Deep-learning-based porous media microstructure quantitative characterization and reconstruction method

Microstructure characterization and reconstruction (MCR) is one of the most important components of discovering processing-structure-property relations of porous media behavior and inverse porous media design in computational materials science. Since the algorithms for describing and controlling the geometric configuration of microstructures need to solve a large number of variables and involve multiobjective conditions, the existing MCR methods have difficulty in gaining a perfect trade-off among the quantitative generation and characterization capability and the reconstruction quality. In this work, an improved 3D Porous Media Microstructure (3DPmmGAN) generative adversarial network based on deep-learning algorithm is demonstrated for high-quality microstructures generation with high controllability and high prediction accuracy. The proposed 3DPmmGAN allows the model to utilize unlabeled data for complex high-randomness microstructures end-to-end training within an acceptable time consumption. Further analysis shows that the trained network has good adaptivity for microstructures with different random geometric configurations, and can quantitatively control the generated structure according to semantic conditions, and can also quantitatively predict complex microstructure features. The key results suggest the proposed 3DPmmGAN is a powerful tool to accelerate the preparation and the initial characterization of 3D porous media, and potentially maximize the design efficiency for porous media.

Figure 1

The flow chart of the proposed deep-learning-based MCR method. The training process of the model can be described as the problem of the generator and discriminator finding a Nash equilibrium. Training stops when sufficient image quality is obtained, at which point the discriminator may be discarded, and the generator can be controlled to create new samples.

Figure 2

Images during Berea parallel training. We turned off the network input at the last resolution level in the Treatment group, and samples are presented as center-section views.

Figure 3

Constructed independent dataset; sizes of samples in this dataset are all ${96}^3$.

Figure 4

Through (a) to (e) are randomly selected typical samples of the constructed artificial aggregation dataset with a size of ${128}^3$ voxels; 324 spheres with diameters ranging from 6 to 15 voxels are filled in all samples. It is clear that the samples have clear visual characteristics, and retain the randomness and complexity of the microstructure. Samples in this dataset have some known characteristics change trend; we use it to validate the network's ability to distinguish and control the microstructure's characteristics.

Figure 5

Taking the Bead pack sample with a size of ${400}^3$ as an example, based on the down-sampled sample, we enrich the dataset by traversing it in three orthogonal directions to obtain 64 subsamples with overlapping parts at first; then, we implement flipping and rotating operation on each obtained subsample to further increase the number of samples by 10 times. We repeat this for the other 21 samples. Finally, we obtain a Mixing dataset with 14 080 samples with a resolution of ${128}^3$ for network training.

Figure 6

Constructed mixing dataset; sizes of samples in this dataset are all ${128}^3$. The voxel size of each kind of sample has been scaled with different down-sampling operations, and the specific sizes are shown in the figure. The total number of samples in the dataset is 14 080.

Figure 7

Comparison of the influence of the morphology controller and the condition controller on the 3DPmmGAN's generation behavior. Each image represents the center-section view of the respective synthesized 3D sample of (a) Bead pack, (b) Berea, (c) Ketton, (d) Estaillades, (e) Doddington, and (f) Bentheimer. The rows above the dotted lines show the influence of morphology controller with fixed condition inputs $Z$, while the rows below the dotted lines show the influence of condition controller with fixed morphology inputs noises. With reference to (b)–(f), it is clear that with fixed CC conditions, MC is capable of causing enough random effects to the samples with different microstructural configurations, which means the realization of independently control between CC and MC, while (a) shows MC being overwhelmed by CC as the Bead pack sample has a more orderly structure than the rest of samples so that no random effects are added.

Figure 8

Comparisons of microstructures quality between the original samples and the synthesis results: (a) for sample of Berea, (b) for sample of Bead pack.

Figure 9

The validation of the network's ability of separating different change directions with the constructed artificial aggregation dataset. All images are presented in 3D binary voxel model; Otsu method is adopted for binarization processing of the sample images and no smooth filters have been coupled. ${\mathrm{Z}}_{\mathrm{X}}$, ${\mathrm{Z}}_{\mathrm{Y}}$, ${\mathrm{Z}}_{\mathrm{Z}}$ and $Z_V$ denote four semantic FVCs, by linearly interpolating along these FCVs at a step size of 0.25, of figure (a) to (d); $X$, $Y$, $Z$ denote the aggregation degree along three Cartesian coordinate directions, respectively; and $V$ denotes the degree of total volume reduction ratio.

Figure 10

The morphological change diagram of the microstructure after applied three kinds of semantic conditions, respectively. All images are presented in 3D binary voxel model, Otsu method is adopted for binarization processing of the sample images, and no smooth filters have been coupled. ${\mathrm{Noise}}_1$, ${\mathrm{Noise}}_2$, and ${\mathrm{Noise}}_3$ represent three different sets of noise inputs, $Z_{\alpha }$, $Z_{\beta }$, and $Z_{\gamma }$ denote three semantic FVCs; $V$, $S$, $B$, $X$ are four Minkowski metrics to characterize the generated samples’ morphological information. We record the measured values of the generated images at each stage on the radar chart as that shown in the last column.