Study on pile driving and sound propagation in shallow water using physics-informed neural network

Abstract

A novel, effective, and precise physical-informed neural network (PINN) is presented in this paper to learn and investigate pile driving and sound propagation in shallow water. The validation of the proposed PINN framework is proved by comparing analytical and predicted displacements of the pile and underwater sound pressure radiated from pile driving. The optimization of the PINN algorithms is studied in detail by tuning the hyperparameters. And then, a fast computing PINN framework with good inverse-solving abilities is constructed. A suggestion to help the neural network learn partial differential equations better by adding non-zero boundary conditions is put forward. It is shown that the neural network made up of a small number of neurons, a shallow network with a few layers and the activation of the sine function is reliable and satisfying. The identification of unknown parameters in the PINN framework is carried out and discussed via various tests, and the PINN method accurately predicts the solution of motion of pile driving and approximates the underwater sound pressure in shallow water for a wide range of frequencies and propagation distance. The advantage of the proposed PINN method is that it is a powerful tool to deal with inverse problems and is independent of the frequency and the distance.