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The constantly increasing wealth of simulation and observation data on geophysical dynamics make more and more appealing data-driven strategies as new means to address key issues in ocean and atmosphere science, including for instance forecasting and assimilation issues. In this respect, recent studies have investigated data-driven strategies to identify governing equations from data using different machine learning frameworks, especially sparse regression models and neural networks. Among others, such data-driven representations of dynamical operators have shown to be of key interest for data assimilation issues, especially the spatio-temporal interpolation of geophysical fields from ocean remote sensing data. The availability of representative training datasets is a strong requirement for the development of such approaches. When considering observation datasets (e.g., satellite-derived data or in-situ observations), the question whether one may learn such data-driven representations from noisy and partial observation data naturally arises. For instance, regarding sea surface dynamics, beyond observation noise patterns, satellite sensors also involve irregular space-time sampling patterns due to their intrinsic characteristics or their sensitivity to the atmospheric conditions. In this work, we investigate these issues. We show that the effectiveness of previously proposed learning-based methods is strongly affected when applied to noisy and partial observation datasets. Within a neural-network-based framework, we address the data-driven identification of governing equations as the joint learning of dynamical models and the assimilation of the hidden states from noisy and partial observations. We restate state-of-the-art assimilation schemes (e.g., Ensemble Kalman Filters, Variational schemes) as neural network architectures, such that the identification of the dynamical operator comes to the minimization of a data assimilation cost, rather than a simple forecasting error. From numerical experiments on Lorenz-63 dynamics and sea surface dynamics, we demonstrate the relevance of the proposed approaches for the data-driven identification of dynamical operators, both in terms of forecasting performance and long-term topological patterns, within respect to the state-of-the-art. These experiments also illustrate that different assimilation-inspired neural-network-based architectures may be of interest depending on the noise levels. [ABSTRACT FROM AUTHOR]

The forecasting and reconstruction of oceanic dynamics is a crucial challenge. While model driven strategies are still the state-of-the-art approaches in the reconstruction of spatio-temporal dynamics. The ever increasing availability of data collections in oceanography raised the relevance of data-driven approaches as computationally efficient representations of spatio-temporal fields reconstruction. This tools proved to outperform classical state-of-the-art interpolation techniques such as optimal interpolation and DINEOF in the retrievement of fine scale structures while still been computationally efficient comparing to model based data assimilation schemes. However, coupling this data-driven priors to classical filtering schemes limits their potential representativity. From this point of view, the recent advances in machine learning and especially neural networks and deep learning can provide a new infrastructure for dynamical modeling and interpolation within a data-driven framework. In this work we adress this challenge and develop a novel Neural-Network-based (NN-based) Kalman filter for spatio-temporal interpolation of sea surface dynamics. Based on a data-driven probabilistic representation of spatio-temporal fields, our approach can be regarded as an alternative to classical filtering schemes such as the ensemble Kalman filters (EnKF) in data assimilation. Overall, the key features of the proposed approach are two-fold: (i) we propose a novel architecture for the stochastic representation of two dimensional (2D) geophysical dynamics based on a neural networks, (ii) we derive the associated parametric Kalman-like filtering scheme for a computationally-efficient spatio-temporal interpolation of Sea Surface Temperature (SST) fields. We illustrate the relevance of our contribution for an OSSE (Observing System Simulation Experiment) in a case-study region off South Africa. Our numerical experiments report significant improvements in terms of reconstruction performance compared with operational and state-of-the-art schemes (e.g., optimal interpolation, Empirical Orthogonal Function (EOF) based interpolation and analog data assimilation). [ABSTRACT FROM AUTHOR]