# An Unsupervised Deep Learning Approach for the Wave Equation Inverse Problem

arXiv: https://arxiv.org/abs/2311.04531 · HTML: https://mlsanity.com/paper/2311.04531/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 8 Nov 2023.

## Builds on (most cited first, 10 of 10)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Deep Learning on Image Denoising: An overview](https://mlsanity.com/paper/1912.13171/) (2019)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness](https://mlsanity.com/paper/2305.17289/) (2023)
- [Deep-learning inversion: a next generation seismic velocity-model building method](https://mlsanity.com/paper/1902.06267/) (2019)
- [Structured Dropout Variational Inference for Bayesian Neural Networks](https://mlsanity.com/paper/2102.07927/) (2021)
- [A Dataset-free Deep learning Method for Low-Dose CT Image Reconstruction](https://mlsanity.com/paper/2205.00463/) (2022)

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

- [Decoupled Latent Optimization of Diffusion Models for Full Waveform Inversion](https://mlsanity.com/paper/2606.14139/) (2026)
- [Physical-State-Guided Diffusion Sampling for Full-Waveform Inversion](https://mlsanity.com/paper/2609.12899/) (2026)

## Abstract (arXiv)

Full-waveform inversion (FWI) is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters by solving a non-convex optimization problem. However, due to limitations in observation, e.g., limited shots or receivers, and random noise, conventional inversion methods are confronted with numerous challenges, such as the local-minimum problem. In recent years, a substantial body of work has demonstrated that the integration of deep neural networks and partial differential equations for solving full-waveform inversion problems has shown promising performance. In this work, drawing inspiration from the expressive capacity of neural networks, we provide an unsupervised learning approach aimed at accurately reconstructing subsurface physical velocity parameters. This method is founded on a re-parametrization technique for Bayesian inference, achieved through a deep neural network with random weights. Notably, our proposed approach does not hinge upon the requirement of the labeled training dataset, rendering it exceedingly versatile and adaptable to diverse subsurface models. Extensive experiments show that the proposed approach performs noticeably better than existing conventional inversion methods.