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.

中文翻译：

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在潜在空间中通过降噪扩散合成真实的沙子组件


砂粒的形状和形态特征在许多工程应用中具有深远的影响，例如岩土工程、计算机动画、石油工程和聚光太阳能。然而，由于高质量 3D 晶粒几何数据的可用性有限，我们对晶粒几何形状对宏观响应的影响的理解通常只是定性的。在本文中，我们介绍了一种去噪扩散算法，该算法使用从单个沙粒表面收集的一组点云来在潜在空间中生成颗粒。通过使用点云自动编码器，沙粒的三维点云结构首先被编码到低维潜在空间中。训练生成式去噪扩散概率模型来生产合成砂，该模型最大化属于由 Kullback-Leibler 散度测量的原始数据分布的生成样本的对数似然。数值实验表明，所提出的方法能够生成形态、形状和尺寸与从 F50 砂数据库推断的训练数据一致的逼真颗粒。然后，我们使用刚性接触动态模拟器将合成砂倒入有限的体积中，以形成具有目标分布特性的静态平衡状态的颗粒组件。为了确保第三方验证，开源存储库中提供了 50,000 个合成砂粒和 1542 个 F50 砂的真实同步加速器微计算机断层扫描 (SMT) 扫描，以及由合成砂粒组成的颗粒组件。