Boundary integrated neural networks (BINNs) for acoustic radiation and scattering

Abstract: 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.