Surrogate Models for Stochastic Al–Cu Phase-Field Solidification

Phase-field models resolve microstructural evolution during rapid alloy solidification, but their computational cost limits long trajectories, stochastic ensembles, and studies across process conditions. We present a variance-preserving denoising diffusion bridge model (VP-DDBM) for state-conditioned prediction of two-dimensional Al--Cu solidification. Given the current phase, concentration, and prescribed temperature fields, the model predicts the subsequent state and is applied autoregressively. Across two held-out thermal gradients, VP-DDBM produces lower long-horizon errors than deterministic U-Net and SI-ConvNeXt baselines in domain-mean phase, domain-mean Cu concentration, and leading-tip position. It also retains fine dendritic structure over long rollouts, whereas the deterministic U-Net progressively smooths the morphology. VP-DDBM predicts the phase and concentration evolution approximately (73\times) faster than the phase-field solver, showing potential for faster process-condition screening and ensemble-based microstructure studies.