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.

翻译：本文提出了一种基于有限元法（FEM）与物理信息核函数神经网络（PIKFNNs）的新型混合方法，并将其应用于无界海洋、深海及浅海环境中由结构振动引起的水下声传播预测。在该混合方法中，PIKFNNs是一类改进的浅层物理信息神经网络（PINNs），通过以物理信息核函数（PIKFs）替代PINNs中的激活函数，从而将先验物理信息融入神经网络模型。此外，该神经网络规避了将控制方程嵌入PINNs损失函数的步骤，仅需在边界数据上进行训练。通过采用格林函数作为PIKFs，并以有限元法获取的结构-声耦合响应信息作为边界训练数据，PIKFNNs能够内在地捕获无穷远处的索末菲辐射条件，天然适用于海洋声传播预测。数值实验通过与真实解及有限元结果对比，验证了FEM-PIKFNNs的准确性与可行性。