A robust numerical method based on a deep-learning operator for solving the 2D acoustic wave equation

Abstract

The numerical solution of wave equations plays a crucial role in computational geophysics problems, which forms the foundation of inverse problems and directly impact the high-precision imaging results of earth models. However, common numerical methods often lead to signifcant computational and storage requirements. Due to the heavy reliance on forward modeling methods in inversion techniques, particularly full waveform inversion, enhancing the computational efficiency and reducing storage demands of traditional numerical methods becomes a key issue in computational geophysics. In this paper, we present the deep Lax-Wendroff correction method (DeepLWC), a deep learning-based numerical format for solving two#xD; dimensional (2D) hyperbolic wave equations. DeepLWC combines the advantages of the traditional numerical schemes with a deep neural network. We provide a detailed comparison of this method with representative traditional Lax-Wendroff correction (LWC) method. Our numerical results indicate that the DeepLWC signifcantly improves calculation speed (by more than ten times) and reduces storage space by over 10000 times compared to traditional numerical methods. In contrast to the more popular Physics Informed Neural Network (PINN) method, DeepLWC maximizes the advantages of traditional mathematical methods in solving PDEs and employs a new sampling approach, leading to improved accuracy and faster computations. It is particularly worth pointing that, DeepLWC introduces a novel research paradigm for numerical equation-solving, which can be combined with various traditional numerical methods, enabling acceleration and reduction in storage requirements of conventional approaches.