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.