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 1,542 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.

翻译：砂粒集合中颗粒的形状与形态特征在岩土工程、计算机动画、石油工程及聚光太阳能等众多工程应用中具有深远影响。然而，由于高质量三维颗粒几何数据的匮乏，目前对颗粒几何形状如何影响宏观响应的理解往往停留在定性层面。本文提出一种去噪扩散算法，该算法利用从单个砂粒表面采集的点云集合，在潜空间中生成砂粒。通过采用点云自编码器，砂粒的三维点云结构首先被编码到低维潜空间中。随后训练一个生成式去噪扩散概率模型，以生成合成砂粒，该模型通过Kullback-Leibler散度测量生成样本属于原始数据分布的对数似然最大性。数值实验表明，所提方法能够生成形态、形状和尺寸均与基于F50砂数据库推断的训练数据一致的逼真砂粒。我们进一步利用刚性接触动力学模拟器将合成砂粒倒入受限体积中，形成具有目标分布特性的静态平衡颗粒集合。为便于第三方验证，50000颗合成砂粒、1542个F50砂的同步辐射显微计算机断层扫描（SMT）原始数据，以及由合成砂粒构成的颗粒集合，均已开源发布。