# Training neural mapping schemes for satellite altimetry with simulation data

arXiv: https://arxiv.org/abs/2309.14350 · HTML: https://mlsanity.com/paper/2309.14350/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 51 references that are in the map.
- First posted on arXiv 19 Sep 2023.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Learning Variational Data Assimilation Models and Solvers](https://mlsanity.com/paper/2007.12941/) (2020)
- [4DVarNet-SSH: end-to-end learning of variational interpolation schemes for nadir and wide-swath satellite altimetry](https://mlsanity.com/paper/2211.05904/) (2022)

## Built on by (most cited first, 4 of 4)

- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)
- [Multi-Modal Learning-based Reconstruction of High-Resolution Spatial Wind Speed Fields](https://mlsanity.com/paper/2312.08933/) (2023)
- [Simulation-informed deep learning for enhanced SWOT observations of fine-scale ocean dynamics](https://mlsanity.com/paper/2503.21303/) (2025)
- [Neural ocean forecasting from sparse satellite-derived observations: a case-study for SSH dynamics and altimetry data](https://mlsanity.com/paper/2512.22152/) (2025)

## Abstract (arXiv)

Satellite altimetry combined with data assimilation and optimal interpolation schemes have deeply renewed our ability to monitor sea surface dynamics. Recently, deep learning (DL) schemes have emerged as appealing solutions to address space-time interpolation problems. The scarcity of real altimetry dataset, in terms of space-time coverage of the sea surface, however impedes the training of state-of-the-art neural schemes on real-world case-studies. Here, we leverage both simulations of ocean dynamics and satellite altimeters to train simulation-based neural mapping schemes for the sea surface height and demonstrate their performance for real altimetry datasets. We analyze further how the ocean simulation dataset used during the training phase impacts this performance. This experimental analysis covers both the resolution from eddy-present configurations to eddy-rich ones, forced simulations vs. reanalyses using data assimilation and tide-free vs. tide-resolving simulations. Our benchmarking framework focuses on a Gulf Stream region for a realistic 5-altimeter constellation using NEMO ocean simulations and 4DVarNet mapping schemes. All simulation-based 4DVarNets outperform the operational observation-driven and reanalysis products, namely DUACS and GLORYS. The more realistic the ocean simulation dataset used during the training phase, the better the mapping. The best 4DVarNet mapping was trained from an eddy-rich and tide-free simulation datasets. It improves the resolved longitudinal scale from 151 kilometers for DUACS and 241 kilometers for GLORYS to 98 kilometers and reduces the root mean squared error (RMSE) by 23% and 61%. These results open research avenues for new synergies between ocean modelling and ocean observation using learning-based approaches.