A joint voxel flow-phase field framework for ultra-long microstructure evolution prediction with physical regularization

Phase-field (PF) modeling is a powerful tool for simulating microstructure evolution. To accelerate the simulation of PF models governed by complex PDEs, machine learning methods such as PINNs and ConvLSTM have been introduced. However, current machine-learning-based approaches still suffer from limited flexibility, poor generalization, and short prediction horizons. To address these challenges, we present a joint framework that couples a voxel-flow network (VFN) with PF simulations in an alternating manner for long-horizon prediction of microstructure evolution with substantial computational acceleration. The VFN iteratively predicts future evolution by generating the next snapshot from the previous two snapshots. Periodic PF simulations suppress nonphysical artifacts, reduce accumulated error, and extend the reliable prediction horizon. The VFN was validated using a grain-growth example, and its accuracy outperforms that of similar prediction methods while preserving topological grain details. For an ultra-long grain-growth prediction of 82 frames from 2 input frames, the grain number decreases from 600 to 29 while the NMSE of the average grain area remains 1.64%. The framework also exhibits good generalizability across different PF models. Overall, this joint framework enables rapid, flexible, generalizable, and physically consistent microstructure forecasting from image-based data over ultra-long time scales.