弹性波反源问题的神经网络方法
Neural Network Method for the Inverse Source Problem of Elastic Wave
DOI: 10.12677/AAM.2023.122070, PDF,   
作者: 柴媛媛*, 孟品超：长春理工大学数学与统计学院，吉林 长春
关键词: 反源问题；神经网络；点源；弹性波；远场数据；Inverse Source Problem； Neural Network； Point Sources； Elastic Wave； Far-Field Data
摘要: 针对弹性波点源的反演问题，构建基于全连接神经网络的点源位置和强度参数反演模型。以远场数据作为输入，以点源位置和强度参数作为输出，设计全连接神经网络，使用Adam优化算法更新网络的权重和偏置，进而反演点源的位置和强度。数值实验说明该方法对点源位置和强度反演问题是有效的。
Abstract: Aiming at the inverse point sources problem of elastic wave, the location and magnitude parame-ters inversion model is constructed based on fully connected neural network. Take far-field data as input, and take the location and magnitude parameters of point sources as output. We design a fully connected neural network and use Adam optimization algorithm to update the weight and bias of the model. Further, we can reconstruct the location and magnitude of the point sources. Numerical experiments show that this method is effective for inverse problem of location and magnitude of point sources.
文章引用：柴媛媛, 孟品超. 弹性波反源问题的神经网络方法[J]. 应用数学进展, 2023, 12(2): 690-697. https://doi.org/10.12677/AAM.2023.122070

参考文献

[1] Barragan, A., Preston, C., Alvarez, A., et al. (2020) Acoustoelectric Imaging of Deep Dipoles in a Human Head Phantom for Guiding Treatment of Epilepsy. Journal of Neural Engineering, 17, Article ID: 056040. [Google Scholar] [CrossRef] [PubMed]
[2] Xue, Y. and Zhai, Z.J. (2017) Inverse Identification of Multiple Outdoor Pollutant Sources with a Mobile Sensor. Building Simulation, 10, 255-263. [Google Scholar] [CrossRef] 
[3] Bleistein, N. and Cohen, J.K. (1977) Nonuniqueness in the In-verse Source Problem in Acoustics and Electromagnetics. Journal of Mathematical Physics, 18, 194-201. [Google Scholar] [CrossRef] 
[4] Bao, G., Hu, G., Kian, Y., et al. (2018) Inverse Source Problems in Elasto-dynamics. Inverse Problems, 34, Article ID: 045009. [Google Scholar] [CrossRef] 
[5] Ohe, T. (2020) Real-Time Reconstruction of Moving Point/Dipole Wave Sources from Boundary Measurements. Inverse Problems in Science and Engineering, 28, 1057-1102. [Google Scholar] [CrossRef] 
[6] Chen, B., Guo, Y., Ma, F., et al. (2020) Numerical Schemes to Reconstruct Three-Dimensional Time-Dependent Point Sources of Acoustic Waves. Inverse Problems, 36, Article ID: 075009. [Google Scholar] [CrossRef] 
[7] Zhang, D., Guo, Y., Li, J., et al. (2018) Retrieval of Acoustic Sources from Multi-Frequency Phaseless Data. Inverse Problems, 34, Arti-cle ID: 094001. [Google Scholar] [CrossRef] 
[8] Wang, X., Guo, Y. and Bousba, S. (2022) Direct Imaging for the Moment Tensor Point Sources of Elastic Waves. Journal of Computational Physics, 448, Article ID: 110731. [Google Scholar] [CrossRef] 
[9] Yin, W., Yang, W. and Liu, H. (2020) A Neural Network Scheme for Recovering Scattering Obstacles with Limited Phaseless Far-Field Data. Journal of Computational Physics, 417, Article ID: 109594. [Google Scholar] [CrossRef] 
[10] Meng, P., Su, L., Yin, W., et al. (2020) Solving a Kind of Inverse Scattering Problem of Acoustic Waves Based on Linear Sampling Method and Neural Network. Alexandria Engineering Journal, 59, 1451-1462. [Google Scholar] [CrossRef] 
[11] Gao, Y., Liu, H., Wang, X., et al. (2022) On an Artificial Neural Network for Inverse Scattering Problems. Journal of Computational Physics, 448, Article ID: 110771. [Google Scholar] [CrossRef] 
[12] 张平, 孟品超, 尹伟石. 点源反演问题的神经网络方法研究[J]. 长春理工大学学报(自然科学版), 2022, 45(5): 117-122.
[13] 陈柳. 声波反源问题的多频机器学习算法[D]: [硕士学位论文]. 长沙: 湖南师范大学, 2020.
[14] Zhang, P., Meng, P., Yin, W., et al. (2023) A Neural Network Method for Time-Dependent Inverse Source Problem with Limited-Aperture Data. Journal of Computational and Applied Mathematics, 421, Article ID: 114842. [Google Scholar] [CrossRef] 

为你推荐