PINN-Phase: A physics-informed neural network for curvature-driven multiphase-field evolution

Abstract

Phase-field simulation of polycrystalline microstructures becomes costly when many related cases must be evolved over long times. We introduce PINN-Phase, a physics-informed neural time integrator that advances the full multiphase field from its initial condition and enforces phase bounds and unit sum at every step; on the reported explicit multiphase-field benchmarks, post-initial-condition reference states serve only for evaluation. Without case-specific tuning, a single trained 25-grain model meets all predefined criteria in seven of eight unseen microstructures fixed before evaluation and in both stress cases, with 0.94-3.71% terminal grain-label disagreement across the ten cases. Each 12,000-step rollout takes about 5.2 min on a single GPU and reaches nearly three times the temporal horizon represented during training. A pre-registered 64-grain model reaches 6.09% disagreement, retaining all 21 reference survivors plus one additional grain; a post-evaluation continuation with a doubled training horizon and 25 additional epochs reaches 3.97% and the exact survivor set. In three dimensions, one trained 16-grain 96^3 model recovers the exact terminal active set and all three extinction identities in six of six unseen microstructures, five of which meet the complete predefined qualification. These results demonstrate structurally admissible long-horizon prediction and prospective initial-condition transfer within fixed benchmark families.