Boundary integrated neural networks and code for acoustic radiation and scattering
Wenzhen Qu, Yan Gu, Shengdong Zhao, Fajie Wang, Ji Lin
Boundary integrated neural networks and code for acoustic radiation and scattering
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.
acoustic / semianalytical / physics-informed neural networks / boundary integral equations / boundary integral neural networks / unbounded domain
[1] |
Koo BU. Shape design sensitivity analysis of acoustic problems using a boundary element method. Comput Struct. 1997;65(5):713-719.
CrossRef
Google scholar
|
[2] |
Zheng C, Matsumoto T, Takahashi T, Chen H. A wideband fast multipole boundary element method for three dimensional acoustic shape sensitivity analysis based on direct differentiation method. Eng Anal Bound Elem. 2012;36(3):361-371.
CrossRef
Google scholar
|
[3] |
Chen L, Zheng C, Chen H. A wideband FMBEM for 2D acoustic design sensitivity analysis based on direct differentiation method. Comput Mech. 2013;52:631-648.
CrossRef
Google scholar
|
[4] |
Jordan MI, Mitchell TM. Machine learning: trends, perspectives, and prospects. Science. 2015;349(6245):255-260.
CrossRef
Google scholar
|
[5] |
Ruthotto L, Haber E. Deep neural networks motivated by partial differential equations. J Math Imaging Vision. 2020;62:352-364.
CrossRef
Google scholar
|
[6] |
Zeng S, Zhang Z, Zou Q. Adaptive deep neural networks methods for high-dimensional partial differential equations. J Comput Phys. 2022;463:111232.
CrossRef
Google scholar
|
[7] |
Raissi M, Perdikaris P, Karniadakis GE. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys. 2019;378:686-707.
CrossRef
Google scholar
|
[8] |
Yang L, Meng X, Karniadakis GE. B-PINNs: Bayesian physicsinformed neural networks for forward and inverse PDE problems with noisy data. J Comput Phys. 2021;425:109913.
CrossRef
Google scholar
|
[9] |
Gu Y, Zhang C, Zhang P, Golub MV, Yu B. Enriched physics-informed neural networks for 2D in-plane crack analysis: theory and MATLAB code. Int J Solids Struct. 2023;276:112321.
CrossRef
Google scholar
|
[10] |
Sirignano J, Spiliopoulos K. DGM: a deep learning algorithm for solving partial differential equations. J Comput Phys. 2018;375:1339-1364.
CrossRef
Google scholar
|
[11] |
Saporito YF, Zhang Z. Path-dependent deep Galerkin method: a neural network approach to solve path-dependent partial differential equations. SIAM J Financial Math. 2021;12(3):912-940.
CrossRef
Google scholar
|
[12] |
E W, Yu B. The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems. Commun Math Stat. 2018;6(1):1-12.
CrossRef
Google scholar
|
[13] |
Gu Y, Ng MK. Deep Ritz method for the spectral fractional laplacian equation using the Caffarelli–Silvestre extension. SIAM J Scientific Comput. 2022;44(4):A2018-A2036.
CrossRef
Google scholar
|
[14] |
Song C, Alkhalifah T, Waheed UB. Solving the frequency-domain acoustic VTI wave equation using physics-informed neural networks. Geophys J Int. 2021;225(2):846-859.
CrossRef
Google scholar
|
[15] |
Zhang Y, Zhu X, Gao J. Seismic inversion based on acoustic wave equations using physics-informed neural network. IEEE Trans Geosci Remote Sensing. 2023;61:1-11.
CrossRef
Google scholar
|
[16] |
Lin G, Hu P, Chen F, et al. BINet: learn to solve partial differential equations with boundary integral networks. CSIAM Trans Appl Math. 2023;4:275-305.
CrossRef
Google scholar
|
[17] |
Zhang H, Anitescu C, Bordas S, Rabczuk T, Atroshchenko E. Artificial neural network methods for boundary integral equations. ???TechRxiv Preprint techrxiv20164769v1???. 2022.
|
[18] |
Sun J, Liu Y, Wang Y, Yao Z, Zheng X. BINN: a deep learning approach for computational mechanics problems based on boundary integral equations. Comput Methods Appl Mech Eng. 2023;410:116012.
CrossRef
Google scholar
|
[19] |
Qu W, Zheng C, Zhang Y, Gu Y, Wang F. A wideband fast multipole accelerated singular boundary method for three-dimensional acoustic problems. Comput Struct. 2018;206:82-89.
CrossRef
Google scholar
|
[20] |
Schot SH. Eighty years of Sommerfeld’s radiation condition. Historia Math. 1992;19:385-401.
CrossRef
Google scholar
|
[21] |
Qu W, Chen W, Zheng C. Diagonal form fast multipole singular boundary method applied to the solution of high-frequency acoustic radiation and scattering. Int J Numer Meth Eng. 2017;111:803-815.
CrossRef
Google scholar
|
[22] |
Guiggiani M, Casalini P. Direct computation of Cauchy principal value integrals in advanced boundary elements. Int J Numer Meth Eng. 1987;24(9):1711-1720.
CrossRef
Google scholar
|
[23] |
Zhang Y. Evaluation of singular and nearly singular integrals in the BEM with exact geometrical representation. J Computat Math. 2013;31:355-369.
CrossRef
Google scholar
|
[24] |
Xie G, Zhou F, Li H, Wen X, Meng F. A family of non-conforming crack front elements of quadrilateral and triangular types for 3D crack problems using the boundary element method. Front Mech Eng. 2019;14:332-341.
CrossRef
Google scholar
|
[25] |
Xie G, Zhang D, Meng F, Du W, Zhang J. Calculation of stress intensity factor along the 3D crack front by dual BIE with new crack front elements. Acta Mech. 2017;228:3135-3153.
CrossRef
Google scholar
|
[26] |
Qu W, Chen W, Fu Z. Solutions of 2D and 3D non-homogeneous potential problems by using a boundary element-collocation method. Eng Anal Bound Elem. 2015;60:2-9.
CrossRef
Google scholar
|
[27] |
Qu W, Gu Y, Fan CM. A stable numerical framework for long-time dynamic crack analysis. Int J Solids Struct. 2024;293:112768.
CrossRef
Google scholar
|
/
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