# An Empirical Study of Large-Scale Data-Driven Full Waveform Inversion

arXiv: https://arxiv.org/abs/2307.15388 · HTML: https://mlsanity.com/paper/2307.15388/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 28 Jul 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFs](https://mlsanity.com/paper/1811.07875/) (2018)
- [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)
- [OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion](https://mlsanity.com/paper/2111.02926/) (2021)
- [Data-driven Seismic Waveform Inversion: A Study on the Robustness and Generalization](https://mlsanity.com/paper/1809.10262/) (2018)
- [Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop](https://mlsanity.com/paper/2110.07584/) (2021)
- [An Intriguing Property of Geophysics Inversion](https://mlsanity.com/paper/2204.13731/) (2022)

## Built on by (most cited first, 9 of 9)

- [WISE: full-Waveform variational Inference via Subsurface Extensions](https://mlsanity.com/paper/2401.06230/) (2023)
- [Edge-InversionNet: Enabling Efficient Inference of InversionNet on Edge Devices](https://mlsanity.com/paper/2310.09667/) (2023)
- [On a Hidden Property in Computational Imaging](https://mlsanity.com/paper/2410.08498/) (2024)
- [Acoustic Waveform Inversion with Image-to-Image Schr"odinger Bridges](https://mlsanity.com/paper/2506.15346/) (2025)
- [Ultrasound Tomography of Musculoskeletal Tissues with Generative Neural Physics](https://mlsanity.com/paper/2508.12226/) (2025)
- [SA-EMO: Structure-Aligned Encoder Mixture of Operators for Generalizable Full-waveform Inversion](https://mlsanity.com/paper/2511.11627/) (2025)
- [Improving Full Waveform Inversion in Large Model Era](https://mlsanity.com/paper/2603.00377/) (2026)
- [Two Teachers Better Than One: Hardware-Physics Co-Guided Distributed Scientific Machine Learning](https://mlsanity.com/paper/2603.09032/) (2026)
- [SubsurfaceGen: Procedural Generation of Field-Scale Earth Models and Seismic Data](https://mlsanity.com/paper/2605.30541/) (2026)

## Abstract (arXiv)

This paper investigates the impact of big data on deep learning models to help solve the full waveform inversion (FWI) problem. While it is well known that big data can boost the performance of deep learning models in many tasks, its effectiveness has not been validated for FWI. To address this gap, we present an empirical study that investigates how deep learning models in FWI behave when trained on OpenFWI, a collection of large-scale, multi-structural, synthetic datasets published recently. In particular, we train and evaluate the FWI models on a combination of 10 2D subsets in OpenFWI that contain 470K pairs of seismic data and velocity maps in total. Our experiments demonstrate that training on the combined dataset yields an average improvement of 13.03% in MAE, 7.19% in MSE and 1.87% in SSIM compared to each split dataset, and an average improvement of 28.60%, 21.55% and 8.22% in the leave-one-out generalization test. We further demonstrate that model capacity needs to scale in accordance with data size for optimal improvement, where our largest model yields an average improvement of 20.06%, 13.39% and 0.72% compared to the smallest one.