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

arXiv: https://arxiv.org/abs/2502.11942 · HTML: https://mlsanity.com/paper/2502.11942/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 60 references that are in the map.
- First posted on arXiv 17 Feb 2025.

## Builds on (most cited first, 16 of 16)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks](https://mlsanity.com/paper/2007.04542/) (2020)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Physics informed deep learning for computational elastodynamics without labeled data](https://mlsanity.com/paper/2006.08472/) (2020)
- [Tackling the Curse of Dimensionality with Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.12306/) (2023)
- [Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective](https://mlsanity.com/paper/2502.00604/) (2025)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [A phase field formulation for dissolution-driven stress corrosion cracking](https://mlsanity.com/paper/2011.12068/) (2020)
- [A generalised, multi-phase-field theory for dissolution-driven stress corrosion cracking and hydrogen embrittlement](https://mlsanity.com/paper/2205.12096/) (2022)

## Built on by (most cited first, 4 of 4)

- [Enforcing hidden physics in physics-informed neural networks](https://mlsanity.com/paper/2511.14348/) (2025)
- [Physics-informed neural operator for parametric phase-field modelling of interfacial degradation and microstructural evolution](https://mlsanity.com/paper/2603.09693/) (2026)
- [On the training of physics-informed neural operators for solving parametric partial differential equations](https://mlsanity.com/paper/2606.06164/) (2026)
- [Tackling multiphysics problems via finite element-guided physics-informed operator learning](https://mlsanity.com/paper/2603.01420/) (2026)

## Abstract (arXiv)

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.