Boundary integrated neural networks and code for acoustic radiation and scattering

• Published in: International journal of mechanical system dynamics Vol. 4; no. 2; pp. 131 - 141
• Main Authors: Qu, Wenzhen, Gu, Yan, Zhao, Shengdong, Wang, Fajie, Lin, Ji
• Format: Journal Article
• Language: English
• Published: Nanjing John Wiley & Sons, Inc 01.06.2024
• Subjects: acoustic; Acoustics; Boundary conditions; boundary integral equations; Boundary integral method; boundary integral neural networks; Collocation; Integral equations; Integrals; Machine learning; Neural networks; Numerical analysis; Partial differential equations; physics‐informed neural networks; Radiation; Scattering; semianalytical; Sound fields; Sound waves; unbounded domain; Wave equations
• ISSN: 2767-1399; 2767-1402
• DOI: 10.1002/msd2.12109

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. First, 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. Second, the loss function of the BINNs is not a composite form and has a fast convergence. Third, the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons. Finally, the semianalytic characteristic of the BIEs contributes to the higher precision of the BINNs. Numerical examples are presented to demonstrate the performance of the proposed method, and a MATLAB code implementation is provided as supplementary material.