arXiv subjects

Alberto Carrassi

Publications and source records attributed to Alberto Carrassi.

At least 19 recordsLinked to original sources

arXiv2026

Hybrid physics-data-driven modeling for sea ice thermodynamics and transfer learning

This study explores a physics-data driven hybrid approach for sea-ice column physics models, in which a machine learning (ML) component acts as a state-dependent parameterization of forecast errors. We examine how perturbations in snow thermodynamics and sea-ice radiative properties affect forecast errors, and train dedicated neural networks (NNs) for each model configuration. The performance of the hybrid models is evaluated for long lead-time forecasts and compared against a benchmark system based on climatological forecast-error estimates. The NN-based hybrids prove to be stable, robust to initial condition and atmospheric forcing errors, and consistently outperform their climatology-based counterpart. To derive guiding principles for efficiently handling possible physical model updates, we perform transfer learning experiments to test whether pretrained NNs optimized for one model configuration can be successfully adapted to another. Results indicate that direct evaluation of pretrained networks on the target task provides useful insights into their adaptability, recommending transfer learning whenever performance exceeds a trivial baseline. Finally, a feature-importance analysis shows that atmospheric forcing inputs have negligible influence on NN predictive skill, while ice-layer enthalpies play a key role in achieving satisfactory performance.

physics.ao-ph↗

arXiv2025

Generative AI models capture realistic sea-ice evolution from days to decades

Sea ice plays an important role in stabilising the Earth system. Yet, representing its dynamics remains a major challenge for models, as the underlying processes are scale-invariant and highly anisotropic. This poses a dilemma: physics-based models that faithfully reproduce the observed dynamics are computationally costly, while efficient AI models sacrifice realism. Here, to resolve this dilemma, we introduce GenSIM, the first generative AI model to predict the evolution of the full Arctic sea-ice state at 12-hour increments. Trained for sub-daily forecasting on 20 years of sea-ice-ocean simulation data, GenSIM makes realistic predictions for 30 years, while reproducing the dynamical properties of sea ice with its leads and ridges and capturing long-term trends in the sea-ice volume. Notably, although solely driven by atmospheric reanalysis, GenSIM implicitly learns hidden signatures of multi-year ice-ocean interaction. Therefore, generative AI can extrapolate from sub-daily forecasts to decadal simulations, while retaining physical consistency.

physics.ao-ph↗

arXiv2025

Multi-Scale Data Assimilation in Turbulent Models

We explore the potential of Data-Assimilation (DA) within the multi-scale framework of a shell model of turbulence, with a focus on the Ensemble Kalman Filter (EnKF). The central objective is to understand how measuring mesoscales (i.e., inertial-range scales) enhances the prediction of both large-scale and small-scale intermittent variables, by systematically varying observation frequency and the set of measured scales. We demonstrate that measurements conducted at frequencies that exceed those of the observed scales enable full synchronization of larger scales, provided that at least two adjacent mesoscale are measured. In addition, we benchmark the EnKF against two other DA methods, namely Nudging and Ensemble 4D-Var. EnKF is clearly superior to the former, and comparable with the latter but achieving the result with a lower computational complexity. Moreover, our results underscore the need for a tailored, scale-aware inflation technique to stabilize the assimilation process, preventing filter divergence and ensuring robust convergence.

physics.flu-dyn↗

arXiv2025

Structural Origins and Real-Time Drivers of Intermittency

In general terms, intermittency is the property for which time evolving systems alternate among two or more different regimes. Predicting the instance when the regime switch will occur is extremely challenging, often practically impossible. Intermittent processes include turbulence, convection, precipitation patterns, as well as several in plasma physics, medicine, neuroscience, and economics. Traditionally, focus has been on global statistical indicators, e.g. the average frequency of regime changes under fixed conditions, or how these vary as a function of the system's parameters. We add a local perspective: we study the causes and drivers of the regime changes in real time, with the ultimate goal of predicting them. Using five different systems, of various complexities, we identify indicators and precursors of regime transitions that are common across the different intermittency mechanisms and dynamical models. For all the systems and intermittency types under study, we find a correlation between the alignment of some Lyapunov vectors and the concomitant, or aftermath, regime change. We discovered peculiar behaviors in the Lorenz 96 and in the Kuramoto-Shivanshinki models. In Lorenz 96 we identified crisis-induced intermittency with laminar intermissions, while in the Kuramoto-Shivanshinki we detected a spatially global intermittency which follows the scaling of type-I intermittency. The identification of general mechanisms driving intermittent behaviors, and in particular the unearthing of indicators spotting the regime change, pave the way to designing prediction tools in more realistic scenarios. These include turbulent geophysical fluids, rainfall patterns, or atmospheric deep convection.

nlin.CD↗

arXiv2025

Hybrid machine learning data assimilation for marine biogeochemistry

Marine biogeochemistry models are critical for forecasting, as well as estimating ecosystem responses to climate change and human activities. Data assimilation (DA) improves these models by aligning them with real-world observations, but marine biogeochemistry DA faces challenges due to model complexity, strong nonlinearity, and sparse, uncertain observations. Existing DA methods applied to marine biogeochemistry struggle to update unobserved variables effectively, while ensemble-based methods are computationally too expensive for high-complexity marine biogeochemistry models. This study demonstrates how machine learning (ML) can improve marine biogeochemistry DA by learning statistical relationships between observed and unobserved variables. We integrate ML-driven balancing schemes into a 1D prototype of a system used to forecast marine biogeochemistry in the North-West European Shelf seas. ML is applied to predict (i) state-dependent correlations from free-run ensembles and (ii), in an ``end-to-end'' fashion, analysis increments from an Ensemble Kalman Filter. Our results show that ML significantly enhances updates for previously not-updated variables when compared to univariate schemes akin to those used operationally. Furthermore, ML models exhibit moderate transferability to new locations, a crucial step toward scaling these methods to 3D operational systems. We conclude that ML offers a clear pathway to overcome current computational bottlenecks in marine biogeochemistry DA and that refining transferability, optimizing training data sampling, and evaluating scalability for large-scale marine forecasting, should be future research priorities.

physics.ao-ph↗

arXiv2025

Ensemble Kalman filter in latent space using a variational autoencoder pair

Popular (ensemble) Kalman filter data assimilation (DA) approaches assume that the errors in both the a priori estimate of the state and those in the observations are Gaussian. For constrained variables, e.g. sea ice concentration or stress, such an assumption does not hold. The variational autoencoder (VAE) is a machine learning (ML) technique that allows to map an arbitrary distribution to/from a latent space in which the distribution is supposedly closer to a Gaussian. We propose a novel hybrid DA-ML approach in which VAEs are incorporated in the DA procedure. Specifically, we introduce a variant of the popular ensemble transform Kalman filter (ETKF) in which the analysis is applied in the latent space of a single VAE or a pair of VAEs. In twin experiments with a simple circular model, whereby the circle represents an underlying submanifold to be respected, we find that the use of a VAE ensures that a posteri ensemble members lie close to the manifold containing the truth. Furthermore, online updating of the VAE is necessary and achievable when this manifold varies in time, i.e. when it is non-stationary. We demonstrate that introducing an additional second latent space for the observational innovations improves robustness against detrimental effects of non-Gaussianity and bias in the observational errors but it slightly lessens the performance if observational errors are strictly Gaussian.

cs.LG↗

arXiv2024

Accurate deep learning-based filtering for chaotic dynamics by identifying instabilities without an ensemble

We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple residual convolutional neural network, while assuming the dynamics to be known. Experiments are performed with the Lorenz 96 dynamics, which display spatiotemporal chaos and for which solid benchmarks for DA performance exist. The accuracy of the states obtained from the learned analysis approaches that of the best possibly tuned ensemble Kalman filter, and is far better than that of variational DA alternatives. Critically, this can be achieved while propagating even just a single state in the forecast step. We investigate the reason for achieving ensemble filtering accuracy without an ensemble. We diagnose that the analysis scheme actually identifies key dynamical perturbations, mildly aligned with the unstable subspace, from the forecast state alone, without any ensemble-based covariances representation. This reveals that the analysis scheme has learned some multiplicative ergodic theorem associated to the DA process seen as a non-autonomous random dynamical system.

nlin.CD↗

arXiv2023

Tailoring data assimilation to discontinuous Galerkin models

During the last few years discontinuous Galerkin (DG) methods have received increased interest from the geophysical community. In these methods the solution in each grid cell is approximated as a linear combination of basis functions. Ensemble data assimilation (EnDA) aims to approximate the true state by combining model outputs with observations using error statistics estimated from an ensemble of model runs. Ensemble data assimilation in geophysical models faces several well-documented issues. In this work we exploit the expansion of the solution in DG basis functions to address some of these issues. Specifically, it is investigated whether a DA-DG combination 1) mitigates the need for observation thinning, 2) reduces errors in the field's gradients, 3) can be used to set up scale-dependent localisation. Numerical experiments are carried out using stochastically generated ensembles of model states, with different noise properties, and with Legendre polynomials as basis functions. It is found that strong reduction in the analysis error is achieved by using DA-DG and that the benefit increases with increasing DG order. This is especially the case when small scales dominate the background error. The DA improvement in the 1st derivative is on the other hand marginal. We think this to be a counter-effect of the power of DG to fit the observations closely, which can deteriorate the estimates of the derivatives. Applying optimal localisation to the different polynomial orders, thus exploiting their different spatial length, is beneficial: it results in a covariance matrix closer to the true covariance than the matrix obtained using traditional optimal localisation in state-space.

physics.ao-ph↗

arXiv2023

Parameter sensitivity analysis of a sea ice melt pond parametrisation and its emulation using neural networks

Accurate simulation of sea ice is critical for predictions of future Arctic sea ice loss, looming climate change impacts, and more. A key feature in Arctic sea ice is the formation of melt ponds. Each year melt ponds develop on the surface of the ice and primarily via affecting the albedo, they have an enormous effect on the energy budget and climate of the Arctic. As melt ponds are subgrid scale and their evolution occurs due to a number of competing, poorly understood factors, their representation in models is parametrised. Sobol sensitivity analysis, a form of variance based global sensitivity analysis is performed on an advanced melt pond parametrisation (MPP), in Icepack, a state-of-the-art thermodynamic column sea ice model. Results show that the model is very sensitive to changing its uncertain MPP parameter values, and that these have varying influences over model predictions both spatially and temporally. Such extreme sensitivity to parameters makes MPPs a potential source of prediction error in sea-ice model, given that the (often many) parameters in MPPs are usually poorly known. Machine learning (ML) techniques have shown great potential in learning and replacing subgrid scale processes in models. Given the complexity of melt pond physics and the need for accurate parameter values in MPPs, we propose an alternative data-driven MPPs that would prioritise the accuracy of albedo predictions. In particular, we constructed MPPs based either on linear regression or on nonlinear neural networks, and investigate if they could substitute the original physics-based MPP in Icepack. Our results shown that linear regression are insufficient as emulators, whilst neural networks can learn and emulate the MPP in Icepack very reliably. Icepack with the MPPs based on neural networks only slightly deviates from the original Icepack and overall offers the same long term model behaviour.

physics.comp-ph↗

arXiv2023

Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review

Data Assimilation (DA) and Uncertainty quantification (UQ) are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical applications span from computational fluid dynamics (CFD) to geoscience and climate systems. Recently, much effort has been given in combining DA, UQ and machine learning (ML) techniques. These research efforts seek to address some critical challenges in high-dimensional dynamical systems, including but not limited to dynamical system identification, reduced order surrogate modelling, error covariance specification and model error correction. A large number of developed techniques and methodologies exhibit a broad applicability across numerous domains, resulting in the necessity for a comprehensive guide. This paper provides the first overview of the state-of-the-art researches in this interdisciplinary field, covering a wide range of applications. This review aims at ML scientists who attempt to apply DA and UQ techniques to improve the accuracy and the interpretability of their models, but also at DA and UQ experts who intend to integrate cutting-edge ML approaches to their systems. Therefore, this article has a special focus on how ML methods can overcome the existing limits of DA and UQ, and vice versa. Some exciting perspectives of this rapidly developing research field are also discussed.

cs.LG↗

arXiv2022

Supervised machine learning to estimate instabilities in chaotic systems: estimation of local Lyapunov exponents

In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure on-the-fly to increase accuracy or reduce computation time. One could, e.g., change the ensemble size, or the distribution and type of target observations. Local Lyapunov exponents are known indicators of the rate at which very small prediction errors grow over a finite time interval. However, their computation is very expensive: it requires maintaining and evolving a tangent linear model, orthogonalisation algorithms and storing large matrices. In this feasibility study, we investigate the accuracy of supervised machine learning in estimating the current local Lyapunov exponents, from input of current and recent time steps of the system trajectory, as an alternative to the classical method. Thus machine learning is not used here to emulate a physical model or some of its components, but non intrusively as a complementary tool. We test four popular supervised learning algorithms: regression trees, multilayer perceptrons, convolutional neural networks and long short-term memory networks. Experiments are conducted on two low-dimensional chaotic systems of ordinary differential equations, the R\"ossler and the Lorenz 63 models. We find that on average the machine learning algorithms predict the stable local Lyapunov exponent accurately, the unstable exponent reasonably accurately, and the neutral exponent only somewhat accurately. We show that greater prediction accuracy is associated with local homogeneity of the local Lyapunov exponents on the system attractor. Importantly, the situations in which (forecast) errors grow fastest are not necessarily the same as those where it is more difficult to predict local Lyapunov exponents with machine learning.

physics.comp-ph↗

arXiv2021

Inferring the instability of a dynamical system from the skill of data assimilation exercises

Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and model error, and at distilling the correct ingredients of its dynamics. DA is of critical importance for the analysis of systems featuring sensitive dependence on the initial conditions, as chaos wins over any finitely accurate knowledge of the state of the system, even in absence of model error. Clearly, the skill of DA is guided by the properties of dynamical system under investigation, as merging optimally observational data and model outputs is harder when strong instabilities are present. In this paper we reverse the usual angle on the problem and show that it is indeed possible to use the skill of DA to infer some basic properties of the tangent space of the system, which may be hard to compute in very high-dimensional systems. Here, we focus our attention on the first Lyapunov exponent and the Kolmogorov-Sinai entropy, and perform numerical experiments on the Vissio-Lucarini 2020 model, a recently proposed generalisation of the Lorenz 1996 model that is able to describe in a simple yet meaningful way the interplay between dynamical and thermodynamical variables.

physics.data-an↗

arXiv2020

Data assimilation for chaotic dynamics

Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in initial conditions is reduced by the astute combination of model predictions and real-time data. This chapter reviews recent findings from investigations on the impact of chaos on data assimilation methods: for the Kalman filter and smoother in linear systems, analytic results are derived; for their ensemble-based versions and nonlinear dynamics, numerical results provide insights. The focus is on characterising the asymptotic statistics of the Bayesian posterior in terms of the dynamical instabilities, differentiating between deterministic and stochastic dynamics. We also present two novel results. Firstly, we study the functioning of the ensemble Kalman filter in the context of a chaotic, coupled, atmosphere-ocean model with a quasi-degenerate spectrum of Lyapunov exponents, showing the importance of having sufficient ensemble members to track all of the near-null modes. Secondly, for the fully non-Gaussian method of the particle filter, numerical experiments are conducted to test whether the curse of dimensionality can be mitigated by discarding observations in the directions of little dynamical growth of uncertainty. The results refute this option, most likely because the particles already embody this information on the chaotic system. The results also suggest that it is the rank of the unstable-neutral subspace of the dynamics, and not that of the observation operator, that determines the required number of particles. We finally discuss how knowledge of the random attractor can play a role in the development of future data assimilation schemes for chaotic multiscale systems with large scale separation.

physics.data-an↗

arXiv2020

Ensemble Kalman Filter for non-conservative moving mesh solvers with a joint physics and mesh location update

Numerical solvers using adaptive meshes can focus computational power on important regions of a model domain capturing important or unresolved physics. The adaptation can be informed by the model state, external information, or made to depend on the model physics. In this latter case, one can think of the mesh configuration {\it as part of the model state}. If observational data is to be assimilated into the model, the question of updating the mesh configuration with the physical values arises. Adaptive meshes present significant challenges when using popular ensemble Data Assimilation (DA) methods. We develop a novel strategy for ensemble-based DA for which the adaptive mesh is updated along with the physical values. This involves including the node locations as a part of the model state itself allowing them to be updated automatically at the analysis step. This poses a number of challenges which we resolve to produce an effective approach that promises to apply with some generality. We evaluate our strategy with two testbed models in 1-d comparing to a strategy that does not update the mesh configuration. We find updating the mesh improves the fidelity and convergence of the filter.

stat.AP↗

arXiv2020

Probabilistic forecasts of sea ice trajectories in the Arctic: impact of uncertainties in surface wind and ice cohesion

We study the response of the Lagrangian sea ice model neXtSIM to the uncertainty in the sea surface wind and sea ice cohesion. The ice mechanics in neXtSIM is based on a brittle-like rheological framework. The study considers short-term ensemble forecasts of the Arctic sea ice from January to April 2008. Ensembles are generated by perturbing the wind inputs and ice cohesion field both separately and jointly. The resulting uncertainty in the probabilistic forecasts is evaluated statistically based on the analysis of Lagrangian sea ice trajectories as sampled by virtual drifters seeded in the model to cover the Arctic Ocean and using metrics borrowed from the search-and-rescue literature. The comparison among the different ensembles indicates that wind perturbations dominate the forecast uncertainty i.e. the absolute spread of the ensemble, while the inhomogeneities in the ice cohesion field significantly increase the degree of anisotropy in the spread i.e. trajectories drift differently in different directions. We suggest that in order to get a full flavor of uncertainties in a sea ice model with brittle-like rheologies, to predict sea ice drift and trajectories, one should consider using ensemble-based simulations where both wind forcing and sea ice cohesion are perturbed.

physics.ao-ph↗

arXiv2020

Combining data assimilation and machine learning to infer unresolved scale parametrisation

In recent years, machine learning (ML) has been proposed to devise data-driven parametrisations of unresolved processes in dynamical numerical models. In most cases, the ML training leverages high-resolution simulations to provide a dense, noiseless target state. Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrisation using direct data, in the realistic scenario of noisy and sparse observations. The algorithm proposed in this work is a two-step process. First, data assimilation (DA) techniques are applied to estimate the full state of the system from a truncated model. The unresolved part of the truncated model is viewed as a model error in the DA system. In a second step, ML is used to emulate the unresolved part, a predictor of model error given the state of the system. Finally, the ML-based parametrisation model is added to the physical core truncated model to produce a hybrid model. The DA component of the proposed method relies on an ensemble Kalman filter while the ML parametrisation is represented by a neural network. The approach is applied to the two-scale Lorenz model and to MAOOAM, a reduced-order coupled ocean-atmosphere model. We show that in both cases the hybrid model yields forecasts with better skill than the truncated model. Moreover, the attractor of the system is significantly better represented by the hybrid model than by the truncated model.

physics.comp-ph↗

arXiv2020

On temporal scale separation in coupled data assimilation with the ensemble Kalman filter

Coupled data assimilation (CDA) distinctively appears as a main concern in numerical weather and climate prediction with major efforts put forward worldwide. The core issue is the scale separation acting as a barrier that hampers the propagation of the information across model components. We provide a brief survey of CDA, and then focus on CDA using the ensemble Kalman filter (EnKF). We consider first coupled equations with temporal scale difference and deduce that: (i) cross components effects are strong from the slow to the fast scale, but, (ii) intra-component effects are much stronger in the fast scale. While observing the slow scale is desirable and benefits the fast, the latter must be observed with high frequency otherwise the error will affect the slow scale. Experiments are performed using the atmosphere-ocean model, MAOOAM. Six configurations are considered, differing for the strength of the atmosphere-ocean coupling and/or the number of model modes. A comprehensive dynamical characterisation of the model configurations is provided by examining the Lyapunov spectrum, Kolmogorov entropy and Kaplan-Yorke attractor dimension. We also compute the covariant Lyapunov vectors and use them to explain how model instabilities act on different model's modes according to the coupling strength. The experiments confirm the importance of observing the fast scale, but show also that, despite its slow temporal scale, frequent observations in the ocean are beneficial. The relation between the ensemble size and the unstable subspace dimension has been studied. Results largely ratify what known for uncoupled system: the condition N>n0 is necessary for the EnKF to converge. But the quasi-degeneracy of the Lyapunov spectrum of MAOOAM, with many near-zero exponents, is potentially the cause of the smooth gradual reduction of the analysis error observed for some model configurations, even when N>n0.

physics.ao-ph↗

arXiv2020

Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization

The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference from the observations over long time series, it has been suggested to combine data assimilation and machine learning in several ways. We show how to unify these approaches from a Bayesian perspective using expectation-maximization and coordinate descents. In doing so, the model, the state trajectory and model error statistics are estimated all together. Implementations and approximations of these methods are discussed. Finally, we numerically and successfully test the approach on two relevant low-order chaotic models with distinct identifiability.

stat.ML↗