# InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFs

arXiv: https://arxiv.org/abs/1811.07875 · HTML: https://mlsanity.com/paper/1811.07875/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2018.

## Built on by (most cited first, 30 of 61)

- [Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness](https://mlsanity.com/paper/2305.17289/) (2023)
- [OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion](https://mlsanity.com/paper/2111.02926/) (2021)
- [Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop](https://mlsanity.com/paper/2110.07584/) (2021)
- [Solving Seismic Wave Equations on Variable Velocity Models with Fourier Neural Operator](https://mlsanity.com/paper/2209.12340/) (2022)
- [InversionNet3D: Efficient and Scalable Learning for 3D Full Waveform Inversion](https://mlsanity.com/paper/2103.14158/) (2021)
- [Controllable seismic velocity synthesis using generative diffusion models](https://mlsanity.com/paper/2402.06277/) (2024)
- [Deep Bayesian inference for seismic imaging with tasks](https://mlsanity.com/paper/2110.04825/) (2021)
- [An Empirical Study of Large-Scale Data-Driven Full Waveform Inversion](https://mlsanity.com/paper/2307.15388/) (2023)
- [An Intriguing Property of Geophysics Inversion](https://mlsanity.com/paper/2204.13731/) (2022)
- [Auto-Linear Phenomenon in Subsurface Imaging](https://mlsanity.com/paper/2305.13314/) (2023)
- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [A Unified Framework for Forward and Inverse Problems in Subsurface Imaging using Latent Space Translations](https://mlsanity.com/paper/2410.11247/) (2024)
- [Physics-informed waveform inversion using pretrained wavefield neural operators](https://mlsanity.com/paper/2509.08967/) (2025)
- [RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion](https://mlsanity.com/paper/2509.21659/) (2025)
- [Making Invisible Visible: Data-Driven Seismic Inversion with Spatio-temporally Constrained Data Augmentation](https://mlsanity.com/paper/2106.11892/) (2021)
- [Inversion of Time-Lapse Surface Gravity Data for Detection of 3D CO2 Plumes via Deep Learning](https://mlsanity.com/paper/2209.02850/) (2022)
- [mathbfmathbbEFWI: Multi-parameter Benchmark Datasets for Elastic Full Waveform Inversion of Geophysical Properties](https://mlsanity.com/paper/2306.12386/) (2023)
- [Coefficient-to-Basis Network: A Fine-Tunable Operator Learning Framework for Inverse Problems with Adaptive Discretizations and Theoretical Guarantees](https://mlsanity.com/paper/2503.08642/) (2025)
- [Applications of physics-informed scientific machine learning in subsurface science: A survey](https://mlsanity.com/paper/2104.04764/) (2021)
- [Revisit Geophysical Imaging in A New View of Physics-informed Generative Adversarial Learning](https://mlsanity.com/paper/2109.11452/) (2021)
- [Extremely Weak Supervision Inversion of Multi-physical Properties](https://mlsanity.com/paper/2202.01770/) (2022)
- [A Frequency-Velocity CNN for Developing Near-Surface 2D Vs Images from Linear-Array, Active-Source Wavefield Measurements](https://mlsanity.com/paper/2207.09580/) (2022)
- [Edge-InversionNet: Enabling Efficient Inference of InversionNet on Edge Devices](https://mlsanity.com/paper/2310.09667/) (2023)
- [A Physics-guided Generative AI Toolkit for Geophysical Monitoring](https://mlsanity.com/paper/2401.03131/) (2024)
- [OpenPros: A Large-Scale Dataset for Limited View Prostate Ultrasound Computed Tomography](https://mlsanity.com/paper/2505.12261/) (2025)
- [Decoupled Latent Optimization of Diffusion Models for Full Waveform Inversion](https://mlsanity.com/paper/2606.14139/) (2026)
- [Enhanced prediction accuracy with uncertainty quantification in monitoring CO2 sequestration using convolutional neural networks](https://mlsanity.com/paper/2212.04567/) (2022)
- [Integrating Physics of the Problem into Data-Driven Methods to Enhance Elastic Full-Waveform Inversion with Uncertainty Quantification](https://mlsanity.com/paper/2406.05153/) (2024)
- [SG-DeepONet: Source-generalized deep operator learning for full waveform inversion](https://mlsanity.com/paper/2408.08005/) (2024)
- [Neumann Series-based Neural Operator for Solving Inverse Medium Problem](https://mlsanity.com/paper/2409.09480/) (2024)

## Abstract (arXiv)

Full-waveform inversion problems are usually formulated as optimization problems, where the forward-wave propagation operator f maps the subsurface velocity structures to seismic signals. The existing computational methods for solving full-waveform inversion are not only computationally expensive, but also yields low-resolution results because of the ill-posedness and cycle skipping issues of full-waveform inversion. To resolve those issues, we employ machine-learning techniques to solve the full-waveform inversion. Specifically, we focus on applying the convolutional neural network~(CNN) to directly derive the inversion operator f-1 so that the velocity structure can be obtained without knowing the forward operator f. We build a convolutional neural network with an encoder-decoder structure to model the correspondence from seismic data to subsurface velocity structures. Furthermore, we employ the conditional random field~(CRF) on top of the CNN to generate structural predictions by modeling the interactions between different locations on the velocity model. Our numerical examples using synthetic seismic reflection data show that the propose CNN-CRF model significantly improve the accuracy of the velocity inversion while the computational time is reduced.