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. Using large amount of training data, deep learning (DL) can successfully capture VIV patterns and generate accurate predictions. Physics Informed Neural Networks (PINNs), a subfield of DL, introduces physics equations into the loss function to reduce the need for large data. However, PINN loss functions often include multiple loss terms, which may interact with each other, causing imbalanced training speeds of the model and a potentially inferior overall performance. To address this issue, the study proposes an adaptive-weight physics-informed neural network (AW-PINN) algorithm built upon the gradient normalization method (GardNorm) from multi-task learning. AW-PINN regulates the weights of each loss term by computing the gradients norms on the network weights, ensuring the norms of the loss terms match predefined target values. This allows for the balance in the training speed for each loss term and improves both prediction precision and robustness of network model alike. In this study, a VIV dataset of a cylindrical body with different degrees of freedom was used to compare the performance of PINN and three PINN optimization algorithms. The findings suggest that, compared to standard PINN, AW-PINN lowers the mean squared error (MSE) on the test set by 50%, significantly improving prediction accuracy. AW-PINN also demonstrates better stability across different datasets compared to other optimization algorithms, which reveals AW-PINN is a robust and reliable algorithm for solving VIV problems.