# Polycrystalline Microstructure Generation

The work represents polycrystalline microstructures as anisotropic power diagrams (APDs), learns a flow-matching generative model over their compact geometric parameters with a graph neural network, and introduces a C4-equivariant architecture so that rotations of the input noise produce corresponding rotations of the generated microstructure; a training-free guidance framework then generates morphologies qualitatively inspired by copper welds, cast metal slabs, 3D-printed stainless steel, and heterogeneous lamella titanium without retraining.

The work represents polycrystalline microstructures as anisotropic power diagrams (APDs), learns a flow-matching generative model over their compact geometric parameters with a graph neural network, and introduces a C4-equivariant architecture so that rotations of the input noise produce corresponding rotations of the generated microstructure; a training-free guidance framework then generates morphologies qualitatively inspired by copper welds, cast metal slabs, 3D-printed stainless steel, and heterogeneous lamella titanium without retraining.