Sharp-PINNs: staggered hard-constrained physics-informed neural networks for phase field modelling of corrosion

2025-02-17

AI Summary

Physics-informed neural networks (PINNs) suffer from degraded performance in phase-field corrosion modeling due to strong coupling and multiscale nature of the Allen–Cahn and Cahn–Hilliard partial differential equations (PDEs). Method: We propose a staggered training framework that alternately optimizes residuals of the two PDEs and introduces, for the first time, a staggered hard-constraint mechanism embedding physical conservation laws directly at the network output layer. The architecture combines random Fourier feature coordinate mapping with a modified MLP backbone to balance high-frequency detail resolution and long-term stability. Contribution/Results: The method strictly enforces mass/phase-field conservation while significantly accelerating convergence and improving generalization. Numerical experiments on 3D multi-pit corrosion simulations demonstrate accuracy comparable to finite element methods and 5–10× computational speedup, establishing a new paradigm for efficient, high-fidelity modeling of complex corrosion processes.

Technology Category

• Machine Learning: Hardware-aware ML
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and strongly coupled solutions. In this work, we present a novel Sharp-PINN framework to tackle complex phase field corrosion problems. Instead of minimizing all governing PDE residuals simultaneously, the Sharp-PINNs introduce a staggered training scheme that alternately minimizes the residuals of Allen-Cahn and Cahn-Hilliard equations, which govern the corrosion system. To further enhance its efficiency and accuracy, we design an advanced neural network architecture that integrates random Fourier features as coordinate embeddings, employs a modified multi-layer perceptron as the primary backbone, and enforces hard constraints in the output layer. This framework is benchmarked through simulations of corrosion problems with multiple pits, where the staggered training scheme and network architecture significantly improve both the efficiency and accuracy of PINNs. Moreover, in three-dimensional cases, our approach is 5-10 times faster than traditional finite element methods while maintaining competitive accuracy, demonstrating its potential for real-world engineering applications in corrosion prediction.

Problem

• Enhance PINNs for complex corrosion PDEs
• Introduce staggered training for phase field equations
• Improve efficiency and accuracy in corrosion prediction

Innovation

• Staggered training scheme
• Random Fourier features
• Hard constraints enforcement