An Adaptive Weight Physics-Informed Neural Network for Vortex-Induced Vibration Problems

Vortex-induced vibration (VIV) is a common fluid–structure interaction phenomenon in practical engineering with significant research value. Traditional methods to solve VIV issues include experimental studies and numerical simulations. However, experimental studies are costly and time-consuming, while numerical simulations are constrained by low Reynolds numbers and simplified models. Deep learning (DL) can successfully capture VIV patterns and generate accurate predictions by using a large amount of training data. The Physics-Informed Neural Network (PINN), a subfield of DL, introduces physics equations into the loss function to reduce the need for large data. Nevertheless, PINN loss functions often include multiple loss terms, which may interact with each other, causing imbalanced training speeds and a potentially inferior overall performance. To address this issue, this study proposes an Adaptive Weight Physics-Informed Neural Network (AW-PINN) algorithm built upon a gradient normalization method (GradNorm) from multi-task learning. The AW-PINN regulates the weights of each loss term by computing the gradient norms on the network weights, ensuring the norms of the loss terms match predefined target values. This ensures balanced training speeds for each loss term and improves both the prediction precision and robustness of the network model. In this study, a VIV dataset of a cylindrical body with different degrees of freedom is used to compare the performance of the PINN and three PINN optimization algorithms. The findings suggest that, compared to a standard PINN, the AW-PINN lowers the mean squared error (MSE) on the test set by 50%, significantly improving the prediction accuracy. The AW-PINN also demonstrates an enhanced stability across different datasets, confirming its robustness and reliability for VIV modeling. Compared with existing methods in the literature, the AW-PINN achieves a comparable lift prediction accuracy using merely 1% of the training data, while simultaneously improving the prediction accuracy of the peak lift.