Physics-Informed Neural Networks for Modeling Linear Waves

Paper in proceeding, 2024

Numerical simulation of water waves is of essential importance for ships and offshore structures design. One promising new method is the training of Physics-Informed Neural Networks (PINNs) for these simulations. The current study is an attempt to train a PINN architecture to analyze the velocity potential of the flow beneath periodic linear waves. It is shown that the developed PINN architecture predicts the pattern of velocity potential distribution near the free surface. The average error of the predicted pattern compared to the results of the analytical solution is 4.34%. The standard deviation of the error after 10 times retraining of the model is found to be 2.79%. The velocity field of the flow can be calculated by the spatial derivation of the velocity potential field. Therefore, the developed PINN can predict the velocity field of the flow beneath the given free surface with the same accuracy. A sensitivity study revealed that the average error and the standard deviation of the error in the prediction of the velocity potential field are highly influenced by the number of neurons, layers, and collocation points of the PINN architecture. The increase in the number of neurons and number of layers is found to have different effects on the average error and the standard deviation of the error.