This paper presents a novel approach called the boundary integrated neural networks (BINNs) for analyzing acoustic radiation and scattering. The method introduces fundamental solutions of the time-harmonic wave equation to encode the boundary integral equations (BIEs) within the neural networks, replacing the conventional use of the governing equation in physics-informed neural networks (PINNs). This approach offers several advantages. Firstly, the input data for the neural networks in the BINNs only require the coordinates of "boundary" collocation points, making it highly suitable for analyzing acoustic fields in unbounded domains. Secondly, the loss function of the BINNs is not a composite form, and has a fast convergence. Thirdly, the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons. Finally, the semi-analytic characteristic of the BIEs contributes to the higher precision of the BINNs. Numerical examples are presented to demonstrate the performance of the proposed method.

翻译：本文提出了一种新颖方法——边界积分神经网络（BINNs），用于分析声辐射与散射问题。该方法引入时谐波动方程的基本解，将边界积分方程（BIEs）编码至神经网络中，取代了物理信息神经网络（PINNs）中传统控制方程的使用。该途径具有多项优势：首先，BINNs中神经网络的输入数据仅需“边界”配置点的坐标，因此特别适用于无界域中的声场分析；其次，BINNs的损失函数并非复合形式，且收敛速度快；第三，与PINNs相比，BINNs使用更少的配置点及隐藏层/神经元即可达到相当精度；最后，BIEs的半解析特性有助于提高BINNs的精确度。文中通过数值算例展示了所提方法的性能。