Our findings indicate that although yielding the same two-point statistics, two microstructures can be morphologically and structurally different, emphasising the need for coupling higher-order correlation functions with reconstruction methods. This is a critical step for future schemes that aim to reconstruct complex heterogeneous systems and couple microstructures to macroscopic phenomena.