# SA-EMO: Structure-Aligned Encoder Mixture of Operators for Generalizable Full-waveform Inversion

arXiv: https://arxiv.org/abs/2511.11627 · HTML: https://mlsanity.com/paper/2511.11627/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 7 Nov 2025.

## Builds on (most cited first, 25 of 25)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [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)
- [Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology](https://mlsanity.com/paper/2211.08939/) (2022)
- [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)
- [Variational Autoencoding Neural Operators](https://mlsanity.com/paper/2302.10351/) (2023)
- [Unchosen Experts Can Contribute Too: Unleashing MoE Models' Power by Self-Contrast](https://mlsanity.com/paper/2405.14507/) (2024)
- [Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solvers](https://mlsanity.com/paper/2207.11417/) (2022)
- [Mesh-Informed Neural Operator : A Transformer Generative Approach](https://mlsanity.com/paper/2506.16656/) (2025)
- [Local neural operator for solving transient partial differential equations on varied domains](https://mlsanity.com/paper/2203.08145/) (2022)
- [An Empirical Study of Large-Scale Data-Driven Full Waveform Inversion](https://mlsanity.com/paper/2307.15388/) (2023)
- [Ensemble and Mixture-of-Experts DeepONets For Operator Learning](https://mlsanity.com/paper/2405.11907/) (2024)
- [Encoder-Decoder Architecture for 3D Seismic Inversion](https://mlsanity.com/paper/2207.14789/) (2022)
- [Ambient Noise Full Waveform Inversion with Neural Operators](https://mlsanity.com/paper/2503.15013/) (2025)
- [Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling](https://mlsanity.com/paper/2510.00233/) (2025)

## Abstract (arXiv)

Full-waveform inversion (FWI) can produce high-resolution subsurface models, yet it remains inherently ill-posed, highly nonlinear, and computationally intensive. Although recent deep learning and numerical acceleration methods have improved speed and scalability, they often rely on single CNN architectures or single neural operators, which struggle to generalize in unknown or complex geological settings and are ineffective at distinguishing diverse geological types. To address these issues, we propose a Structure-Aligned Encoder-Mixture-of-Operators (SA-EMO) architecture for velocity-field inversion under unknown subsurface structures. First, a structure-aligned encoder maps high-dimensional seismic wavefields into a physically consistent latent space, thereby eliminating spatio-temporal mismatch between the waveform and velocity domains, recovering high-frequency components, and enhancing feature generalization. Then, an adaptive routing mechanism selects and fuses multiple neural-operator experts, including spectral, wavelet, multiscale, and local operators, to predict the velocity model. We systematically evaluate our approach on the OpenFWI benchmark and the Marmousi2 dataset. Results show that SA-EMO significantly outperforms traditional CNN or single-operator methods, achieving an average MAE reduction of approximately 58.443% and an improvement in boundary resolution of about 10.308%. Ablation studies further reveal that the structure-aligned encoder, the expert-fusion mechanism, and the routing module each contribute markedly to the performance gains. This work introduces a new paradigm for efficient, scalable, and physically interpretable full-waveform inversion.