aiqbench analysis
This paper proposes a generative model using flow matching and graph neural networks to synthesize realistic polycrystalline microstructures, addressing the high cost of acquiring experimental EBSD data. By integrating $C_4$-equivariant architecture and anisotropic power diagrams, the approach ensures rotational symmetry and allows for training-free guidance based on user-defined objectives to simulate complex material geometries like welds and cast slabs. The method offers a scalable computational alternative for modeling material behavior where physical experimentation is impractical.
$C_4$-Equivariant Flow Matching on Anisotropic Power-Diagram Graphs for Microstructure Generation
arXiv:2610.11549v1 Announce Type: new 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.
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.
Accepted at the NeurIPS 2026 workshops on Representations for the Physical Sciences and Geometric Distributional Deep Learning. 12 pages, 2 figures, 1 table
Machine Learning (cs.LG)
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)
Full text under the publisher's open licence · 180 words
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