Bertrand Chapron

Ronan Fablet, Bertrand Chapron, Julien Le Sommer et al.

Satellite altimetry is a unique way for direct observations of sea surface dynamics. This is however limited to the surface-constrained geostrophic component of sea surface velocities. Ageostrophic dynamics are however expected to be significant for horizontal scales below 100~km and time scale below 10~days. The assimilation of ocean general circulation models likely reveals only a fraction of this ageostrophic component. Here, we explore a learning-based scheme to better exploit the synergies between the observed sea surface tracers, especially sea surface height (SSH) and sea surface temperature (SST), to better inform sea surface currents. More specifically, we develop a 4DVarNet scheme which exploits a variational data assimilation formulation with trainable observations and {\em a priori} terms. An Observing System Simulation Experiment (OSSE) in a region of the Gulf Stream suggests that SST-SSH synergies could reveal sea surface velocities for time scales of 2.5-3.0 days and horizontal scales of 0.5$^\circ$-0.7$^\circ$, including a significant fraction of the ageostrophic dynamics ($\approx$ 47\%). The analysis of the contribution of different observation data, namely nadir along-track altimetry, wide-swath SWOT altimetry and SST data, emphasizes the role of SST features for the reconstruction at horizontal spatial scales ranging from \nicefrac{1}{20}$^\circ$ to \nicefrac{1}{4}$^\circ$.

Nicolae-Cătălin Ristea, Andrei Anghel, Mihai Datcu et al.

Spaceborne synthetic aperture radar (SAR) can provide accurate images of the ocean surface roughness day-or-night in nearly all weather conditions, being an unique asset for many geophysical applications. Considering the huge amount of data daily acquired by satellites, automated techniques for physical features extraction are needed. Even if supervised deep learning methods attain state-of-the-art results, they require great amount of labeled data, which are difficult and excessively expensive to acquire for ocean SAR imagery. To this end, we use the subaperture decomposition (SD) algorithm to enhance the unsupervised learning retrieval on the ocean surface, empowering ocean researchers to search into large ocean databases. We empirically prove that SD improve the retrieval precision with over 20% for an unsupervised transformer auto-encoder network. Moreover, we show that SD brings important performance boost when Doppler centroid images are used as input data, leading the way to new unsupervised physics guided retrieval algorithms.

Nicolae-Catalin Ristea, Andrei Anghel, Mihai Datcu et al.

Spaceborne synthetic aperture radar can provide meters scale images of the ocean surface roughness day or night in nearly all weather conditions. This makes it a unique asset for many geophysical applications. Sentinel 1 SAR wave mode vignettes have made possible to capture many important oceanic and atmospheric phenomena since 2014. However, considering the amount of data provided, expanding applications requires a strategy to automatically process and extract geophysical parameters. In this study, we propose to apply subaperture decomposition as a preprocessing stage for SAR deep learning models. Our data centring approach surpassed the baseline by 0.7, obtaining state of the art on the TenGeoPSARwv data set. In addition, we empirically showed that subaperture decomposition could bring additional information over the original vignette, by rising the number of clusters for an unsupervised segmentation method. Overall, we encourage the development of data centring approaches, showing that, data preprocessing could bring significant performance improvements over existing deep learning models.

Ronan Fablet, Bertrand Chapron

For numerous earth observation applications, one may benefit from various satellite sensors to address the reconstruction of some process or information of interest. A variety of satellite sensors deliver observation data with different sampling patterns due satellite orbits and/or their sensitivity to atmospheric conditions (e.g., clour cover, heavy rains,...). Beyond the ability to account for irregularly-sampled observations, the definition of model-driven inversion methods is often limited to specific case-studies where one can explicitly derive a physical model to relate the different observation sources. Here, we investigate how end-to-end learning schemes provide new means to address multimodal inversion problems. The proposed scheme combines a variational formulation with trainable observation operators, {\em a priori} terms and solvers. Through an application to space oceanography, we show how this scheme can successfully extract relevant information from satellite-derived sea surface temperature images and enhance the reconstruction of sea surface currents issued from satellite altimetry data.

Said Ouala, Bertrand Chapron, Fabrice Collard et al.

Artificial intelligence and deep learning are currently reshaping numerical simulation frameworks by introducing new modeling capabilities. These frameworks are extensively investigated in the context of model correction and parameterization where they demonstrate great potential and often outperform traditional physical models. Most of these efforts in defining hybrid dynamical systems follow {offline} learning strategies in which the neural parameterization (called here sub-model) is trained to output an ideal correction. Yet, these hybrid models can face hard limitations when defining what should be a relevant sub-model response that would translate into a good forecasting performance. End-to-end learning schemes, also referred to as online learning, could address such a shortcoming by allowing the deep learning sub-models to train on historical data. However, defining end-to-end training schemes for the calibration of neural sub-models in hybrid systems requires working with an optimization problem that involves the solver of the physical equations. Online learning methodologies thus require the numerical model to be differentiable, which is not the case for most modeling systems. To overcome this difficulty and bypass the differentiability challenge of physical models, we present an efficient and practical online learning approach for hybrid systems. The method, called EGA for Euler Gradient Approximation, assumes an additive neural correction to the physical model, and an explicit Euler approximation of the gradients. We demonstrate that the EGA converges to the exact gradients in the limit of infinitely small time steps. Numerical experiments are performed on various case studies, including prototypical ocean-atmosphere dynamics. Results show significant improvements over offline learning, highlighting the potential of end-to-end online learning for hybrid modeling.

Salil Parth Tripathi, Bertrand Chapron, Fabrice Collard et al.

While optimal transport (OT) enforces a rigid constraint by requiring two measures to be matched exactly, partial optimal transport relaxes this requirement by allowing mass to remain unmatched through a global budget, scalar rebate, or uniform rejection rule. However, many applications call for more structured, pointwise rejection mechanisms, where the decision to leave mass unmatched depends on side-specific reliability, support geometry, or external information about which components should participate in the comparison. We introduce \emph{intent-controlled partial optimal transport} (IC-POT), a targeted generalization of partial transport that replaces the global rejection paradigm with pointwise rejection costs over both measures. We show that the resulting optimization problem admits a dual interpretation in terms of local acceptance thresholds and can be solved by recasting it as a balanced Kantorovich OT problem on an augmented support. Beyond theoretical analysis, we demonstrate the practical relevance of IC-POT in settings where rejection is driven by side information. In positive-unlabeled learning and open-partial domain adaptation, incorporating pointwise rejection rules that encode statistical structure improves fixed baseline pipelines. Finally, we motivate the use of IC-POT with a geophysical practical case: multi-modal satellite ocean measurements, for which physical and sensors priors naturally inform the rejection mechanism and define the retrieved comparable signal information.

Alexandre Tuel, Thomas Kerdreux, Quentin Febvre et al.

We present OceanSAR-2, the second generation of our foundation model for SAR-based ocean observation. Building on our earlier release, which pioneered self-supervised learning on Sentinel-1 Wave Mode data, OceanSAR-2 relies on improved SSL training and dynamic data curation strategies, which enhances performance while reducing training cost. OceanSAR-2 demonstrates strong transfer performance across downstream tasks, including geophysical pattern classification, ocean surface wind vector and significant wave height estimation, and iceberg detection. We release standardized benchmark datasets, providing a foundation for systematic evaluation and advancement of SAR models for ocean applications.

Thomas Kerdreux, Alexandre Tuel, Quentin Febvre et al.

Self-supervised learning (SSL) has enabled the development of vision foundation models for Earth Observation (EO), demonstrating strong transferability across diverse remote sensing tasks. While prior work has focused on network architectures and training strategies, the role of dataset curation, especially in balancing and diversifying pre-training datasets, remains underexplored. In EO, this challenge is amplified by the redundancy and heavy-tailed distributions common in satellite imagery, which can lead to biased representations and inefficient training. In this work, we propose a dynamic dataset pruning strategy designed to improve SSL pre-training by maximizing dataset diversity and balance. Our method iteratively refines the training set without requiring a pre-existing feature extractor, making it well-suited for domains where curated datasets are limited or unavailable. We demonstrate our approach on the Sentinel-1 Wave Mode (WV) Synthetic Aperture Radar (SAR) archive, a challenging dataset dominated by ocean observations. We train models from scratch on the entire Sentinel-1 WV archive spanning 10 years. Across three downstream tasks, our results show that dynamic pruning improves both computational efficiency and representation quality, leading to stronger transferability. We also release the weights of OceanSAR-1, the first model in the OceanSAR family, a series of foundation models for ocean observation and analysis using SAR imagery, at github.com/galeio-research/OceanSAR-models/.

Maxime Beauchamp, Ronan Fablet, Simon Benaichouche et al.

The spatio-temporal interpolation of large geophysical datasets has historically been addressed by Optimal Interpolation (OI) and more sophisticated equation-based or data-driven Data Assimilation (DA) techniques. Recent advances in the deep learning community enables to address the interpolation problem through a neural architecture incorporating a variational data assimilation framework. The reconstruction task is seen as a joint learning problem of the prior involved in the variational inner cost, seen as a projection operator of the state, and the gradient-based minimization of the latter. Both prior models and solvers are stated as neural networks with automatic differentiation which can be trained by minimizing a loss function, typically the mean squared error between some ground truth and the reconstruction. Such a strategy turns out to be very efficient to improve the mean state estimation, but still needs complementary developments to quantify its related uncertainty. In this work, we use the theory of Stochastic Partial Differential Equations (SPDE) and Gaussian Processes (GP) to estimate both space-and time-varying covariance of the state. Our neural variational scheme is modified to embed an augmented state formulation with both state and SPDE parametrization to estimate. We demonstrate the potential of the proposed framework on a spatio-temporal GP driven by diffusion-based anisotropies and on realistic Sea Surface Height (SSH) datasets. We show how our solution reaches the OI baseline in the Gaussian case. For nonlinear dynamics, as almost always stated in DA, our solution outperforms OI, while allowing for fast and interpretable online parameter estimation.

Daria Botvynko, Pierre Haslée, Lucile Gaultier et al.

We present an end-to-end deep learning framework for short-term forecasting of global sea surface dynamics based on sparse satellite altimetry data. Building on two state-of-the-art architectures: U-Net and 4DVarNet, originally developed for image segmentation and spatiotemporal interpolation respectively, we adapt the models to forecast the sea level anomaly and sea surface currents over a 7-day horizon using sequences of sparse nadir altimeters observations. The model is trained on data from the GLORYS12 operational ocean reanalysis, with synthetic nadir sampling patterns applied to simulate realistic observational coverage. The forecasting task is formulated as a sequence-to-sequence mapping, with the input comprising partial sea level anomaly (SLA) snapshots and the target being the corresponding future full-field SLA maps. We evaluate model performance using (i) normalized root mean squared error (nRMSE), (ii) averaged effective resolution, (iii) percentage of correctly predicted velocities magnitudes and angles, and benchmark results against the operational Mercator Ocean forecast product. Results show that end-to-end neural forecasts outperform the baseline across all lead times, with particularly notable improvements in high variability regions. Our framework is developed within the OceanBench benchmarking initiative, promoting reproducibility and standardized evaluation in ocean machine learning. These results demonstrate the feasibility and potential of end-to-end neural forecasting models for operational oceanography, even in data-sparse conditions.

Yannik Glaser, Justin E. Stopa, Linnea M. Wolniewicz et al.

The European Space Agency's Copernicus Sentinel-1 (S-1) mission is a constellation of C-band synthetic aperture radar (SAR) satellites that provide unprecedented monitoring of the world's oceans. S-1's wave mode (WV) captures 20x20 km image patches at 5 m pixel resolution and is unaffected by cloud cover or time-of-day. The mission's open data policy has made SAR data easily accessible for a range of applications, but the need for manual image annotations is a bottleneck that hinders the use of machine learning methods. This study uses nearly 10 million WV-mode images and contrastive self-supervised learning to train a semantic embedding model called WV-Net. In multiple downstream tasks, WV-Net outperforms a comparable model that was pre-trained on natural images (ImageNet) with supervised learning. Experiments show improvements for estimating wave height (0.50 vs 0.60 RMSE using linear probing), estimating near-surface air temperature (0.90 vs 0.97 RMSE), and performing multilabel-classification of geophysical and atmospheric phenomena (0.96 vs 0.95 micro-averaged AUROC). WV-Net embeddings are also superior in an unsupervised image-retrieval task and scale better in data-sparse settings. Together, these results demonstrate that WV-Net embeddings can support geophysical research by providing a convenient foundation model for a variety of data analysis and exploration tasks.

Said Ouala, Steven L. Brunton, Ananda Pascual et al.

The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables. These latent variables include unresolved small scales and/or rapidly evolving processes, partially observed couplings, or forcings in coupled systems. This is the case in ocean-atmosphere dynamics, for which unknown interior dynamics can affect surface observations. The identification of computationally-relevant representations of such partially-observed and highly nonlinear systems is thus challenging and often limited to short-term forecast applications. Here, we investigate the physics-constrained learning of implicit dynamical embeddings, leveraging neural ordinary differential equation (NODE) representations. A key objective is to constrain their boundedness, which promotes the generalization of the learned dynamics to arbitrary initial condition. The proposed architecture is implemented within a deep learning framework, and its relevance is demonstrated with respect to state-of-the-art schemes for different case-studies representative of geophysical dynamics.

Said Ouala, Laurent Debreu, Ananda Pascual et al.

Deriving analytical solutions of ordinary differential equations is usually restricted to a small subset of problems and numerical techniques are considered. Inevitably, a numerical simulation of a differential equation will then always be distinct from a true analytical solution. An efficient integration scheme shall further not only provide a trajectory throughout a given state, but also be derived to ensure the generated simulation to be close to the analytical one. Consequently, several integration schemes were developed for different classes of differential equations. Unfortunately, when considering the integration of complex non-linear systems, as well as the identification of non-linear equations from data, this choice of the integration scheme is often far from being trivial. In this paper, we propose a novel framework to learn integration schemes that minimize an integration-related cost function. We demonstrate the relevance of the proposed learning-based approach for non-linear equations and include a quantitative analysis w.r.t. classical state-of-the-art integration techniques, especially where the latter may not apply.

Ronan Fablet, Bertrand Chapron, Lucas. Drumetz et al.

This paper addresses variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic differentiation tools embedded in deep learning frameworks, we introduce end-to-end neural network architectures for data assimilation. It comprises two key components: a variational model and a gradient-based solver both implemented as neural networks. A key feature of the proposed end-to-end learning architecture is that we may train the NN models using both supervised and unsupervised strategies. Our numerical experiments on Lorenz-63 and Lorenz-96 systems report significant gain w.r.t. a classic gradient-based minimization of the variational cost both in terms of reconstruction performance and optimization complexity. Intriguingly, we also show that the variational models issued from the true Lorenz-63 and Lorenz-96 ODE representations may not lead to the best reconstruction performance. We believe these results may open new research avenues for the specification of assimilation models in geoscience.

Said Ouala, Duong Nguyen, Lucas Drumetz et al.

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications, including long-term asymptotic patterns. Whereas state-of-the-art data-driven approaches rely on delay embeddings and linear decompositions of the underlying operators, we introduce a framework based on the data-driven identification of an augmented state-space model using a neural-network-based representation. For a given training dataset, it amounts to jointly learn an ODE (Ordinary Differential Equation) representation in the latent space and reconstructing latent states. Through numerical experiments, we demonstrate the relevance of the proposed framework w.r.t. state-of-the-art approaches in terms of short-term forecasting performance and long-term behaviour. We further discuss how the proposed framework relates to Koopman operator theory and Takens' embedding theorem.