发表机构
School of Mathematical Sciences; Lancaster University（数学科学学院; 兰卡斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出结合流匹配与图神经网络的生成模型，以各向异性幂图表示微观结构，采用$C_4$等变架构，可生成多种真实多晶微观结构样本。
AI 中文摘要
通过电子背散射衍射（EBSD）获取真实微观结构数据成本高且耗时，通常依赖专用设备。由于微观结构强烈影响材料性能，生成真实样本对多晶材料行为建模至关重要。我们提出一种生成模型，结合流匹配与图神经网络合成真实多晶微观结构。该模型将微观结构表示为各向异性幂图，学习紧凑几何参数化，可生成任意像素分辨率的样本。$C_4$等变架构直接将旋转对称性融入模型，确保输入噪声旋转时生成的微观结构对应旋转。我们还展示了基于用户定义目标函数，使用无训练引导生成复杂微观结构的方法，具体生成了类似铜焊缝、铸金属板、3D打印不锈钢及异质层状钛的微观结构。
英文摘要
Acquiring realistic microstructure data through Electron Backscatter Diffraction (EBSD) is costly and time consuming, often relying on specialised equipment. As microstructures strongly influence material properties, generating realistic samples is essential for modelling the behaviour of polycrystalline materials. We introduce a generative model for synthesising realistic polycrystalline microstructures using flow matching and graph neural networks. By representing microstructures as anisotropic power diagrams, our model learns a compact geometric parametrisation and can render generated samples at arbitrary pixel resolution. A $C_4$-equivariant architecture incorporates rotational symmetry directly into the model, ensuring that rotations of the input noise produce corresponding rotations of the generated microstructure. We also demonstrate how training-free guidance can be used to generate complex microstructures, based on user defined objective function. In particular, we generate microstructures resembling a copper weld, cast metal slab, 3D-printed stainless steel and heterogeneous lamella titanium.
CommentsAccepted at the NeurIPS 2026 workshops on Representations for the Physical Sciences and Geometric Distributional Deep Learning. 12 pages, 2 figures, 1 table
