Conditional grain-graph diffusion for property-guided inverse design of polycrystalline microstructures
Graph representations compactly encode polycrystalline microstructures while retaining grain topology and grain boundary information. We present a conditional graph diffusion framework for property-guided inverse design of dual-phase Ti-6Al-4V microstructures. An enhanced grain graph neural network (GNN) with grain boundary edge features, learnable node and edge embeddings, and multi-statistic pooling serves as a forward surrogate for stress prediction and candidate evaluation. The conditional diffusion model generates candidates through reverse diffusion under prescribed {\alpha}-phase volume fraction, elastic modulus, and yield-stress proxy targets. Across four target regimes and independently seeded starting sets, generated candidates consistently approach the prescribed properties, including a target outside the property envelope of the existing microstructures. Local crystallographic consistency is evaluated post-generation from deviations from the Burgers orientation relationship (BOR). BOR-aware ranking increases mean BOR consistency by up to 44.9% and 56.4% for the in- and out-of-envelope targets, respectively, while maintaining property alignment. Finite element validation of the five best candidates in each primary design case yields a maximum absolute relative error of 1.0% in their mean properties. In a representative benchmark, diffusion requires 32 candidate evaluations per input graph, compared with approximately 40,000 for random search and evolutionary optimization, and reduces runtime by approximately two orders of magnitude in the tested implementations. These results establish conditional grain-graph diffusion as an efficient framework for property-guided polycrystalline microstructure design.