FEM-PIKFNN for underwater acoustic propagation induced by structural vibrations in different ocean environments

In this paper, a novel hybrid method based on the finite element method (FEM) and physics-informed kernel function neural network (PIKFNN) is proposed. The method is applied to predict underwater acoustic propagation induced by structural vibrations in diverse ocean environments, including the unbounded ocean, deep ocean, and shallow ocean. In the hybrid method, PIKFNN is regarded as an improved shallow physics-informed neural network (PINN) in which the activation function in the PINN is replaced with a physics-informed kernel function (PIKF). This ensures the integration of prior physical information into the neural network model. Moreover, PIKFNN circumvents embedding the governing equations into the loss function in the PINN and requires only training on boundary data. By using Green's function as PIKF and the structural-acoustic coupling response information obtained from the FEM as training data, PIKFNN can inherently capture the Sommerfeld radiation condition at infinity, which are naturally suitable for predicting ocean acoustic propagation. Numerical experiments demonstrate the accuracy and feasibility of FEM-PIKFNN in comparison with analytical solutions and finite element results.