Simon BENAÏCHOUCHE Thesis defense

This thesis focuses on the assimilation of surface ocean currents from AIS data. This problem is an ill-posed inverse problem that falls within the scope of data assimilation. The main contribution of this thesis is to propose a new variational formulation for the assimilation of surface ocean currents from AIS data and the use of deep learning techniques to solve the associated assimilation problem. Different learning paradigms (supervised or unsupervised) are studied on real and simulated datasets, demonstrating significant gains in reconstruction performance compared to the state of the art. The ability of AIS data to estimate total currents is evaluated, as well as the possible synergies between AIS and altimetric data for reconstruction. Finally, the quantification of uncertainties associated with data assimilation problems is investigated. A new family of generative models based on the transport of the measure on divergence-free fields is proposed: these models have the property of conserving volumes, which allows extending the calculation of Shannon's differential entropy to families of complex probability distributions. Their generative capacity and their application to ill-posed inverse problems are evaluated on toy datasets.