基于改进的傅里叶神经算子数值求解频率域声波方程
Numerical Solution of Frequency-Domain Acoustic Wave Equation Based on Improved Fourier Neural Operator
摘要: 在许多应用中，频率域声波方程的数值求解发挥着重要作用，如医学成像和地震勘探。传统的频率域声波方程求解方法，如有限差分法、有限元法等，通常具有参数依赖性，导致计算成本高昂。本文提出了一种结合残差网络(ResNet)和傅里叶神经算子(FNO)的神经网络方法(RFNO)，以快速求解频域声波方程。RFNO可以学习从速度参数函数空间到波场函数空间的映射。因此，当神经网络经过适当训练后，对于不同的速度可以快速高效给出波动方程的近似解。基于简单分层模型和Marmousi模型数据集进行的数值实验，以验证RFNO的有效性。数值结果表明，RFNO在计算效率方面表现出良好的性能。因此，在反问题求解过程中，RFNO是非常具有竞争力的一种正问题求解器。
Abstract: Frequency-domain numerical solutions of acoustic wave equation play an essential role in many applications, such as the medical imaging, and seismic exploriation. Traditional methods for solving the frequency-domain acoustic wave equation, such as the finite-difference method, the finite-element method and so on, usually are parametric dependence, resulting in high computational cost. In this study, we propose a neural network method that combines the residual networks (ResNet) and Fourier neural operators (FNO) to solve the acoustic wave equation in the frequency domain (RFNO). RFNO can learn the mapping from the velocity parametric function space to the wavefield function space. Therefore, it is very efficient to give the approximate solution for different velocities when the neural network is properly trained. Numerical experiments based on the simple layered model and Marmousi model, are presented. The numerical results show that the RFNO has a good performance in solving acoustic wave equation in terms of the computational efficiency. It thus may be a competitive forward problem solver for the inverse problems.
文章引用：潘代英, 何清龙. 基于改进的傅里叶神经算子数值求解频率域声波方程[J]. 运筹与模糊学, 2023, 13(6): 5978-5990. https://doi.org/10.12677/ORF.2023.136594

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