Scaling End-to-end neural DA up to real-world problems: a case study for global-scale SLAmapping and 4DVarNets

End-to-end neural schemes have become state-of-the-art approaches for the reconstruction of ocean variables from irregularly-sampled observations, especially for sea surface dynamics (e.g., SST, SLA, ocean colour…).While most studies rely on the direct application of state-of-the-art architectures developed in imaging science, especially Unets, a class of approaches explicitly leverage state-space formulation and generalize in a neural fashion established data assimilation schemes such as 4DVar algorithms and EnKF schemes. Most of these approaches have been demonstrated for toy examples or intermediate-complexity case-studies. Here, we focus on 4DVarNet architectures which generalizes weak-constraint 4DVar solvers. Drawing inspirations from unrolled neural architectures used in computational imaging, especially in diffusion and flow matching models, we extend the original 4DVarNet architectures to a broader class of unrolled architectures which differ according to the specific parameterization of the considered iterative residual update. Leveraging diffusion-based Unet schemes with time embedding blocks, the resulting 4DVarNet schemes range from 1-million-parameter configurations to 50-million-parameter ones. Through an application to satellite altimetry and Sea Level Anomaly mapping, we assess the performance of the proposed architectures. Our contributions are three-fold: (i) we report state-of-the-art performance of considered neural global SLA mapping schemes compared to the state-of-the-art (eg, MIOST, NeuROST); (ii) unrolled architectures with just very few iterations, typically 5 to 10, reach the best mapping performance, (iii) the best unrolled architecture explicitly benefits from the knowledge conveyed by the underlying variational representation of the mapping problem. We discuss how these results could pave the way towards at-scale demonstrations of end-to-end neural DA schemes for the reconstruction of global ocean states from partial observations, including uncertainty quantification issues.