Powder crystallography is the experimental science of determining the structure of molecules provided in crystalline-powder form, by analyzing their x-ray diffraction (XRD) patterns. Since many materials are readily available as crystalline powder, powder crystallography is of growing usefulness to many fields. However, powder crystallography does not have an analytically known solution, and therefore the structural inference typically involves a laborious process of iterative design, structural refinement, and domain knowledge of skilled experts. A key obstacle to fully automating the inference process computationally has been formulating the problem in an end-to-end quantitative form that is suitable for machine learning, while capturing the ambiguities around molecule orientation, symmetries, and reconstruction resolution. Here we present an ML approach for structure determination from powder diffraction data. It works by estimating the electron density in a unit cell using a variational coordinate-based deep neural network. We demonstrate the approach on computed powder x-ray diffraction (PXRD), along with partial chemical composition information, as input. When evaluated on theoretically simulated data for the cubic and trigonal crystal systems, the system achieves up to 93.4% average similarity (as measured by structural similarity index) with the ground truth on unseen materials, both with known and partially-known chemical composition information, showing great promise for successful structure solution even from degraded and incomplete input data. The approach does not presuppose a crystalline structure and the approach are readily extended to other situations such as nanomaterials and textured samples, paving the way to reconstruction of yet unresolved nanostructures.

粉末晶体学是通过分析 X 射线衍射 (XRD) 图案来确定结晶粉末形式的分子结构的实验科学。由于许多材料很容易以结晶粉末的形式获得，因此粉末晶体学在许多领域的用途越来越广泛。然而，粉末晶体学没有已知的分析解决方案，因此结构推断通常涉及迭代设计、结构细化和熟练专家的领域知识的费力过程。在计算上完全自动化推理过程的一个关键障碍是以适合机器学习的端到端定量形式来表述问题，同时捕获分子方向、对称性和重建分辨率的模糊性。在这里，我们提出了一种根据粉末衍射数据确定结构的机器学习方法。它的工作原理是使用基于变分坐标的深度神经网络来估计晶胞中的电子密度。我们演示了计算粉末 X 射线衍射 (PXRD) 的方法以及部分化学成分信息作为输入。当对立方和三角晶体系统的理论模拟数据进行评估时，该系统与未知材料的真实情况（具有已知和部分已知的化学成分信息）的平均相似性高达 93.4%（通过结构相似性指数测量），即使输入数据退化和不完整，也显示出成功结构解决方案的巨大前景。 该方法不预设晶体结构，并且该方法很容易扩展到其他情况，例如纳米材料和纹理样品，为重建尚未解决的纳米结构铺平了道路。