用分步训练提升腐蚀模拟精度，速度比有限元快5-10倍
Sharp-PINNs: staggered hard-constrained physics-informed neural networks for phase field modelling of corrosion
- 分步优化相场方程，交替最小化Allen-Cahn与Cahn-Hilliard残差
- 三维场景下计算速度比传统有限元方法快5-10倍，精度相当
- 融合随机傅里叶特征与硬约束输出，提升模型稳定性和泛化能力
物理信息神经网络在求解各类偏微分方程方面展现出巨大潜力，但在处理具有复杂强耦合解的方程时性能常下降。本文提出一种新型Sharp-PINN框架，用于解决复杂的相场腐蚀问题。不同于同时最小化所有控制方程残差，Sharp-PINNs采用分步训练策略，交替优化描述腐蚀系统的Allen-Cahn和Cahn-Hilliard方程残差。为进一步提升效率与精度，设计了结合随机傅里叶特征坐标嵌入、改进多层感知机主干结构，并在输出层施加硬约束的神经网络架构。通过多坑腐蚀模拟进行基准测试，分步训练与网络结构显著提升了PINNs的效率与准确性。在三维情形下，该方法相较传统有限元方法快5-10倍，且保持相当的精度，展现出在真实工程腐蚀预测中的应用潜力。
原文摘要 · Abstract (English)
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.
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