Antiferroelectric phase-field simulations via scale-invariant physics-informed neural operators

Abstract

Optimizing antiferroelectric (AFE) energy-storage microstructures via phase-field modeling is computationally prohibitive due to immense spatial and temporal constraints. First, accurately capturing the highly frustrated commensurate and incommensurate AFE phases requires exceptionally fine spatial resolutions to resolve sharp, high-frequency antiparallel dipole gradients. Second, simulating path-dependent double hysteresis loops requires quasi-static loading, where time-dependent evolution equations must be rigorously integrated at every electric-field increment until the macroscopic polarization reaches thermodynamic equilibrium. Together, these requirements render high-throughput simulations of polycrystalline structures practically unfeasible. To overcome this, we introduce a physics-informed multigrid neural operator (PI-MgNO) as a highly scalable, autoregressive surrogate model. Constrained by the physical Landau free energy, PI-MgNO accurately tracks AFE-to-FE domain evolution without catastrophic integration drift. This physical regularization imparts a distinct thermodynamic error-healing mechanism, bounding spatial phase-shift errors during coercive switching and rapidly forcing the system into stable energy minima. Rigorous evaluations demonstrate exceptional scale-invariance, effectively bypassing the quasi–static relaxation bottleneck and reducing simulation times from hours to seconds while maintaining R2 > 0.96.