Acoustic radiation and scattering: a new era with BINNs technology

Acoustic analysis often relies on the boundary element method (BEM) for its semi-analytical nature and boundary-only discretization. Despite its advantages, challenges in solving unbounded domain problems persist, prompting the need for improved computational methods. Deep neural networks (DNNs) have shown promise in function approximation for partial differential equations, yet they struggle with unbounded domains. Due to these challenges, an in-depth study on integrating neural networks with boundary integral equations is necessary.

Researchers from Qingdao University and Hohai University have developed a new method for acoustic field analysis called boundary integrated neural networks (BINNs). Published in the International Journal of Mechanical System Dynamics in June 2024, this study (DOI: 10.1002/msd2.12109) leverages BINNs to encode boundary integral equations into neural networks. This innovation aims to enhance precision and reduce computational costs in acoustic radiation and scattering analysis, offering a promising tool for both bounded and unbounded domains.

The BINNs method integrates boundary integral equations (BIEs) into neural networks, offering a significant improvement over traditional methods like physics-informed neural networks (PINNs). By focusing on boundary collocation points, BINNs reduce computational complexity and resource requirements. This approach features a simplified loss function based on BIE residuals, leading to faster convergence without needing special balancing techniques. Key advantages include being ideal for unbounded domain problems, requiring only boundary point coordinates, achieving faster convergence with fewer computational resources, and maintaining high precision with fewer collocation points and neural network layers. The semi-analytical nature of BIEs further enhances accuracy. Three numerical examples demonstrate BINNs’ effectiveness in various acoustic scenarios, validating its superiority over PINNs in terms of precision and efficiency. This method promises significant advancements in acoustic field analysis, particularly for complex unbounded domains.

Prof. Yan Gu from Qingdao University stated, “The development of BINNs marks a significant advancement in the field of acoustic analysis. By effectively integrating boundary integral equations with neural networks, we can achieve unprecedented accuracy and efficiency in solving complex acoustic problems, particularly in unbounded domains.”

The BINNs method has far-reaching implications for various fields requiring precise acoustic analysis, such as underwater acoustics, noise control, and structural health monitoring. Its ability to handle unbounded domains with high precision and efficiency makes it a valuable tool for engineers and researchers. Future applications may extend to structural-acoustic sensitivity analysis and high-frequency acoustic problems, paving the way for innovations in both academic research and practical implementations.

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References

DOI

10.1002/msd2.12109

Original Source URL

https://doi.org/10.1002/msd2.12109

Funding information

The research presented in this paper received support from the Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2022YQ06 and ZR2021JQ02), the Development Plan of Youth Innovation Team in Colleges and Universities of Shandong Province (Grant No. 2022KJ140), the National Natural Science Foundation of China (Grant No. 12372199), the Key Laboratory of Road Construction Technology and Equipment (Chang’an University, Grant No. 300102253502), and the Water Affairs Technology Project of Nanjing (Grant No. 202203).

About International Journal of Mechanical System Dynamics

International Journal of Mechanical System Dynamics (IJMSD) is an open-access journal that aims to systematically reveal the vital effect of mechanical system dynamics on the whole lifecycle of modern industrial equipment. The mechanical systems may vary in different scales and are integrated with electronic, electrical, optical, thermal, magnetic, acoustic, aero, fluidic systems, etc. The journal welcomes research and review articles on dynamics concerning advanced theory, modeling, computation, analysis, software, design, control, manufacturing, testing, and evaluation of general mechanical systems.