Multi-level physics-informed neural networks (ML-PINN): A framework for long-term atmospheric corrosion prediction

Long-term atmospheric corrosion prediction in low-alloy steels is essential for infrastructure durability, but it is challenged by data scarcity and complex physicochemical interactions. Although machine learning models offer strong nonlinear approximation capability, purely data-driven approaches often exhibit poor generalization and physical inconsistency when trained on limited data. To address these issues, a Multi-Level Physics-Informed Neural Network (ML-PINN) is proposed. The framework employs a dual-branch architecture to decouple environmental and compositional features and incorporates hierarchical physical constraints. A kinetic decoding layer enforces power-law corrosion kinetics as a hard constraint, while gradient-based regularization introduces electrochemical acceleration priors as soft constraints. Additionally, an adaptive multi-task learning strategy balances the regression of latent kinetic parameters with corrosion rate prediction. The model is validated using a 16-year atmospheric exposure dataset comprising 24 low-alloy steels. ML-PINN achieves state-of-the-art performance, with a testing coefficient of determination (R²) of 0.960 and a 35.73% reduction in root mean square error (RMSE) compared with standard physics-informed neural networks (PINNs). Importantly, the proposed framework eliminates physical inconsistency and yields smooth, monotonic corrosion trajectories consistent with degradation kinetics. Model interpretability analysis using SHapley Additive exPlanations (SHAP) further confirms that the learned feature–parameter relationships are align with established electrochemical mechanisms. These results demonstrate that integrating physical constraints with data-driven learning provides a robust and generalizable approach for long-term atmospheric corrosion prediction, particularly in data-sparse regimes.