Microstructure reconstruction of 2D/3D random materials via diffusion-based deep generative models

Abstract

Microstructure reconstruction serves as a crucial foundation for establishing process-structure-property (PSP) relationship in material design. Confronting the limitations of variational autoencoder and generative adversarial network within generative models, this study adopted the denoising diffusion probabilistic model (DDPM) to learn the probability distribution of high-dimensional raw data and successfully reconstructed the microstructures of various composite materials, such as inclusion materials, spinodal decomposition materials, chessboard materials, fractal noise materials, and so on. The quality of generated microstructure was evaluated using quantitative measures like spatial correlation functions and Fourier descriptor. On this basis, this study also achieved the regulation of microstructure randomness and the generation of gradient materials through continuous interpolation in latent space using denoising diffusion implicit model (DDIM). Furthermore, the two-dimensional microstructure reconstruction was extended to three-dimensional framework and integrated permeability as a feature encoding embedding. This enables the conditional generation of three-dimensional microstructures for random porous materials within a defined permeability range. The permeabilities of these generated microstructures were further validated through the application of the lattice Boltzmann method. The above methods provide new ideas and references for material reverse design.

Figure 1

The forward noising process and reverse denoising process in diffusion model.

Figure 2

3D U-Net network architecture in diffusion model.

Figure 3

The training process of conditional diffusion model.

Figure 4

Comparison between generated microstructures based on DDPM and original microstructures;(a–d,i–l) Original microstructures. (e–h,m–p) Generated microstructures.

Figure 5

Comparison of $S_2\left(r\right)$ between generated microstructures and original microstructures; (a) Texture material; (b) Spinodal decomposition. (c) Circular inclusion, (d) Fractal noise.

Figure 6

Comparison of $L\left(r\right)$ between generated microstructures and original microstructures; (a) Texture material. (b) Spinodal decomposition. (c) Circular inclusion. (d) Fractal noise.

Figure 7

Diversified generated microstructures based on DDPM; (a) Circular inclusions. (b) Metamaterials.

Figure 8

The feature distribution of Fourier descriptors for random microstructures; (a) The amplitude of Fourier descriptor. (b) The phase angle of Fourier descriptor.

Figure 9

Randomness control and gradient materials based on DDIM.

Figure 10

Randomness measurement of microstructure based on detail coefficient energy; (a) Comparison of randomness in different microstructures. (b) The evolution process of microstructures and corresponding randomness metric values.

Figure 11

Comparison between original three-dimensional microstructure and reconstructed microstructure of composite materials; (a) Original spherical inclusion. (b) Original ellipsoidal inclusion. (c) Original random porous material. (d) Generated spherical inclusion. (e) Generated ellipsoidal inclusion. (f) Generated random porous material.

Figure 12

Three dimensional random porous materials generated by feature encoding embeddings.

Figure 13

Velocity distribution in generated random porous material; (a) permeability = 0.14; (b) permeability = 0.44; (c) permeability = 0.66; (d) permeability = 1.83; (e) permeability = 4.57; (f) permeability = 10.93.