# SG-DeepONet: Source-generalized deep operator learning for full waveform inversion

arXiv: https://arxiv.org/abs/2408.08005 · HTML: https://mlsanity.com/paper/2408.08005/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 15 Aug 2024.

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

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Wavelet Convolutions for Large Receptive Fields](https://mlsanity.com/paper/2407.05848/) (2024)
- [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)
- [OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion](https://mlsanity.com/paper/2111.02926/) (2021)
- [A prior regularized full waveform inversion using generative diffusion models](https://mlsanity.com/paper/2306.12776/) (2023)
- [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)

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

- [PreAdaptFWI: Pretrained-Based Adaptive Residual Learning for Full-Waveform Inversion Without Dataset Dependency](https://mlsanity.com/paper/2502.11913/) (2025)

## Abstract (arXiv)

Full waveform inversion (FWI) aims to reconstruct subsurface velocity models from observed seismic wavefields and has recently benefited from advances in deep learning (DL). The performance of DL-based FWI critically depends on the diversity of training data, yet existing datasets such as OpenFWI rely on fixed or weakly varying source conditions, limiting their ability to represent realistic seismic scenarios and hindering source generalization. To address this issue, we construct a new source-variable seismic dataset, termed SVFWI, by systematically varying the frequencies and horizontal locations of multiple surface sources. SVFWI is further divided into three subsets that respectively model frequency variations, location variations, and their combined effects, providing a challenging benchmark in data-driven FWI. We further propose SG-DeepONet, a novel DeepONet-based encoder-decoder framework tailored for FWI. The branch network extracts multi-scale time-frequency features from seismic observations, the trunk network explicitly embeds source physical parameters, and an interactive decoding network enables effective nonlinear fusion and high-fidelity velocity reconstruction. Extensive experiments on SVFWI demonstrate that SG-DeepONet achieves superior inversion accuracy and robustness under varying source conditions compared with existing DL-based FWI methods.