Physics-informed Neural Networks with Fourier Features for Seismic Wavefield Simulation in Time-Domain Nonsmooth Complex Media

TL;DR

This paper introduces Fourier feature physics-informed neural networks (FF-PINNs) that effectively model high-frequency seismic wave propagation in complex media by mitigating spectral bias and incorporating boundary conditions.

Contribution

The paper develops a unified FF-PINNs framework combining Fourier features, pre-trained surrogates, and boundary regularization to improve seismic wavefield simulation accuracy in complex media.

Findings

FF-PINNs outperform traditional PINNs in high-frequency wave modeling.

Fourier feature mappings from different distributions affect model accuracy.

Incorporating absorbing boundary conditions reduces spurious reflections.

Abstract

Physics-informed neural networks (PINNs) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias" pathology, which greatly limits their ability to model high-frequency wave propagation in sharp and complex media. We propose a unified framework of Fourier feature physics-informed neural networks (FF-PINNs) for solving the time-domain wave equations. The proposed framework combines the stochastic gradient descent (SGD) strategy with an independently pre-trained wave velocity surrogate model to mitigate the singularity at the point source. The performance of the activation functions and gradient descent strategies are discussed through ablation experiments. In addition, we evaluate the accuracy comparison of Fourier feature mappings sampled from different families of distributions (Gaussian, Laplace, and uniform). The second-order paraxial approximation-based boundary conditions are incorporated into the loss function as a soft regularizer to eliminate spurious boundary reflections. Through the non-smooth Marmousi and Overthrust model cases, we emphasized the necessity of the absorbing boundary conditions (ABCs) constraints. The results of a series of numerical experiments demonstrate the accuracy and effectiveness of the proposed method for modeling high-frequency wave propagation in sharp and complex media.