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

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 deep Convolutional Neural Network for topology optimization with strong generalization ability

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and up-sampling operations. In addition, a popular technique, namely U-Net, was adopted to improve the performance of the proposed neural network. The input of the neural network is a well-designed tensor with each channel includes different information for the problem, and the output is the layout of the optimal structure. To train the neural network, a large dataset is generated by a conventional topology optimization approach, i.e. SIMP. The performance of the proposed method was evaluated by comparing its efficiency and accuracy with SIMP on a series of typical optimization problems. Results show that a significant reduction in computation cost was achieved with little sacrifice on the optimality of design solutions. Furthermore, the proposed method can intelligently solve problems under boundary conditions not being included in the training dataset.