  In this paper, a novel hybrid method based on the finite element method (FEM)
and physics-informed kernel function neural networks (PIKFNNs) is proposed and
applied to the prediction of underwater acoustic propagation induced by
structural vibrations in the unbounded ocean, deep ocean and shallow ocean. In
the hybrid method, PIKFNNs are a class of improved shallow physics-informed
neural networks (PINNs) that replace the activation functions in PINNs with the
physics-informed kernel functions (PIKFs), thereby integrating prior physical
information into the neural network model. Moreover, this neural network
circumvents the step of embedding the governing equations into the loss
function in PINNs, and requires only training on boundary data. By using the
Green's functions as the PIKFs and the structural-acoustic coupling response
information obtained from the FEM as boundary training data, the PIKFNNs can
inherently capture the Sommerfeld radiation condition at infinity, which is
naturally suitable for predicting ocean acoustic propagation. Numerical
experiments demonstrate the accuracy and feasibility of the FEM-PIKFNNs in
comparison with the true solutions and finite element results.
