# Learning Sentinel-2 reflectance dynamics for data-driven assimilation and forecasting

arXiv: https://arxiv.org/abs/2305.03743 · HTML: https://mlsanity.com/paper/2305.03743/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 5 May 2023.

## Builds on (most cited first, 7 of 7)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Self-supervised Learning in Remote Sensing: A Review](https://mlsanity.com/paper/2206.13188/) (2022)
- [BreizhCrops: A Time Series Dataset for Crop Type Mapping](https://mlsanity.com/paper/1905.11893/) (2019)
- [Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data](https://mlsanity.com/paper/2303.06972/) (2023)
- [Learning Sentinel-2 Spectral Dynamics for Long-Run Predictions Using Residual Neural Networks](https://mlsanity.com/paper/2011.08746/) (2020)

## Built on by (most cited first, 3 of 3)

- [Neural Koopman prior for data assimilation](https://mlsanity.com/paper/2309.05317/) (2023)
- [Augmented Invertible Koopman Autoencoder for long-term time series forecasting](https://mlsanity.com/paper/2503.12930/) (2025)
- [Koopman Ensembles for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2403.06757/) (2024)

## Abstract (arXiv)

Over the last few years, massive amounts of satellite multispectral and hyperspectral images covering the Earth's surface have been made publicly available for scientific purpose, for example through the European Copernicus project. Simultaneously, the development of self-supervised learning (SSL) methods has sparked great interest in the remote sensing community, enabling to learn latent representations from unlabeled data to help treating downstream tasks for which there is few annotated examples, such as interpolation, forecasting or unmixing. Following this line, we train a deep learning model inspired from the Koopman operator theory to model long-term reflectance dynamics in an unsupervised way. We show that this trained model, being differentiable, can be used as a prior for data assimilation in a straightforward way. Our datasets, which are composed of Sentinel-2 multispectral image time series, are publicly released with several levels of treatment.