arXiv：cs.LG· Dawid Lipinski, Jixiang Qing, Henry Moss·· 3 小时前
基于各向异性功率图图的 C4 等变流匹配用于微观结构生成
$C_4$-Equivariant Flow Matching on Anisotropic Power-Diagram Graphs for Microstructure Generation
AI 导读
研究者提出一种基于流匹配与图神经网络的生成模型，将多晶微观结构表示为各向异性功率图，学习紧凑的几何参数化，并可在任意像素分辨率下渲染生成样本。该模型采用 C4 等变架构，使输入噪声的旋转对应生成微观结构的旋转；同时支持基于用户自定义目标函数的免训练引导，生成了类似铜焊缝、铸金属板、3D 打印不锈钢和异质层状钛的微观结构。
正文
Abstract: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.
| Comments: | Accepted at the NeurIPS 2026 workshops on Representations for the Physical Sciences and Geometric Distributional Deep Learning. 12 pages, 2 figures, 1 table |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.11549 [cs.LG] |
| (or arXiv:2610.11549v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.11549 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Dawid Lipinski [view email]
[v1]
Thu, 8 Oct 2026 09:14:39 UTC (1,545 KB)
来源：arXiv：cs.LG · arxiv.org