Skip to content

Ocean4DVarNet

Core Concept

4DVarNet blends:

  • 4D-Variational data assimilation (4D-Var): A method used to optimally combine a numerical model with observations over a time window.
  • Deep learning: Neural networks learn to model complex dynamics and correct for model errors.

It learns to reconstruct missing data over both space and time (the "4D" stands for 3D space + time).

How It Works

  • It uses a neural network within a variational optimization loop.
  • Given partial observations (like satellite data), it:
    1. Predicts the full state over time.
    2. Minimizes a loss function that balances between:
      • Staying close to the observations.
      • Being consistent with a learned dynamical prior (the network).
    3. Refines its predictions iteratively (like traditional 4D-Var).

Applications

  • Oceanographic reconstructions (e.g. Sea Surface Height fields).
  • Climate modeling.
  • Atmospheric reanalysis.
  • Any setting where data is sparse, noisy, and spatiotemporal.

4DVarNet papers

  • Fablet, R.; Amar, M. M.; Febvre, Q.; Beauchamp, M.; Chapron, B. END-TO-END PHYSICS-INFORMED REPRESENTATION LEARNING FOR SA℡LITE OCEAN REMOTE SENSING DATA: APPLICATIONS TO SA℡LITE ALTIMETRY AND SEA SURFACE CURRENTS. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences 2021, V-3–2021, 295–302. https://doi.org/10.5194/isprs-annals-v-3-2021-295-2021.
  • Fablet, R.; Chapron, B.; Drumetz, L.; Mmin, E.; Pannekoucke, O.; Rousseau, F. Learning Variational Data Assimilation Models and Solvers. Journal of Advances in Modeling Earth Systems n/a (n/a), e2021MS002572. https://doi.org/10.1029/2021MS002572.
  • Fablet, R.; Beauchamp, M.; Drumetz, L.; Rousseau, F. Joint Interpolation and Representation Learning for Irregularly Sampled Satellite-Derived Geophysical Fields. Frontiers in Applied Mathematics and Statistics 2021, 7. https://doi.org/10.3389/fams.2021.655224.