Supervision : Dominique BÉRÉZIAT

Co-supervision : CHARANTONIS Anastase, BRAJARD Julien

Variational Data Assimilation with Deep Prior. Application to Geophysical Motion Estimation

The recent revival of deep learning has impacted the state of the art in many scientific fields handling high-dimensional data. In particular, the availability and flexibility of algorithms have allowed the automation of inverse problem solving, learning estimators directly from data. This paradigm shift has also reached the research field of numerical weather prediction. However, the inherent issues in geosciences such as imperfect data and the lack of ground truth complicate the direct application of learning methods. Classical data assimilation algorithms, framing these issues and allowing the use of physics-based constraints, are currently the methods of choice in operational weather forecasting centers.
In this thesis, we experimentally study the hybridization of deep learning and data assimilation algorithms, with the objective of correcting forecast errors due to incomplete physical models or uncertain initial conditions. First, we highlight the similarities and nuances between variational data assimilation and deep learning. Following the state of the art, we exploit the complementarity of the two approaches in an iterative algorithm to then propose an end-to-end learning method. In the second part, we address the core of the thesis: variational data assimilation with deep prior, regularizing classical estimators with convolutional neural networks. The idea is declined in various algorithms including optimal interpolation, 4DVAR with strong and weak constraints, simultaneous assimilation, and super-resolution or uncertainty estimation. We conclude with perspectives on the proposed hybridization.

2020-2023 Publications

• 2023
  • Th. Archambault, A. Filoche, A. Charantonnis, D. Béréziat : “Multimodal Unsupervised Spatio-Temporal Interpolation of satellite ocean altimetry maps”, Proceedings of the 18^th International Conference on Computer Vision Theory and Applications, Lisboa, Portugal (2023)
• 2022
  • A. Filoche : “Variational Data Assimilation with Deep Prior. Application to Geophysical Motion Estimation”, thesis, defence 11/30/2022, supervision Béréziat, Dominique, co-supervision : Charantonis, Anastase, Brajard, Julien (2022)
  • A. Filoche, J. Brajard, A. Charantonis, D. Béréziat : “LEARNING 4DVAR INVERSION DIRECTLY FROM OBSERVATIONS”, (2022)
  • A. Filoche, Th. Archambault, A. Charantonis, D. Béréziat : “Statistics-free interpolation of ocean observations with deep spatio-temporal prior”, ECML/PKDD Workshop on Machine Learning for Earth Observation and Prediction (MACLEAN), Grenoble, France (2022)
  • A. Filoche, D. Béréziat : “Simultaneous Assimilation and Downscaling of Simulated Sea Surface Heights with Deep Image Prior”, RFIAP (Congrès Reconnaissance des Formes, Image, Apprentissage et Perception), Vannes, France (2022)
  • A. Filoche, D. Béréziat, A. Charantonis : “Deep prior in variational assimilation to estimate ocean circulation without explicit regularization”, Climate Informatics, Asheville, NC, United States (2022)
  • Th. Archambault, A. Filoche, A. Charantonis, D. Béréziat : “Unsupervised Downscaling of sea surface height with Deep Image Prior”, IA for Earth Sciences Workshop The International Conference on Learning Representations (ICLR), Virtual conference, United States (2022)
• 2021
  • A. Filoche, D. Béréziat, J. Brajard, A. Charantonis : “Variational assimilation of Geophysical images leveraging deep learning tools”, ORASIS 2021, Saint Ferréol, France (2021)
  • V. Bouget, D. Béréziat, J. Brajard, A. Charantonis, A. Filoche : “Fusion of Rain Radar Images and Wind Forecasts in a Deep Learning Model Applied to Rain Nowcasting”, Remote Sensing, vol. 13 (2), pp. 246, (MDPI) (2021)
• 2020
  • A. Filoche, J. Brajard, A. Charantonis, D. Béréziat : “Completing physics-based models by learning hidden dynamics through data assimilation”, NeurIPS 2020, workshop AI4Earth, Vancouver (virtual), Canada (2020)