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.

A variety of numerical methods have sprung up later, including SIMP (Bendse, 1989; Zhou and Rozvany, 1991; Rozvany et al., 1992), evolutionary approaches(Xie and Steven, 1993), level-set method (Wang et al., 2003; Allaire et al., 2004), moving morphable components (Guo et al., 2014), and others. However, the computational cost is still one of the main hinders to widely introduce them into design practices, in particular for large structures (Sigmund and Maute, 2013). Withthe recent boost of machine learning algorithms andadvances in graphics processing units (GPU), machine learning (ML), especially the deep learning, which has been seen to make many successful stories in various fields, including automatic drive, image recognition, naturallanguage processing, and even art, may shed light on accelerating the adoption of topology optimization inmore design practices. Recently, a few attempts have been seen to apply ML on topology optimizations (Leiet al., 2018; Sosnovik and Oseledets, 2017; Banga et al., 2018; Yu et al., 2018). Theoretically, theoptimal layout of the material is a complicated function of the initial conditions based on the optimization objectiveand constraints. The neural network can implement approximating nonlinear functions by arbitrary accuracyas its depth increases. This characteristic makes it possible for the neural network to learn a target function which can directly give us the optimal structure without any iteration and effectively reduce computational time. Sosnovik and Oseledets (2017) first introduced the deep learning model to topology optimization and improved theefficiency of the optimization process by stating the problem as an image segmentation task.