Synthesizing realistic sand assemblies with denoising diffusion in latent space

• Published in: International journal for numerical and analytical methods in geomechanics 2024-11, Vol.48 (16), p.3933-3956
• Main Authors: Vlassis, Nikolaos N., Sun, WaiChing, Alshibli, Khalid A., Regueiro, Richard A.
• Format: Article
• Language: English
• Subjects: Algorithms; Assemblies; Availability; Computed tomography; denoising diffusion; Diffusion; fine‐tuning material properties; Geotechnical engineering; Grains; inverse design; latent space; Morphology; Noise reduction; Petroleum engineering; Probabilistic models; Qualitative analysis; Sand; sand grain generation; Simulators; Solar energy; Solar power; Static equilibrium; Three dimensional models; Tomography
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.3818

The shapes and morphological features of grains in sand assemblies have far‐reaching implications in many engineering applications, such as geotechnical engineering, computer animations, petroleum engineering, and concentrated solar power. Yet, our understanding of the influence of grain geometries on macroscopic response is often only qualitative, due to the limited availability of high‐quality 3D grain geometry data. In this paper, we introduce a denoising diffusion algorithm that uses a set of point clouds collected from the surface of individual sand grains to generate grains in the latent space. By employing a point cloud autoencoder, the three‐dimensional point cloud structures of sand grains are first encoded into a lower‐dimensional latent space. A generative denoising diffusion probabilistic model is trained to produce synthetic sand that maximizes the log‐likelihood of the generated samples belonging to the original data distribution measured by a Kullback‐Leibler divergence. Numerical experiments suggest that the proposed method is capable of generating realistic grains with morphology, shapes and sizes consistent with the training data inferred from an F50 sand database. We then use a rigid contact dynamic simulator to pour the synthetic sand in a confined volume to form granular assemblies in a static equilibrium state with targeted distribution properties. To ensure third‐party validation, 50,000 synthetic sand grains and the 1542 real synchrotron microcomputed tomography (SMT) scans of the F50 sand, as well as the granular assemblies composed of synthetic sand grains are made available in an open‐source repository.