# Integrating Physics of the Problem into Data-Driven Methods to Enhance Elastic Full-Waveform Inversion with Uncertainty Quantification

arXiv: https://arxiv.org/abs/2406.05153 · HTML: https://mlsanity.com/paper/2406.05153/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 98 references that are in the map.
- First posted on arXiv 4 Jun 2024.

## Builds on (most cited first, 12 of 12)

- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFs](https://mlsanity.com/paper/1811.07875/) (2018)
- [A Review of Deep Learning Techniques for Speech Processing](https://mlsanity.com/paper/2305.00359/) (2023)
- [Deep-learning inversion: a next generation seismic velocity-model building method](https://mlsanity.com/paper/1902.06267/) (2019)
- [Stochastic seismic waveform inversion using generative adversarial networks as a geological prior](https://mlsanity.com/paper/1806.03720/) (2018)
- [Deep-Learning Inversion of Seismic Data](https://mlsanity.com/paper/1901.07733/) (2019)
- [Solving Bayesian Inverse Problems via Variational Autoencoders](https://mlsanity.com/paper/1912.04212/) (2019)
- [Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop](https://mlsanity.com/paper/2110.07584/) (2021)
- [WISE: full-Waveform variational Inference via Subsurface Extensions](https://mlsanity.com/paper/2401.06230/) (2023)
- [Physics-Consistent Data-driven Waveform Inversion with Adaptive Data Augmentation](https://mlsanity.com/paper/2009.01807/) (2020)
- [Progressive transfer learning for low frequency data prediction in full waveform inversion](https://mlsanity.com/paper/1912.09944/) (2019)
- [ML-misfit: Learning a robust misfit function for full-waveform inversion using machine learning](https://mlsanity.com/paper/2002.03163/) (2020)

## Built on by (most cited first, 1 of 1)

- [Performance of Machine Learning Methods for Gravity Inversion: Successes and Challenges](https://mlsanity.com/paper/2510.09632/) (2025)

## Abstract (arXiv)

Full-Waveform Inversion (FWI) is a nonlinear iterative seismic imaging technique that, by reducing the misfit between recorded and predicted seismic waveforms, can produce detailed estimates of subsurface geophysical properties. Nevertheless, the strong nonlinearity of FWI can trap the optimization in local minima. This issue arises due to factors such as improper initial values, the absence of low frequencies in the measurements, noise, and other related considerations. To address this challenge and with the advent of advanced machine-learning techniques, data-driven methods, such as deep learning, have attracted significantly increasing attention in the geophysical community. Furthermore, the elastic wave equation should be included in FWI to represent elastic effects accurately. The intersection of data-driven techniques and elastic scattering theories presents opportunities and challenges. In this paper, by using the knowledge of elastic scattering (physics of the problem) and integrating it with machine learning techniques, we propose methods for the solution of time-harmonic FWI to enhance accuracy compared to pure data-driven and physics-based approaches. Moreover, to address uncertainty quantification, by modifying the structure of the Variational Autoencoder, we introduce a probabilistic deep learning method based on the physics of the problem that enables us to explore the uncertainties of the solution. According to the limited availability of datasets in this field and to assess the performance and accuracy of the proposed methods, we create a comprehensive dataset close to reality and conduct a comparative analysis of the presented approaches to it.