Physics-informed neural operator for predictive parametric phase-field modelling

TL;DR

This paper introduces PF-PINO, a physics-informed neural operator that efficiently predicts complex phase-field evolutions by embedding physical laws into the learning process, outperforming traditional neural operators in accuracy and stability.

Contribution

The paper develops a novel physics-informed neural operator framework for phase-field PDEs, enhancing accuracy and generalisation over existing neural operators like FNO.

Findings

PF-PINO outperforms FNO in accuracy and stability

Enforces physical constraints during training effectively

Demonstrates robustness across multiple phase-field problems

Abstract

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural operator (FNO) show promise in accelerating the solution of parametric partial differential equations (PDEs), the lack of explicit physical constraints, may limit generalisation and long-term accuracy for complex phase-field dynamics. Here, we develop a physics-informed neural operator framework to learn parametric phase-field PDEs, namely PF-PINO. By embedding the residuals of phase-field governing equations into the data-fidelity loss function, our framework effectively enforces physical constraints during training. We validate PF-PINO against benchmark phase-field problems, including electrochemical corrosion, dendritic crystal solidification, and spinodal decomposition. Our results demonstrate that PF-PINO significantly outperforms conventional FNO in accuracy, generalisation capability, and long-term stability. This work provides a robust and efficient computational tool for phase-field modelling and highlights the potential of physics-informed neural operators to advance scientific machine learning for complex interfacial evolution problems.