Wave simulation in non-smooth media by PINN with quadratic neural network and PML condition

TL;DR

This paper enhances physics-informed neural networks (PINN) for seismic wave simulation in complex, non-smooth media by introducing PML boundary conditions and quadratic neurons, improving accuracy and efficiency in frequency-domain wavefield modeling.

Contribution

It proposes a novel PINN framework with PML and quadratic neurons to better handle non-smooth media in seismic wave simulations, and introduces a pre-training strategy for iterative applications.

Findings

PML and quadratic neurons improve wavefield accuracy in non-smooth media.

Pre-training accelerates convergence in iterative wavefield simulations.

PINN with these enhancements effectively models complex seismic wave phenomena.

Abstract

Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has achieved successful applications in solving a wide range of partial differential equations (PDEs), and there is still room for improvement on this front. For example, PINN can lead to inaccurate solutions when PDE coefficients are non-smooth and describe structurally-complex media. In this paper, we solve the acoustic and visco-acoustic scattered-field wave equation in the frequency domain with PINN instead of the wave equation to remove source singularity. We first illustrate that non-smooth velocity models lead to inaccurate wavefields when no boundary conditions are implemented in the loss function. Then, we add the perfectly matched layer (PML) conditions in the loss function of PINN and design a quadratic neural network to overcome the detrimental effects of non-smooth models in PINN. We show that PML and quadratic neurons improve the results as well as attenuation and discuss the reason for this improvement. We also illustrate that a network trained during a wavefield simulation can be used to pre-train the neural network of another wavefield simulation after PDE-coefficient alteration and improve the convergence speed accordingly. This pre-training strategy should find application in iterative full waveform inversion (FWI) and time-lag target-oriented imaging when the model perturbation between two consecutive iterations or two consecutive experiments can be small.