arXiv subjects

Andrea Nóvoa

Publications and source records attributed to Andrea Nóvoa.

11 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

Transferable inference of turbulence models for urban flows with the Parameter-Regularised Ensemble Kalman Filter

The accurate simulation of urban flow is key to designing building ventilation, understanding cities' micrometeorology, and predicting pollutant dispersion. Reynolds-Averaged Navier-Stokes (RANS) simulations are a common modelling approach for simulating urban flow, but their accuracy depends on the closure model and its parameters. These parameters are inferred from benchmark cases, but they are not necessarily suitable for realistic urban environments, which involve different physical mechanisms. This is referred to as the transferability problem of RANS urban modelling. The objective of this work is to propose a robust Bayesian method to {sequentially} infer RANS parameters for urban flow modelling. Key to the approach is the mathematical derivation of the parameter-regularised ensemble Kalman filter (PR-EnKF), which is the analytical solution of the data assimilation problem for the sequential parameter estimation. The cost functional is regularised using the prior knowledge on the turbulence parameters, thereby ensuring that the Bayesian updates remain within physical ranges. The parameters are first inferred on an isolated building, and then transferred to three cases of increasing complexity: (i) a high-rise building, (ii) a multi-building array, and (iii) the Shinjuku district urban environment. Results show that the PR-EnKF achieves faster convergence, reducing parameter uncertainty by an order of magnitude and reconstruction errors by up to 50%. Because of the regularisation, the PR-EnKF selectively updates the most important parameters. This work enables robust large-scale urban flow simulation whilst reducing the computational overhead of model optimisation for urban planning and air quality assessment.

physics.flu-dyn↗

arXiv2026

Prediction of chaotic dynamics from data: An introduction

This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for time-forecasting chaotic dynamics, such as echo state networks and long-short-term memory networks, whilst keeping a dynamical systems' perspective. Third, the lecture contains informal interpretations and pedagogical examples with prototypical chaotic systems (e.g., the Lorenz system), which elucidate the theory. The chapter is complemented by coding tutorials (online) at https://github.com/MagriLab/Tutorials.

nlin.CD↗

arXiv2026

Latent attention on masked patches for flow reconstruction

Vision transformers have shown outstanding performance in image generation, yet their adoption in fluid dynamics remains 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) patch-wise dimensionality reduction via 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 laminar wake past a bluff body, and a chaotic wake past two cylinders. On the laminar case, LAMP accurately reconstructs the full flow field from a 90%-masked and noisy input, across signal-to-noise ratios between 10 and 30dB. Further, the learned attention matrix yields interpretable multi-fidelity optimal sensor-placement maps. LAMP's performance on the chaotic wake is limited, but outperforms other regression methods such as gappy POD. The modularity of the framework, however, naturally accommodates nonlinear compression and deep attention blocks, thereby providing an efficient baseline for nonlinear, high-dimensional masked flow reconstruction.

cs.LG↗

arXiv2025

Data-assimilated model-informed reinforcement learning

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.

eess.SY↗

arXiv2025

Real-time forecasting of chaotic dynamics from sparse data and autoencoders

The real-time prediction of chaotic systems requires a nonlinear-reduced order model (ROM) to forecast the dynamics, and a stream of data from sensors to update the ROM. Data-driven ROMs are typically built with a two-step strategy: data compression in a lower-dimensional latent space, and prediction of the temporal dynamics on it. To achieve real-time prediction, however, there are two challenges to overcome: (i) ROMs of chaotic systems can become numerically unstable; and (ii) sensors' data are sparse, i.e., partial, and noisy. To overcome these challenges, we propose a three-step strategy: (i) a convolutional autoencoder (CAE) compresses the system's state onto a lower-dimensional latent space; (ii) a latent ROM (echo state network, ESN), which is formulated as a state-space model, predicts the temporal evolution on the latent space; and (iii) sequential data assimilation based on the Ensemble Kalman filter (EnKF) adaptively corrects the latent ROM by assimilating noisy and sparse measurements. This provides a numerically stable method (DA-CAE-ESN), which corrects itself every time that data becomes available from sensors. The DA-CAE-ESN is tested on spatio-temporally chaotic partial differential equations: the Kuramoto-Sivashinsky equation, and a two-dimensional Navier-Stokes equation (Kolmogorov flow). We show that the method provides accurate and stable forecasts across different levels of noise, sparsity, and sampling rates. As a by-product, the DA-CAE-ESN acts as a localization strategy that mitigates spurious correlations, which arise when applying the EnKF to high-dimensional systems. The DA-CAE-ESN provides a numerically stable method to perform real-time predictions, which opens opportunities for deploying data-driven latent models.

nlin.CD↗

arXiv2025

Online model learning with data-assimilated reservoir computers

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.

cs.LG↗

arXiv2025

Data-Assimilated Model-Based Reinforcement Learning for Partially Observed Chaotic Flows

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.

eess.SY↗

arXiv2024

Inferring unknown unknowns: Regularized bias-aware ensemble Kalman filter

Because of physical assumptions and numerical approximations, low-order models are affected by uncertainties in the state and parameters, and by model biases. Model biases, also known as model errors or systematic errors, are difficult to infer because they are `unknown unknowns', i.e., we do not necessarily know their functional form a priori. With biased models, data assimilation methods may be ill-posed because either (i) they are 'bias-unaware' because the estimators are assumed unbiased, (ii) they rely on an a priori parametric model for the bias, or (iii) they can infer model biases that are not unique for the same model and data. First, we design a data assimilation framework to perform combined state, parameter, and bias estimation. Second, we propose a mathematical solution with a sequential method, i.e., the regularized bias-aware ensemble Kalman Filter (r-EnKF), which requires a model of the bias and its gradient (i.e., the Jacobian). Third, we propose an echo state network as the model bias estimator. We derive the Jacobian of the network, and design a robust training strategy with data augmentation to accurately infer the bias in different scenarios. Fourth, we apply the r-EnKF to nonlinearly coupled oscillators (with and without time-delay) affected by different forms of bias. The r-EnKF infers in real-time parameters and states, and a unique bias. The applications that we showcase are relevant to acoustics, thermoacoustics, and vibrations; however, the r-EnKF opens new opportunities for combined state, parameter and bias estimation for real-time and on-the-fly prediction in nonlinear systems.

stat.ME↗

arXiv2024

A real-time digital twin of azimuthal thermoacoustic instabilities

When they occur, azimuthal thermoacoustic oscillations can detrimentally affect the safe operation of gas turbines and aeroengines. We develop a real-time digital twin of azimuthal thermoacoustics of a hydrogen-based annular combustor. The digital twin seamlessly combines two sources of information about the system (i) a physics-based low-order model; and (ii) raw and sparse experimental data from microphones, which contain both aleatoric noise and turbulent fluctuations. First, we derive a low-order thermoacoustic model for azimuthal instabilities, which is deterministic. Second, we propose a real-time data assimilation framework to infer the acoustic pressure, the physical parameters, and the model and measurement biases simultaneously. This is the bias-regularized ensemble Kalman filter (r-EnKF), for which we find an analytical solution that solves the optimization problem. Third, we propose a reservoir computer, which infers both the model bias and measurement bias to close the assimilation equations. Fourth, we propose a real-time digital twin of the azimuthal thermoacoustic dynamics of a laboratory hydrogen-based annular combustor for a variety of equivalence ratios. We find that the real-time digital twin (i) autonomously predicts azimuthal dynamics, in contrast to bias-unregularized methods; (ii) uncovers the physical acoustic pressure from the raw data, i.e., it acts as a physics-based filter; (iii) is a time-varying parameter system, which generalizes existing models that have constant parameters, and capture only slow-varying variables. The digital twin generalizes to all equivalence ratios, which bridges the gap of existing models. This work opens new opportunities for real-time digital twinning of multi-physics problems.

physics.flu-dyn↗

arXiv2022

Real-time thermoacoustic data assimilation

Low-order thermoacoustic models are qualitatively correct, but they are typically quantitatively inaccurate. We propose a time-domain bias-aware method to make qualitatively low--order models quantitatively (more) accurate. First, we develop a Bayesian ensemble data assimilation method for a low-order model to self-adapt and self-correct any time that reference data becomes available. Second, we apply the methodology to infer the thermoacoustic states and heat release parameters on the fly without storing data (real-time). We perform twin experiments using synthetic acoustic pressure measurements to analyse the performance of data assimilation in all nonlinear thermoacoustic regimes, from limit cycles to chaos, and interpret the results physically. Third, we propose practical rules for thermoacoustic data assimilation. An increase, reject, inflate strategy is proposed to deal with the rich nonlinear behaviour; and physical time scales for assimilation are proposed in non-chaotic regimes (with the Nyquist-Shannon criterion) and in chaotic regimes (with the Lyapunov time). Fourth, we perform data assimilation using data from a higher-fidelity model. We introduce an echo state network to estimate in real-time the forecast bias, which is the model error of the low-fidelity model. We show that (i) the correct acoustic pressure, parameters, and model bias can be accurately inferred; (ii) the learning is robust as it can tackle large uncertainties in the observations (up to 50% the mean values); (iii) the uncertainty of the prediction and parameters is naturally part of the output; and (iv) both the time-accurate solution and statistics can be successfully inferred. Data assimilation opens up new possibility for real-time prediction of thermoacoustics by synergistically combining physical knowledge and experimental data.

physics.flu-dyn↗