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

2026-03-10

AI Summary

This work addresses the high computational cost of phase-field modeling in high-throughput parameter studies and the limited generalization and long-term prediction accuracy of existing neural operators due to the absence of explicit physical constraints. To overcome these challenges, the authors propose PF-PINO, a novel framework that, for the first time, embeds the residual of the phase-field governing equations directly into the data fidelity loss of a neural operator, thereby enforcing explicit physical constraints during training. Built upon the Fourier Neural Operator (FNO) architecture and integrating key ideas from Physics-Informed Neural Networks (PINNs), PF-PINO constructs a parametric solver with strong physical consistency. Benchmark evaluations on electrochemical corrosion, dendritic solidification, and spinodal decomposition demonstrate that PF-PINO significantly outperforms conventional FNO, achieving notable improvements in accuracy, generalization, and long-term stability.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Learning to Search
• Machine Learning: Deep Neural Architectures and Foundation Models

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• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
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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.

Problem

• phase-field modelling
• parametric PDEs
• neural operators
• physics-informed learning
• microstructural evolution

Innovation

• physics-informed neural operator
• phase-field modeling
• parametric PDEs
• Fourier neural operator
• scientific machine learning