A-PeARCNN: a Physics-encoded AutoRegressive Convolutional Neural Network with AttentionNet for Solving Partial Differential Equations

Recently, the Physics-encoded Recurrent Convolutional Neural Network (PeRCNN) has garnered significant attention for solving partial differential equations (PDEs) using deep learning methods. It acts as a discrete learning model to force encoding a given physical structure in a recurrent convolutional neural network, which outperforms other methods such as Physics-Informed Neural Network (PINN). However, PeRCNN often struggles to converge when solving PDEs with large time steps. To address this limitation, we propose an enhanced approach, Physics-encoded AutoRegressive Convolutional Neural Network with AttentionNet (A-PeARCNN), which integrates Coordinate Attention and AttentionNet within a spatiotemporal autoregressive architecture, while incorporating historical information through a sliding window. Experimental results show that A-PeARCNN improves solution accuracy by approximately 30% compared to the baseline PeRCNN, demonstrating the effectiveness of the proposed method and extending the capabilities of PeRCNN.