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).

In this paper, we propose new methodologies to decrease the computational cost of safe screening tests for LASSO. We first introduce a new screening strategy, dubbed ``joint screening test'', which allows the rejection of a set of atoms by performing one single test. Our approach enables to find good compromises between complexity of implementation and effectiveness of screening. Second, we propose two new methods to decrease the computational cost inherent to the construction of the (so-called) ``safe region''. Our numerical experiments show that the proposed procedures lead to significant computational gains as compared to standard methodologies.

In this paper we propose a methodology to accelerate the resolution of the so-called Sorted L-One Penalized Estimation (SLOPE) problem. Our method leverages the concept of “safe screening", well studied in the literature for group-separable sparsity-inducing norms, and aims ato identify the zeros in the solution of SLOPE. More specifically, we derive a set of [Formula: see text] inequalities for each element of the [Formula: see text]-dimensional primal vector and prove that the latter can be safely screened if some subsets of these inequalities are verified. We propose moreover an efficient algorithm to jointly apply the proposed procedure to all the primal variables. Our procedure has a complexity [Formula: see text] where [Formula: see text] is a problem-dependent constant and [Formula: see text] is the number of zeros identified by the test. Numerical experiments confirm that, for a prescribed computational budget, the proposed methodology leads to significant improvements in the solving precision.

Spreading the information over all coefficients of a representation is a desirable property in many applications such as digital communication or machine learning. This so-called antisparse representation can be obtained by solving a convex program involving an l∞-norm penalty combined with a quadratic discrepancy. In this paper, we propose a new methodology, dubbed safe squeezing, to accelerate the computation of antisparse representation. We describe a test that allows to detect saturated entries in the solution of the optimization problem. The contribution of these entries is compacted into a single vector, thus operating a form of dimensionality reduction. We propose two algorithms to solve the resulting lower dimensional problem. Numerical experiments show the effectiveness of the proposed method to detect the saturated components of the solution and illustrates the induced computational gains in the resolution of the antisparse problem.

We adapt and import into the TomoPIV scenery a fast algorithm for solving the volume reconstruction problem. Our approach is based on the reformulation of the volume reconstruction task as a constrained optimization problem and the resort to the 'alternating directions method of multipliers' (ADMM). The inherent primal-dual algorithm is summarized in this article to solve the optimization problem related to the TomoPIV. In particular, the general formulation of the volume reconstruction problem considered in this paper allows one to: (i) take explicitly into account the level of the noise affecting the data; (ii) account for both the nonnegativity and the sparsity of the solution. Experiments on a numerical TomoPIV benchmark show that the proposed framework is a serious contender for the state-of-the-art.