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

TL;DR

Sharp-PINN tackles complex phase-field corrosion by decoupling the strongly coupled Allen–Cahn and Cahn–Hilliard equations through a staggered training scheme, and by enforcing hard concentration constraints via a KKS-based output layer embedded in a Fourier-feature backbone. The method combines a random Fourier feature input, a modified MLP, and physically constrained outputs to stabilize training and improve accuracy. Empirical results across 2D and 3D pit scenarios show substantial efficiency gains over traditional FEM (3D speedups of 5–10x) while maintaining high fidelity to reference solutions, with ablation studies highlighting the critical role of each component. The work suggests broad applicability of staggered PINNs to other multi-physics, multi-scale problems and points toward physics-informed neural operators for parametric, real-time simulations.

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.

Figures (16)

• Figure 1: Schematic of the proposed Sharp-PINNs framework. (a) The staggered training scheme alternates between optimizing the Allen-Cahn (AC) and Cahn-Hilliard (CH) equations, effectively decoupling their optimization processes and mitigating competing gradients. Each training stage incorporates boundary conditions (BC) and initial conditions (IC) and the respective governing equation. (b) The proposed neural network architecture consists of three key components: random Fourier feature ($\mathcal{F}$) for coordinate embedding, a modified MLP ($\mathcal{M}$) as the backbone, and a hard constraint layer ($\mathcal{H}$) that explicitly encodes the concentration field according to the KKS corrosion model.
• Figure 1: Schematic of the modified MLP architecture.
• Figure 2: Cosine similarity between the gradients of the loss terms corresponding to the Allen-Cahn and Cahn-Hilliard equations during (a) standard training scheme and (b) staggered training scheme for the phase field corrosion model.
• Figure 3: Two-dimensional corrosion with two-pits interactions: Geometric setup, initial conditions, and boundary conditions.
• Figure 4: Two-dimensional corrosion with two-pits interactions. Contours of field variable $\phi$ obtained from PINNs ($\hat{\phi}$), FEniCS ($\phi_\text{ref}$), and their absolute error ($|\hat{\phi} - \phi_\text{ref}|$).