[S-CG50] Driving Solid Earth Science through Machine Learning

[SCG50-03] Physics-driven deep learning method for seismic wave modeling

*Yi Ding¹, Su Chen¹, Xiaojun Li^1,2, Suyang Wang¹ (1.Beijing University of Technology, 2.Institute of Geophysics, China Earthquake Administration)

Keywords:Physics-driven deep learning, Self-adaptive physics-informed neural networks, Seismic wave propagation simulation, Neural tangent kernel

Solving the scattered wavefield is a key scientific problem in seismology and earthquake engineering. Physics-informed neural networks (PINNs) developed in recent years have great potential in possibly increasing the flexibility and efficacy of seismic modeling and inversion. We developed two novel frameworks for modeling seismic waves, e.g., self-adaptive physics-informed neural networks (SA-PINNs) and physics-constrained neural networks (PCNNs). Using SA-PINNs and combining them with sparse initial wavefield data formed by the spectral element method (SEM), we carry out a numerical simulation of wave propagation to realize typical cases such as infinite/semi-infinite domain and arc-shaped canyon/hill topography. For complex scattered wavefield, a sequential learning method with time-domain decomposition was introduced in SA-PINNs to improve the scalability and solution accuracy of the network. In PCNNs, the method of images is incorporated to effectively implement the free stress boundary conditions of the Earth's surface, leading to the propagation of plane and cylindrical waves in a half-space. We analyze the training dynamics of neural networks when solving wave equations from the neural tangent kernel (NTK) perspective. An adaptive training algorithm is introduced to mitigate the unbalanced gradient flow dynamics of the different components of the loss function of PCNNs. The results of numerical experiments demonstrate the accuracy and effectiveness of our approach. We herein demonstrated the ability of SA-PINNs/PCNNs in forward modeling of seismic waves in complex topography in order to lay the foundation for tackling seismic inversion issues. The proposed methods have the following features: (1) These methods can avoid point-source singularities by incorporating sparse initial wavefield data when simulating 2D seismic wave propagation. (2) Compared to PINNs method, SA-PINNs can obtain self-adaptation weights for each collocation point and have the advantages of fast convergence and high accuracy in solving the wave equation. (3) SA-PINNs/PCNNs simulate the wave propagation problem in homogeneous media without adding the "soft constraint" of the absorbing boundary to achieve a boundary transmission.