Physics-informed neural networks for efficient aeroacoustic computational based on two time sequence prediction models

Physics-informed neural networks (PINNs) have been proven powerful for solving partial differential equations (PDEs). However, conventional PINNs fail handling time/space variables in the training data distinctly and overlook the temporal relationships among data points, which is critical for accurately modeling dynamic systems. To address this issue, this work proposes two novel PINN models based on the transformer and the convolutional long short-term memory (ConvLSTM) architectures, respectively. An encoder-decoder neural network structure is adopted to enhance handling of time-space variables and a high-order finite-difference method is used to compute partial derivatives. These computations are implemented using the convolution within the PyTorch framework that incorporates both physical and mathematical information into the neural networks. The efficacy of the proposed methods has been evaluated for the wave equation and the Reynolds-Averaged Navier-Stokes equations. Results suggest that the transformer-based PINN outperforms both the conventional and ConvLSTM-based PINN in terms of accuracy, efficiency and generalizability.