# Physics-informed neural network for seismic wave inversion in layered semi-infinite domain

arXiv: https://arxiv.org/abs/2305.05150 · HTML: https://mlsanity.com/paper/2305.05150/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
- [Physics informed deep learning for computational elastodynamics without labeled data](https://mlsanity.com/paper/2006.08472/) (2020)
- [Physics-informed deep learning for incompressible laminar flows](https://mlsanity.com/paper/2002.10558/) (2020)
- [Seismic wave propagation and inversion with Neural Operators](https://mlsanity.com/paper/2108.05421/) (2021)
- [EikoNet: Solving the Eikonal equation with Deep Neural Networks](https://mlsanity.com/paper/2004.00361/) (2020)
- [Learning to Solve PDE-constrained Inverse Problems with Graph Networks](https://mlsanity.com/paper/2206.00711/) (2022)
- [PINNup: Robust neural network wavefield solutions using frequency upscaling and neuron splitting](https://mlsanity.com/paper/2109.14536/) (2021)
- [SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domain](https://mlsanity.com/paper/2210.14044/) (2022)
- [Physics-informed Deep Super-resolution for Spatiotemporal Data](https://mlsanity.com/paper/2208.01462/) (2022)

## Built on by (most cited first, 2 of 2)

- [Optimization Landscapes Learned: Proxy Networks Boost Convergence in Physics-based Inverse Problems](https://mlsanity.com/paper/2501.16573/) (2025)
- [Diffusion priors enhanced velocity model building from time-lag images using a neural operator](https://mlsanity.com/paper/2512.23375/) (2025)

## Abstract (arXiv)

Estimating the material distribution of Earth's subsurface is a challenging task in seismology and earthquake engineering. The recent development of physics-informed neural network (PINN) has shed new light on seismic inversion. In this paper, we present a PINN framework for seismic wave inversion in layered (1D) semi-infinite domain. The absorbing boundary condition is incorporated into the network as a soft regularizer for avoiding excessive computation. In specific, we design a lightweight network to learn the unknown material distribution and a deep neural network to approximate solution variables. The entire network is end-to-end and constrained by both sparse measurement data and the underlying physical laws (i.e., governing equations and initial/boundary conditions). Various experiments have been conducted to validate the effectiveness of our proposed approach for inverse modeling of seismic wave propagation in 1D semi-infinite domain.