arXiv subjects

Ismaël Zighed

Publications and source records attributed to Ismaël Zighed.

4 recordsLinked to original sources

arXiv2026

Efficient Adaptation of ROMs for Unsteady Flows Using Data Assimilation

We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse observations of the full system. The architecture employs an encode-process-decode structure: a Variational Autoencoder (VAE) to perform dimensionality reduction, and a transformer network to evolve the latent states and model the dynamics. The ROM is parameterized by an external control variable, the Reynolds number in the Navier-Stokes setting, with the transformer exploiting attention mechanisms to capture both temporal dependencies and parameter effects. The probabilistic VAE enables stochastic sampling of trajectory ensembles, providing predictive means and uncertainty quantification through the first two moments. After initial training on a limited set of dynamical regimes, the model is adapted to out-of-sample parameter regions using only sparse data. Its probabilistic formulation naturally supports ensemble generation, which we employ within an ensemble Kalman filtering framework to assimilate data and reconstruct full-state trajectories from minimal observations. We further show that, for the dynamical system considered, the dominant source of error in out-of-sample forecasts stems from distortions of the latent manifold rather than changes in the latent dynamics. Consequently, retraining can be limited to the autoencoder, allowing for a lightweight, computationally efficient adaptation procedure with very sparse fine-tuning data.

cs.LG↗

arXiv2026

Modelisation of chaotic systems with a latent Stochastic Differential Equation

Stochastic Differential Equations (SDEs) have become a cornerstone of scientific machine learning, though they are predominantly utilized as algorithmic tools for uncertainty quantification or distribution matching. In contrast, leveraging SDEs fundamentally to model macroscopic, nonlinear physics as stochastic processes remains largely unexplored. This work introduces a probabilistic, non-intrusive reduced-order model (ROM) for chaotic dynamical systems. We argue that projecting high-dimensional nonlinear dynamics onto a low-dimensional manifold introduces irreducible uncertainty, compounded by the chaotic attractors and multi-admissible futures inherent to turbulent flows. Consequently, a chaotic system governed by a partial differential equation can be effectively modeled by an SDE in a suitable latent space. To this end, a nonlinear autoencoder is employed to map the flow field into a low-dimensional representation, within which the temporal evolution is explicitly governed by an SDE. The predictable component of the dynamics is captured by a learned drift term, while state-dependent stochasticity is absorbed by a diffusion term. We demonstrate that this probabilistic framework successfully propagates highly nonlinear states, offering a robust alternative to traditional deterministic methodologies for chaotic regimes. Ultimately, our model generates new chaotic flow trajectories that remain locally and globally consistent with the true transition kernel learned from Direct Numerical Simulation (DNS) data. Even though these generated trajectories are unique and distinct from the training set, they preserve the underlying statistics and manifolds, validating the strong generative performance and robustness of our methodology.

physics.flu-dyn↗

arXiv2025

Leveraging Scale Separation and Stochastic Closure for Data-Driven Prediction of Chaotic Dynamics

Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct numerical simulation (DNS) applied to real-world turbulent applications. Consequently, extensive research has focused on analysing turbulent flows from a data-driven perspective. However, due to the complex and chaotic nature of these systems, traditional models often become unstable as they accumulate errors through autoregression, severely degrading even short-term predictions. To overcome these limitations, we propose a purely stochastic approach that separately addresses the evolution of large-scale coherent structures and the closure of high-fidelity statistical data. To this end, the dynamics of the filtered data (i.e. coherent motion) are learnt using an autoregressive model. This combines a VAE and Transformer architecture. The VAE projection is probabilistic, ensuring consistency between the model's stochasticity and the flow's statistical properties. To recover high-fidelity velocity fields from the filtered latent space, Gaussian Process (GP) regression is employed. This strategy has been tested in the context of a Kolmogorov flow exhibiting chaotic behaviour analogous to real-world turbulence. We compare the performance of our model with state-of-the-art probabilistic baselines, including a VAE and a diffusion model. We demonstrate that our Gaussian process-based closure outperforms these baselines in capturing first and second moment statistics in this particular test bed, providing robust and adaptive confidence intervals.

physics.flu-dyn↗

arXiv2025

UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flows

Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise well across different regimes, but also provide a measure of confidence in their predictions. While recent data-driven approaches have begun to address nonlinear reduction techniques to improve predictions in transient environments, challenges remain in terms of robustness and parametrisation. In this work, we present a nonlinear reduction strategy specifically designed for transient flows that incorporates parametrisation and uncertainty quantification. Our reduction strategy features a variational auto-encoder (VAE) that uses variational inference for confidence measurement. We use a latent space transformer that incorporates recent advances in attention mechanisms to predict dynamical systems. Attention's versatility in learning sequences and capturing their dependence on external parameters enhances generalisation across a wide range of dynamics. Prediction, coupled with confidence, enables more informed decision making and addresses the need for more robust models. In addition, this confidence is used to cost-effectively sample the parameter space, improving model performance a priori across the entire parameter space without requiring evaluation data for the entire domain.

cs.LG↗