Oceanic processes at fine scales are crucial yet difficult to observe accurately due to limitations in satellite and in-situ measurements. The Surface Water and Ocean Topography (SWOT) mission provides high-resolution Sea Surface Height (SSH) data, though noise patterns often obscure fine scale structures. Current methods struggle with noisy data or require extensive supervised training, limiting their effectiveness on real-world observations. We introduce SIMPGEN (Simulation-Informed Metric and Prior for Generative Ensemble Networks), an unsupervised adversarial learning framework combining real SWOT observations with simulated reference data. SIMPGEN leverages wavelet-informed neural metrics to distinguish noisy from clean fields, guiding realistic SSH reconstructions. Applied to SWOT data, SIMPGEN effectively removes noise, preserving fine-scale features better than existing neural methods. This robust, unsupervised approach not only improves SWOT SSH data interpretation but also demonstrates strong potential for broader oceanographic applications, including data assimilation and super-resolution.

Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior physical knowledge. The size of the systems involved and the complexity of the underlying physical equations make it a challenging task from a computational point of view. Neural networks represent a promising method of emulating the physics at low cost, and therefore have the potential to considerably improve and accelerate data assimilation. In this work, we introduce a deep learning approach where the physical system is modeled as a sequence of coarse-to-fine Gaussian prior distributions parametrized by a neural network. This allows us to define an assimilation operator, which is trained in an end-to-end fashion to minimize the reconstruction error on a dataset with different observation processes. We illustrate our approach on chaotic dynamical physical systems with sparse observations, and compare it to traditional variational data assimilation methods.

Maritime transportation is paramount in achieving global economic growth, entailing concurrent ecological obligations in sustainability and safeguarding endangered marine species, most notably preserving large whale populations. In this regard, the Automatic Identification System (AIS) data plays a significant role by offering real-time streaming data on vessel movement, allowing enhanced traffic monitoring. This study explores using AIS data to prevent vessel-to-whale collisions by forecasting long-term vessel trajectories from engineered AIS data sequences. For such a task, we have developed an encoder-decoder model architecture using Bidirectional Long Short-Term Memory Networks (Bi-LSTM) to predict the next 12 hours of vessel trajectories using 1 to 3 hours of AIS data as input. We feed the model with probabilistic features engineered from historical AIS data that refer to each trajectory's potential route and destination. The model then predicts the vessel's trajectory, considering these additional features by leveraging convolutional layers for spatial feature learning and a position-aware attention mechanism that increases the importance of recent timesteps of a sequence during temporal feature learning. The probabilistic features have an F1 Score of approximately 85% and 75% for each feature type, respectively, demonstrating their effectiveness in augmenting information to the neural network. We test our model on the Gulf of St. Lawrence, a region known to be the habitat of North Atlantic Right Whales (NARW). Our model achieved a high R2 score of over 98% using various techniques and features. It stands out among other approaches as it can make complex decisions during turnings and path selection. Our study highlights the potential of data engineering and trajectory forecasting models for marine life species preservation.

The spatio-temporal interpolation of large geophysical datasets has historically been adressed by Optimal Interpolation (OI) and more sophisticated model-based or data-driven DA techniques. In the last ten years, the link established between Stochastic Partial Differential Equations (SPDE) and Gaussian Markov Random Fields (GMRF) opened a new way of handling both large datasets and physically-induced covariance matrix in Optimal Interpolation. Recent advances in the deep learning community also enables to adress this problem as neural architecture embedding data assimilation variational framework. The reconstruction task is seen as a joint learning problem of the prior involved in the variational inner cost 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 stated as the mean squared error between some ground truth and the reconstruction. In this work, we draw from the SPDE-based Gaussian Processes to estimate complex prior models able to handle non-stationary covariances in both space and time and provide a stochastic framework for interpretability and uncertainty quantification. Our neural variational scheme is modified to embed an augmented state formulation with both state and SPDE parametrization to estimate. Instead of a neural prior, we use a stochastic PDE as surrogate model along the data assimilation window. The training involves a loss function for both reconstruction task and SPDE prior model, where the likelihood of the SPDE parameters given the true states is involved in the training. Because the prior is stochastic, we can easily draw samples in the prior distribution before conditioning to provide a flexible way to estimate the posterior distribution based on thousands of members.

Wind speed at sea surface is a key quantity for a variety of scientific applications and human activities. Due to the non-linearity of the phenomenon, a complete description of such variable is made infeasible on both the small scale and large spatial extents. Methods relying on Data Assimilation techniques, despite being the state-of-the-art for Numerical Weather Prediction, can not provide the reconstructions with a spatial resolution that can compete with satellite imagery. In this work we propose a framework based on Variational Data Assimilation and Deep Learning concepts. This framework is applied to recover rich-in-time, high-resolution information on sea surface wind speed. We design our experiments using synthetic wind data and different sampling schemes for high-resolution and low-resolution versions of original data to emulate the real-world scenario of spatio-temporally heterogeneous observations. Extensive numerical experiments are performed to assess systematically the impact of low and high-resolution wind fields and in-situ observations on the model reconstruction performance. We show that in-situ observations with richer temporal resolution represent an added value in terms of the model reconstruction performance. We show how a multi-modal approach, that explicitly informs the model about the heterogeneity of the available observations, can improve the reconstruction task by exploiting the complementary information in spatial and local point-wise data. To conclude, we propose an analysis to test the robustness of the chosen framework against phase delay and amplitude biases in low-resolution data and against interruptions of in-situ observations supply at evaluation time

In this paper, we propose a generic algorithm to train machine learning-based subgrid parametrizations online, i.e., with a posteriori loss functions, but for non-differentiable numerical solvers. The proposed approach leverages a neural emulator to approximate the reduced state-space solver, which is then used to allow gradient propagation through temporal integration steps. We apply this methodology on a single layer quasi-geostrophic system with topography, known to be highly unstable in around 500 temporal iterations with offline strategies. Using our algorithm, we are able to train a parametrization that recovers most of the benefits of online strategies without having to compute the gradient of the original solver. It is demonstrated that training the neural emulator and parametrization components separately with different loss quantities is necessary in order to minimize the propagation of approximation biases. Experiments on emulator architectures with different complexities also indicates that emulator performance is key in order to learn an accurate parametrization. This work is a step towards learning parametrization with online strategies for realistic climate models.

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.

The ocean profoundly influences human activities and plays a critical role in climate regulation. Our understanding has improved over the last decades with the advent of satellite remote sensing data, allowing us to capture essential quantities over the globe, e.g., sea surface height (SSH). However, ocean satellite data presents challenges for information extraction due to their sparsity and irregular sampling, signal complexity, and noise. Machine learning (ML) techniques have demonstrated their capabilities in dealing with large-scale, complex signals. Therefore we see an opportunity for ML models to harness the information contained in ocean satellite data. However, data representation and relevant evaluation metrics can be the defining factors when determining the success of applied ML. The processing steps from the raw observation data to a ML-ready state and from model outputs to interpretable quantities require domain expertise, which can be a significant barrier to entry for ML researchers. OceanBench is a unifying framework that provides standardized processing steps that comply with domain-expert standards. It provides plug-and-play data and pre-configured pipelines for ML researchers to benchmark their models and a transparent configurable framework for researchers to customize and extend the pipeline for their tasks. In this work, we demonstrate the OceanBench framework through a first edition dedicated to SSH interpolation challenges. We provide datasets and ML-ready benchmarking pipelines for the long-standing problem of interpolating observations from simulated ocean satellite data, multi-modal and multi-sensor fusion issues, and transfer-learning to real ocean satellite observations. The OceanBench framework is available at github.com/jejjohnson/oceanbench and the dataset registry is available at github.com/quentinf00/oceanbench-data-registry.

Satellite altimetry combined with data assimilation and optimal interpolation schemes have deeply renewed our ability to monitor sea surface dynamics. Recently, deep learning (DL) schemes have emerged as appealing solutions to address space-time interpolation problems. The scarcity of real altimetry dataset, in terms of space-time coverage of the sea surface, however impedes the training of state-of-the-art neural schemes on real-world case-studies. Here, we leverage both simulations of ocean dynamics and satellite altimeters to train simulation-based neural mapping schemes for the sea surface height and demonstrate their performance for real altimetry datasets. We analyze further how the ocean simulation dataset used during the training phase impacts this performance. This experimental analysis covers both the resolution from eddy-present configurations to eddy-rich ones, forced simulations vs. reanalyses using data assimilation and tide-free vs. tide-resolving simulations. Our benchmarking framework focuses on a Gulf Stream region for a realistic 5-altimeter constellation using NEMO ocean simulations and 4DVarNet mapping schemes. All simulation-based 4DVarNets outperform the operational observation-driven and reanalysis products, namely DUACS and GLORYS. The more realistic the ocean simulation dataset used during the training phase, the better the mapping. The best 4DVarNet mapping was trained from an eddy-rich and tide-free simulation datasets. It improves the resolved longitudinal scale from 151 kilometers for DUACS and 241 kilometers for GLORYS to 98 kilometers and reduces the root mean squared error (RMSE) by 23% and 61%. These results open research avenues for new synergies between ocean modelling and ocean observation using learning-based approaches.

Generating accurate extremes from an observational data set is crucial when seeking to estimate risks associated with the occurrence of future extremes which could be larger than those already observed. Applications range from the occurrence of natural disasters to financial crashes. Generative approaches from the machine learning community do not apply to extreme samples without careful adaptation. Besides, asymptotic results from extreme value theory (EVT) give a theoretical framework to model multivariate extreme events, especially through the notion of multivariate regular variation. Bridging these two fields, this paper details a variational autoencoder (VAE) approach for sampling multivariate heavy-tailed distributions, i.e., distributions likely to have extremes of particularly large intensities. We illustrate the relevance of our approach on a synthetic data set and on a real data set of discharge measurements along the Danube river network. The latter shows the potential of our approach for flood risks' assessment. In addition to outperforming the standard VAE for the tested data sets, we also provide a comparison with a competing EVT-based generative approach. On the tested cases, our approach improves the learning of the dependency structure between extremes.