{"title":"Physics-informed Neural Networks with Fourier Features for Seismic Wavefield Simulation in Time-Domain Nonsmooth Complex Media","authors":"Yi Ding, Su Chen, Hiroe Miyake, Xiaojun Li","doi":"arxiv-2409.03536","DOIUrl":null,"url":null,"abstract":"Physics-informed neural networks (PINNs) have great potential for flexibility\nand effectiveness in forward modeling and inversion of seismic waves. However,\ncoordinate-based neural networks (NNs) commonly suffer from the \"spectral bias\"\npathology, which greatly limits their ability to model high-frequency wave\npropagation in sharp and complex media. We propose a unified framework of\nFourier feature physics-informed neural networks (FF-PINNs) for solving the\ntime-domain wave equations. The proposed framework combines the stochastic\ngradient descent (SGD) strategy with a pre-trained wave velocity surrogate\nmodel to mitigate the singularity at the point source. The performance of the\nactivation functions and gradient descent strategies are discussed through\nablation experiments. In addition, we evaluate the accuracy comparison of\nFourier feature mappings sampled from different families of distributions\n(Gaussian, Laplace, and uniform). The second-order paraxial approximation-based\nboundary conditions are incorporated into the loss function as a soft\nregularizer to eliminate spurious boundary reflections. Through the non-smooth\nMarmousi and Overthrust model cases, we emphasized the necessity of the\nabsorbing boundary conditions (ABCs) constraints. The results of a series of\nnumerical experiments demonstrate the accuracy and effectiveness of the\nproposed method for modeling high-frequency wave propagation in sharp and\ncomplex media.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"52 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Geophysics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.03536","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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 a 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.