Andrea Nóvoa

Ismaël Zighed, Andrea Nóvoa, Luca Magri et al.

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, real-time adaptation procedure with very sparse fine-tuning data.

Ben Eze, Luca Magri, Andrea Nóvoa

Vision transformers have demonstrated outstanding performance on image generation applications, but their adoption in scientific disciplines, like fluid dynamics, has been limited. We introduce the Latent Attention on Masked Patches (LAMP) model, an interpretable regression-based modified vision transformer designed for masked flow reconstruction. LAMP follows a three-fold strategy: (i) partition of each flow snapshot into patches, (ii) dimensionality reduction of each patch via patch-wise proper orthogonal decomposition, and (iii) reconstruction of the full field from a masked input using a single-layer transformer trained via closed-form linear regression. We test the method on two canonical 2D unsteady wakes: a wake past a bluff body, and a chaotic wake past a flat plate. We show that the LAMP accurately reconstructs the full flow field from a 90\%-masked and noisy input, across signal-to-noise ratios between 10 and 30\,dB. Incorporating nonlinear measurement states can reduce the prediction error by up to an order of magnitude. The learned attention matrix yields physically interpretable multi-fidelity optimal sensor-placement maps. The modularity of the framework enables nonlinear compression and deep attention blocks, thereby providing an efficient baseline for nonlinear and high-dimensional masked flow reconstruction.

Defne E. Ozan, Andrea Nóvoa, Luca Magri

The goal of many applications in energy and transport sectors is to control turbulent flows. However, because of chaotic dynamics and high dimensionality, the control of turbulent flows is exceedingly difficult. Model-free reinforcement learning (RL) methods can discover optimal control policies by interacting with the environment, but they require full state information, which is often unavailable in experimental settings. We propose a data-assimilated model-based RL (DA-MBRL) framework for systems with partial observability and noisy measurements. Our framework employs a control-aware Echo State Network for data-driven prediction of the dynamics, and integrates data assimilation with an Ensemble Kalman Filter for real-time state estimation. An off-policy actor-critic algorithm is employed to learn optimal control strategies from state estimates. The framework is tested on the Kuramoto-Sivashinsky equation, demonstrating its effectiveness in stabilizing a spatiotemporally chaotic flow from noisy and partial measurements.

Andrea Nóvoa, Luca Magri

We propose an online learning framework for forecasting nonlinear spatio-temporal signals (fields). The method integrates (i) dimensionality reduction, here, a simple proper orthogonal decomposition (POD) projection; (ii) a generalized autoregressive model to forecast reduced dynamics, here, a reservoir computer; (iii) online adaptation to update the reservoir computer (the model), here, ensemble sequential data assimilation. We demonstrate the framework on a wake past a cylinder governed by the Navier-Stokes equations, exploring the assimilation of full flow fields (projected onto POD modes) and sparse sensors. Three scenarios are examined: a naïve physical state estimation; a two-fold estimation of physical and reservoir states; and a three-fold estimation that also adjusts the model parameters. The two-fold strategy significantly improves ensemble convergence and reduces reconstruction error compared to the naïve approach. The three-fold approach enables robust online training of partially-trained reservoir computers, overcoming limitations of a priori training. By unifying data-driven reduced order modelling with Bayesian data assimilation, this work opens new opportunities for scalable online model learning for nonlinear time series forecasting.

Defne E. Ozan, Andrea Nóvoa, Georgios Rigas et al.

The control of spatio-temporally chaos is challenging because of high dimensionality and unpredictability. Model-free reinforcement learning (RL) discovers optimal control policies by interacting with the system, typically requiring observations of the full physical state. In practice, sensors often provide only partial and noisy measurements (observations) of the system. The objective of this paper is to develop a framework that enables the control of chaotic systems with partial and noisy observability. The proposed method, data-assimilated model-informed reinforcement learning (DA-MIRL), integrates (i) low-order models to approximate high-dimensional dynamics; (ii) sequential data assimilation to correct the model prediction when observations become available; and (iii) an off-policy actor-critic RL algorithm to adaptively learn an optimal control strategy based on the corrected state estimates. We test DA-MIRL on the spatiotemporally chaotic solutions of the Kuramoto-Sivashinsky equation. We estimate the full state of the environment with (i) a physics-based model, here, a coarse-grained model; and (ii) a data-driven model, here, the control-aware echo state network, which is proposed in this paper. We show that DA-MIRL successfully estimates and suppresses the chaotic dynamics of the environment in real time from partial observations and approximate models. This work opens opportunities for the control of partially observable chaotic systems.