Physics-informed neural operator for parametric phase-field modelling of interfacial degradation and microstructural evolution

Predicting interfacial degradation and microstructural evolution through phase-field modelling is computationally intensive, particularly for parametric studies. While neural operators such as the Fourier neural operator (FNO) offer a promising route to acceleration, the absence of physical constraints compromises their generalisation and long-term stability. Here, we present PF-PINO, a physics-informed neural operator framework that embeds phase-field governing equation residuals directly into the training loss, together with gradient normalisation loss balancing and a staggered training scheme for coupled multi-field systems. PF-PINO is validated on four benchmarks including pencil-electrode corrosion, electro-polishing corrosion, dendritic solidification, and spinodal decomposition, collectively probing parametric generalisation across orders-of-magnitude kinetic regimes, non-periodic boundaries with stochastic morphologies, coupled multi-field dynamics with out-of-distribution extrapolation, and long-term autoregressive stability under complex pattern formation. Across all benchmarks, PF-PINO reduces relative L2 errors by up to an order of magnitude over FNO and achieves sub-mesh-size interface accuracy, establishing a data-efficient surrogate for high-throughput parametric phase-field assessment in computational materials science and engineering applications.