Project Summary

• Developed INR4torch, an open-source PyTorch library for Implicit Neural Representations (INR) and Physics-Informed Neural Networks (PINNs) tailored for Earth Observation applications, providing a flexible and GPU-optimised framework for multiple geoscience use cases.
• Applied PINNs to six Earth Observation sub-projects: ice sheet monitoring (Greenland), ocean topography estimation, tropical cyclone super-resolution, hydrological basin modelling, riverbed and coastal reconstruction, and looting detection for cultural heritage.
• Produced multiple peer-reviewed publications and open-source code repositories, and supervised over ten visiting researchers and PhD students from European and international institutions on remote sensing and machine learning projects.

Development Tools

The following research and development tools were used throughout the project:

• PyTorch: the core deep learning framework used for all PINN and INR implementations, including the INR4torch library.
• Python scientific stack (NumPy, SciPy, pandas, xarray): data preprocessing, manipulation, and analysis of satellite and geoscience datasets including altimetry, LiDAR, SAR, and multi-spectral imagery.
• Sentinel-1 and Sentinel-2 satellite data, CryoSat-2 altimetry, and LiDAR point clouds served as the primary Earth Observation data sources across the various sub-projects. GitHub was used for version control and open-source code distribution.

Development Outputs

• INR4torch: PyTorch library for INR and PINNs for EO — Github Repo
• IceSheetReconstruction: Greenland ice sheet monitoring — Github Repo
• NN-4-change-detection: Change detection for looting detection — Github Repo
• OceanTopography: Ocean topography estimation — Github Repo
• PINNS4TC: Tropical cyclone super-resolution — Github Repo
• coastal_mathilda: Riverbed and beach reconstruction — Github Repo

If any, provide the list of publications of the outputs developed during this collaboration

• Ice Sheet Reconstruction with Implicit Neural Representations
• Implicit Neural Representation for change detection (published in WACV 2024)
• Altimetry fusion workshop paper (EurIPS REO Workshop)
• Spatiotemporal reconstruction of 4D point clouds at different time scales through implicit neural representations for topographic monitoring applications — to be published in ISPRS

Project Description

The AI4EO / PINNs4EO project at ESA Φ-lab investigates the use of Physics-Informed Neural Networks (PINNs) and Implicit Neural Representations (INR) for Earth Observation applications. PINNs are a class of neural networks that try to reduce deviations from physical laws, typically expressed as partial differential equations (PDEs), directly into the learning process. By encoding known physics as soft constraints in the loss function, PINNs can produce physically consistent predictions even in data-sparse regimes, making them particularly well-suited for geoscience problems where observations are irregularly sampled in space and time.

A central outcome of the project is INR4torch, an open-source PyTorch library that provides a high-level, modular implementation of INR and PINNs. The library is optimised for lightweight geoscience data where all operations can be performed on the GPU, such as satellite altimetry measurements. INR4torch is designed to be flexible and versatile, with multiple example projects bundled in the repository. The package was originally a re-implementation of a Jax-based approach from the literature, ported to PyTorch to improve accessibility and integration with the broader deep learning ecosystem. It continues to be extended with unit tests and new PINN developments informed by recent research and end-user feedback.

The project explored six distinct Earth Observation sub-projects, each applying PINNs or INR to a different geoscience challenge:

Ice Sheet Monitoring (ISRIN) — In collaboration with DTU (Andreas R. Stokholm, Natalia H. Andersen, Sebastian B. Simonsen), this sub-project applied INR to monitor the Greenland ice sheet. The objective was to increase the spatial-temporal resolution of ice sheet elevation products by fusing multiple data modalities, in particular altimetry and velocity measurements. A paper has been submitted to ISPRS for peer review, and a workshop paper was presented at EurIPS REO. Ongoing work focuses on extending the approach to the whole of Greenland and incorporating ICESat-2 data.

Looting Detection for Cultural Heritage — In collaboration with CCHT (Marco Fiorucci), this sub-project developed a change detection method for identifying looting at archaeological sites using LiDAR point cloud data. INR with a change detection loss was applied, and the unsupervised method outperformed a supervised baseline with 100 times fewer parameters. The results were published in WACV and demonstrated the suitability of PINNs for cultural heritage preservation applications.

Ocean Topography Estimation — In collaboration with the ESA Science Hub (Florian Le Guillou, Marie-Helene Rio) and Bertrand Le Saux, this sub-project aimed to encode ocean dynamics using INR and PINNs applied to Sea Surface Height measurements from altimetry satellites. The team successfully reproduced baseline INR results from the literature and investigated whether solving the underlying PDE could improve the product. The code is integrated into the INR4torch package.

Tropical Cyclone Super-Resolution — In collaboration with the ESA Science Hub (Arthur Avenas), this sub-project explored encoding tropical cyclone dynamics using PINNs applied to SAR velocity magnitude and wind profile measurements. The approach aimed to increase the spatial-temporal resolution of cyclone products. The code is available in a dedicated repository.

Hydrology & Basin Water Estimation — In collaboration with the ESA Science Hub (Karim Douch), this sub-project investigated a data-driven approach for modelling hydrological behaviour using PINNs with conservation-of-mass constraints. The code is integrated into the INR4torch package.

Riverbed and Coastal Reconstruction — In collaboration with Mathilde Letard (TUM, formerly OSUR, University of Rennes), this sub-project used PINNs for the reconstruction of environmental scenes from LiDAR data. Applications include bathymetry (riverbed reconstruction) and beach reconstruction. A paper on beach reconstruction is to be published in ISPRS, and the bathymetry paper is forthcoming.

Beyond the core PINNs research, the project also encompassed broader AI4EO activities at Φ-lab. As technical officer and expert, I managed and contributed to multiple ESA activities with a cumulated value exceeding 1.5 M€. He supervised over ten visiting researchers and PhD students from European and international institutions, covering topics such as geospatial foundation models (TerraMind), desertification detection, marine dynamics monitoring, solar irradiance mapping, aerosol characterisation, smart farming, urban heat island detection, and climate change in the Mediterranean. This supervision work fostered knowledge transfer between ESA and the broader research community, ensuring that visitors reached a high level of proficiency in remote sensing and machine learning during their stay.