arXiv subjects

Luca Magri

Publications and source records attributed to Luca Magri.

At least 19 recordsLinked to original sources

arXiv2026

Fuzzy local reduced order models (fl-ROMs)

Nonlinear dynamical systems often evolve on low-dimensional manifolds with intricate geometry, making them difficult to approximate with a single global reduced-order model (ROM). To address this, we previously introduced quantized local reduced-order models (ql-ROMs), which partition the solution manifold into $K$ clusters and construct local ROMs around the corresponding centroids. In the sharp formulation, discontinuous switching between clusters can induce discontinuities, spurious oscillations, and loss of accuracy near cluster boundaries. Here, we propose a fuzzy extension of ql-ROMs based on fuzzy c-means clustering. The resulting fuzzy local ROM (fl-ROM) advances all local reduced states in parallel and combines their predictions through continuous membership weights, yielding a smooth partition-of-unity coupling of the local dynamics. We also introduce a pseudo-Bayesian information criterion to guide the selection of the number of clusters in the fuzzy setting. The methodology is assessed on the two-dimensional Kuramoto-Sivashinsky equation in periodic, travelling-wave-like, quasi-periodic, and chaotic regimes. In all cases, the local ROMs outperform the global ROM, while the fl-ROM provides smoother and generally more accurate predictions than the sharp formulation. In the chaotic regime, where long-time trajectory tracking is inherently limited, the fl-ROM achieves the best compromise between short-time predictive accuracy and long-term statistics. These results show that fl-ROM provides an effective, robust, and interpretable framework for reduced-order modeling of nonlinear dynamical systems with regime transitions and complex attractor geometry.

nlin.CD↗

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

Cell Phantom Video Generation in Elliptical Fourier Descriptor Domain

Training Deep Neural Networks for tracking individual cells in biomedical videos requires a large amount of annotated data. The annotation of videos for cell tracking is very time consuming and often requires domain expertise; this explains the limited availability of public annotated data to address important medical problems like tissue repair or cancer treatment. Generating synthetic videos along with their Ground Truth annotations is a promising solution that relies, as a foundational first step, on the synthesis of single cell annotations (or phantoms). Phantoms need to be time consistent, as they have to replicate biological processes that are specific to the cell types. In this work, we propose a novel framework for generating videos of cell phantoms in the Elliptical Fourier Descriptors (EFDs) domain, a compact and geometrically interpretable representation for 2D closed contours. We represent the cell phantom evolution as a multivariate time series of EFD coefficients, introducing a strong prior for cell morphology and enabling the efficient generation of sequences that evolve coherently in time. Our experimental validation proves that modelling the temporal evolution in EFD space enables the generation of biologically plausible phantom videos. Our method can be used in generative pipelines for synthesizing annotated data for cell tracking, thus strongly mitigating the annotation effort for creating new datasets. Our code is available for download here: https://github.com/FrancescoBenedetto99/efd-cell-video-gen.

cs.CV↗

arXiv2026

Precursors of extreme events and critical transitions

We propose a theory based on dynamical systems to explain and predict the occurrence of extreme events, of which critical transitions form a subset. In fast-slow nonlinear systems, we identify a cascade of events preceding extreme events: (i) a slow regime, in which the fast covariant Lyapunov vectors (CLVs) are both tangent to the fast eigenvectors and remain transversal to the slow subspace; (ii) a transition regime, in which the fast eigenvalues become neutrally stable while the fast CLVs are no longer tangent to the fast eigenvectors; and (iii) a critical regime, in which a strong spectral gap in the eigenvalues causes both fast and slow CLVs to become tangent along the dominant fast direction, breaking the transversality between fast and slow subspaces. Building on this cascade, we propose two precursors to forewarn the occurrence of extreme events. We numerically test the theory and precursors on low- and higher-dimensional systems. The proposed precursors predict extreme events and critical transitions with 100% precision and recall. This work opens opportunities for time-forecasting extreme events using theoretically grounded precursors.

nlin.CD↗

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

Adjoint-based optimization with quantized local reduced-order models for spatiotemporally chaotic systems

We introduce a computationally efficient and accurate reduced order modelling approach for the optimization of spatiotemporally chaotic systems. The proposed method combines quantized local reduced order modelling with adjoint-based optimization. We employ the methodology in a variational data assimilation problem for the chaotic Kuramoto-Sivashinsky equation and show that it successfully reconstructs the full trajectory for up to 0.25 Lyapunov times given full state measurements at the final time. The proposed algorithm provides 3.5 times speed-up when compared to the full-order model. The proposed method opens up new possibilities for the reduced order modelling of spatiotemporally chaotic systems.

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↗

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

LCF3D: A Robust and Real-Time Late-Cascade Fusion Framework for 3D Object Detection in Autonomous Driving

Accurately localizing 3D objects like pedestrians, cyclists, and other vehicles is essential in Autonomous Driving. To ensure high detection performance, Autonomous Vehicles complement RGB cameras with LiDAR sensors, but effectively combining these data sources for 3D object detection remains challenging. We propose LCF3D, a novel sensor fusion framework that combines a 2D object detector on RGB images with a 3D object detector on LiDAR point clouds. By leveraging multimodal fusion principles, we compensate for inaccuracies in the LiDAR object detection network. Our solution combines two key principles: (i) late fusion, to reduce LiDAR False Positives by matching LiDAR 3D detections with RGB 2D detections and filtering out unmatched LiDAR detections; and (ii) cascade fusion, to recover missed objects from LiDAR by generating new 3D frustum proposals corresponding to unmatched RGB detections. Experiments show that LCF3D is beneficial for domain generalization, as it turns out to be successful in handling different sensor configurations between training and testing domains. LCF3D achieves significant improvements over LiDAR-based methods, particularly for challenging categories like pedestrians and cyclists in the KITTI dataset, as well as motorcycles and bicycles in nuScenes. Code can be downloaded from: https://github.com/CarloSgaravatti/LCF3D.

cs.CV↗

arXiv2025

One target to align them all: LiDAR, RGB and event cameras extrinsic calibration for Autonomous Driving

We present a novel multi-modal extrinsic calibration framework designed to simultaneously estimate the relative poses between event cameras, LiDARs, and RGB cameras, with particular focus on the challenging event camera calibration. Core of our approach is a novel 3D calibration target, specifically designed and constructed to be concurrently perceived by all three sensing modalities. The target encodes features in planes, ChArUco, and active LED patterns, each tailored to the unique characteristics of LiDARs, RGB cameras, and event cameras respectively. This unique design enables a one-shot, joint extrinsic calibration process, in contrast to existing approaches that typically rely on separate, pairwise calibrations. Our calibration pipeline is designed to accurately calibrate complex vision systems in the context of autonomous driving, where precise multi-sensor alignment is critical. We validate our approach through an extensive experimental evaluation on a custom built dataset, recorded with an advanced autonomous driving sensor setup, confirming the accuracy and robustness of our method.

cs.CV↗

arXiv2025

Towards extreme event prediction of turbulent flows with quantized local reduced-order models

This work develops quantized local reduced-order models (ql-ROMs) of the turbulent Minimal Flow Unit (MFU) for the analysis and interpretation of intermittent dissipative dynamics and extreme events. The ql-ROM combines data-driven clustering of the flow state space with intrusive Galerkin projection on locally defined Proper Orthogonal Decomposition (POD) bases. This construction enables an accurate and stable low-dimensional representation of nonlinear flow dynamics whilst preserving the structure of the governing equations. The model is trained on direct numerical simulation data of the MFU. When deployed, the ql-ROM is numerically stable for long-term integration, and correctly infers the statistical behavior of the kinetic energy and dissipation observed of the full-order system. A local modal energy-budget formulation is employed to quantify intermodal energy transfer and viscous dissipation within each region of the attractor. The analysis reveals that dissipation bursts correspond to localized energy transfer from streamwise streaks and travelling-wave modes toward highly dissipative vortical structures, consistent with the self-sustaining process of near-wall turbulence. Beyond reduced modeling, the ql-ROM framework provides a pathway for the reduced-space characterization and potential prediction of extreme events. ql-ROM offer an interpretable and computationally efficient framework for the analysis and prediction of extreme events in turbulent flows.

physics.flu-dyn↗

arXiv2025

Reconstruction of three-dimensional turbulent flows from sparse and noisy planar measurements: A weight-sharing neural network approach

This paper proposes a method for reconstructing three-dimensional turbulent flows from sparse measurements without the need for ground truth data during training. A weight-sharing network is developed to infer the full flow fields from measurements of velocity sampled at three planes and boundary pressure at one additional plane, inspired by experimental configurations. The weight-sharing network shares identical parameters along homogeneous directions, which results in efficient data utilization and reduced computational memory requirements. First, we compare the weight-sharing network to the PC-DualConvNet, adapted from prior work, by reconstructing a 3D Kolmogorov flow from noise-free measurements with a snapshot-enforced loss. Both networks accurately recover time-averaged 3D flow fields and the correct energy spectrum up to wavenumber 10. The weight-sharing network has the ability to infer flow structures distant from measurement planes. Second, we carry out reconstruction from measurements corrupted with white noise (SNR 15) using a mean-enforced loss. We show that, for the weight-sharing network, validation sensor loss on unseen data decreases with training sensor loss -- unlike PC-DualConvNet. This shows improved generalization and that training sensor loss estimates generalization error. The weight-sharing network offers good generalization, parameter efficiency, and hyperparameter robustness. The proposed method opens the possibility of three-dimensional flow reconstruction from experiments.

physics.flu-dyn↗

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

Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability

We show that recurrent quantum reservoir computers (QRCs) and their recurrence-free architectures (RF-QRCs) are robust tools for learning and forecasting chaotic dynamics from time-series data. First, we formulate and interpret quantum reservoir computers as coupled dynamical systems, where the reservoir acts as a response system driven by training data; in other words, quantum reservoir computers are generalized-synchronization (GS) systems. Second, we show that quantum reservoir computers can learn chaotic dynamics and their invariant properties, such as Lyapunov spectra, attractor dimensions, and geometric properties such as the covariant Lyapunov vectors. This analysis is enabled by deriving the Jacobian of the quantum reservoir update. Third, by leveraging tools from generalized synchronization, we provide a method for designing robust quantum reservoir computers. We propose the criterion $GS=ESP$: GS implies the echo state property (ESP), and vice versa. We analytically show that RF-QRCs, by design, fulfill $GS=ESP$. Finally, we analyze the effect of simulated noise. We find that dissipation from noise enhances the robustness of quantum reservoir computers. Numerical verifications on systems of different dimensions support our conclusions. This work opens opportunities for designing robust quantum machines for chaotic time series forecasting on near-term quantum hardware.

quant-ph↗

arXiv2025

Quantized local reduced-order modeling in time (ql-ROM)

Spatiotemporally chaotic systems, such as the solutions of some nonlinear partial differential equations, are dynamical systems that evolve toward a lower dimensional manifold. This manifold has an intricate geometry with heterogeneous density, which makes the design of a single (global) nonlinear reduced-order model (ROM) challenging. In this paper, we turn this around. Instead of modeling the manifold with one single model, we partition the manifold into clusters within which the dynamics are locally modeled. This results in a quantized local reduced-order model (ql-ROM), which consists of (i) quantizing the manifold via unsupervised clustering; (ii) constructing intrusive ROMs for each cluster; and (iii) seamlessly patch the local models with a change of basis and assignment functions. We test the method on two nonlinear partial differential equations, i.e., the Kuramoto-Sivashinsky and 2D Navier-Stokes equations (Kolmogorov flow), across bursting, chaotic, quasiperiodic, and turbulent regimes. The local models are built via Galerkin projection onto the local principal directions, which are centered on the cluster centroids. The dynamics are modeled by switching a local ROM based on the cluster proximity. The proposed ql-ROM framework has three advantages over global ROMs (g-ROMs): (i) numerical stability, (ii) improved short-term prediction accuracy in time, and (iii) accurate prediction of long-term statistics, such as energy spectra and probability distributions. The computational overhead is minimal with respect to g-ROMs. The proposed framework retains the interpretability and simplicity of intrusive projection-based ROMs, whilst overcoming their limitations in modeling complex, high-dimensional, nonlinear dynamics.

physics.comp-ph↗

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

Hashing for Structure-based Anomaly Detection

We focus on the problem of identifying samples in a set that do not conform to structured patterns represented by low-dimensional manifolds. An effective way to solve this problem is to embed data in a high dimensional space, called Preference Space, where anomalies can be identified as the most isolated points. In this work, we employ Locality Sensitive Hashing to avoid explicit computation of distances in high dimensions and thus improve Anomaly Detection efficiency. Specifically, we present an isolation-based anomaly detection technique designed to work in the Preference Space which achieves state-of-the-art performance at a lower computational cost. Code is publicly available at https://github.com/ineveLoppiliF/Hashing-for-Structure-based-Anomaly-Detection.

cs.LG↗

arXiv2025

Preference Isolation Forest for Structure-based Anomaly Detection

We address the problem of detecting anomalies as samples that do not conform to structured patterns represented by low-dimensional manifolds. To this end, we conceive a general anomaly detection framework called Preference Isolation Forest (PIF), that combines the benefits of adaptive isolation-based methods with the flexibility of preference embedding. The key intuition is to embed the data into a high-dimensional preference space by fitting low-dimensional manifolds, and to identify anomalies as isolated points. We propose three isolation approaches to identify anomalies: $i$) Voronoi-iForest, the most general solution, $ii$) RuzHash-iForest, that avoids explicit computation of distances via Local Sensitive Hashing, and $iii$) Sliding-PIF, that leverages a locality prior to improve efficiency and effectiveness.

cs.LG↗