arXiv subjects

Soledad Le Clainche

Publications and source records attributed to Soledad Le Clainche.

At least 19 recordsLinked to original sources

arXiv2026

A hybrid proper orthogonal decomposition and diffusion framework for reduced-order forecasting of turbulent flow dynamics

Forecasting turbulent flow dynamics requires a balance between predictive fidelity and computational efficiency. Diffusion-based generative models can represent complex spatiotemporal dynamics, but their application to high-dimensional turbulent flows remains computationally expensive. In contrast, proper orthogonal decomposition (POD) provides compact, physically interpretable reduced-order representations, although aggressive modal truncation can remove relevant flow structures. This work introduces a hybrid reduced-order generative forecasting framework that combines POD with Generative Learning of Effective Dynamics (G-LED). The method performs temporal prediction in a physics-based modal space and uses diffusion-based reconstruction to recover physically meaningful flow-field representations. It is assessed using experimental measurements of the turbulent wake behind a circular cylinder. Three configurations are compared: full-field G-LED, global POD-G-LED, and localized POD-G-LED. Full-field G-LED provides the highest fidelity, preserving richer vorticity fluctuations and more consistent turbulent kinetic energy distributions, but requires approximately 17 h for diffusion-model training, 7 h for Transformer training, and 3 min to predict 100 future snapshots. By transferring prediction to a reduced POD space, global POD-G-LED reduces these costs to approximately 8 h, 2 h, and 50 s, respectively, while retaining dominant wake organization and coherent energetic structures. A localized POD-G-LED formulation assigns different modal resolutions to distinct wake regions and improves vorticity statistics and energetic distributions relative to the global reduced-order configuration. These results show that coupling physics-based modal representations with diffusion-based generative reconstruction offers an effective route to efficient turbulent-flow forecasting.

physics.flu-dyn↗

arXiv2026

GenDA: Generative Data Assimilation on Complex Urban Areas via Classifier-Free Diffusion Guidance

Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available. We propose GenDA, a generative data assimilation framework that reconstructs high-resolution wind fields on unstructured meshes from limited observations. The model employs a multiscale graph-based diffusion architecture trained on computational fluid dynamics (CFD) simulations and interprets classifier-free guidance as a learned posterior reconstruction mechanism: the unconditional branch learns a geometry-aware flow prior, while the sensor-conditioned branch injects observational constraints during sampling. This formulation enables obstacle-aware reconstruction and generalization to held-out mesh geometries, wind directions, and sensor configurations within the studied urban-flow setting, without retraining. We consider both sparse fixed sensors and trajectory-based observations using the same reconstruction procedure. When evaluated against supervised graph neural network (GNN) baselines and classical reduced-order data assimilation methods, GenDA reduces the relative root-mean-square error (RRMSE) by 25-57% and increases the structural similarity index (SSIM) by 23-33% across the tested meshes. Experiments are conducted on Reynolds-averaged Navier-Stokes (RANS) simulations of a real urban neighborhood in Bristol, United Kingdom, at a characteristic Reynolds number of $\mathrm{Re}\approx2\times10^{7}$, featuring complex building geometry and irregular terrain. The proposed framework provides a scalable path toward generative, geometry-aware data assimilation for environmental monitoring in complex domains.

cs.LG↗

arXiv2026

Low-Cost High-Order Singular Value Decomposition for Tensor-Based Reconstruction from Sparse Sensor Measurements: Urban Flow and Air-Quality Applications

Urban flow and air-quality simulations generate high-dimensional datasets describing velocity and pollutant transport across multiple spatial, temporal, and physical-variable dimensions. Reconstructing these fields from sparse sensor measurements is a fundamental challenge in environmental monitoring, digital twins, forecasting, and data assimilation. Existing low-cost reconstruction approaches are commonly based on matrix decompositions, which require multidimensional datasets to be flattened into two-dimensional snapshot matrices, thereby discarding important structural information. This work introduces the low-cost High-Order Singular Value Decomposition (lcHOSVD), a novel tensor-based sparse-sensing reconstruction framework for high-dimensional environmental fields. To the authors' knowledge, this is the first methodology that combines sparse sensing and HOSVD for field reconstruction. Unlike matrix-based approaches, lcHOSVD preserves the natural tensor structure of the data, enabling the exploitation of correlations across spatial, temporal, and physical-variable dimensions while substantially reducing the computational requirements of conventional HOSVD. The methodology is applied to urban flow and air-quality datasets, where three-dimensional velocity and pollutant concentration fields are reconstructed using only 1-4% of the available spatial locations. While lcSVD provides larger computational speed-ups, lcHOSVD consistently achieves lower reconstruction errors in configurations characterized by strong multidimensional coupling and heterogeneous dynamics across dimensions. Additional sensor-anisotropy analyses demonstrate that the tensor formulation is significantly more robust to uneven sensor distributions, a common situation in practical environmental monitoring networks.

cs.LG↗

arXiv2026

Divergence-aware adaptive prediction framework for accelerating CFD simulations of unsteady flows

Reliable long-horizon prediction remains a challenge for data-driven CFD surrogates, because offline-trained models accumulate autoregressive errors and lose accuracy when operating conditions change. This work develops a divergence-aware adaptive CFD-surrogate framework that couples a CFD solver with a proper orthogonal decomposition-deep learning (POD-DL) surrogate in a closed-loop workflow. CFD snapshots are compressed by POD, and a neural-network predictor advances the reduced state in time. The surrogate performs autoregressive forecasting, while its reliability is monitored online. When a prescribed update interval is reached or prediction degradation is detected, the CFD solver is automatically recalled to generate new snapshots and update the surrogate. The framework is assessed for three-dimensional flow past a circular cylinder at Re = 160-400. Baseline non-adaptive predictions exhibit progressive error growth over long forecast horizons, confirming the need for online correction. With prescribed update intervals, the adaptive framework preserves the dominant wake dynamics and reduces error growth after retraining compared with the non-adaptive model. For a representative 200-snapshot interval, the framework achieves a speed-up ratio of approximately 92 relative to CFD. An event-triggered mode is introduced using ensemble uncertainty and dynamically estimated thresholds. This mode terminates unreliable forecasts without requiring ground-truth CFD data during prediction, and the detected triggers are consistent with the onset of deterioration in the lift-coefficient evolution. Under varying inlet conditions, the framework detects regime changes, recalls CFD, and recovers reliable predictions. These results demonstrate that divergence-aware CFD-surrogate coupling provides a robust and efficient route for adaptive long-horizon flow prediction under evolving operating conditions.

physics.flu-dyn↗

arXiv2026

AeroJEPA: Learning Semantic Latent Representations for Scalable 3D Aerodynamic Field Modeling

Aerodynamic surrogate models are increasingly used to replace repeated high-fidelity CFD evaluations in many-query design settings, but current approaches still face two important limitations: they often scale poorly to the very large fields arising in realistic 3D aerodynamics, and they rarely produce latent representations that are directly useful for analysis and design. We introduce AeroJEPA, a Joint-Embedding Predictive Architecture for aerodynamic field modeling that addresses both issues. Rather than predicting the full flow field directly from geometry, AeroJEPA predicts a target latent representation of the flow from a context latent representation of the geometry and operating conditions, and optionally reconstructs the field through a continuous implicit decoder. This formulation decouples latent prediction from field resolution while encouraging the latent space to organize semantically. We evaluate AeroJEPA on two complementary datasets: HiLiftAeroML, which stresses the method in a high-fidelity regime with extremely large boundary-layer fields, and SuperWing, which tests large-scale generalization and latent-space optimization over a broad family of transonic wings. Across these benchmarks, AeroJEPA is competitive as a continuous surrogate for aerodynamic fields, scales naturally to high-resolution outputs, and learns context and predicted latents that encode geometry and aerodynamic quantities not used directly as supervision. We further show that the resulting latent space supports controlled interpolation, linear probing, concept-vector arithmetic, and a constrained design latent-optimization experiment. These results suggest that predictive latent learning is a promising direction for scalable and design-meaningful aerodynamic surrogate modeling.

cs.LG↗

arXiv2026

MoTIF: A Mode-Structured Tensor Framework for Multi-Parametric Approximation, Super-Resolution and Forecasting of Unsteady Systems

We introduce MoTIF, a mode-structured tensor framework for multi-parametric approximation, super-resolution, and temporal forecasting of high-dimensional unsteady systems. The methodology leverages High-Order Singular Value Decomposition (HOSVD) to obtain a structured multilinear representation of multi-dimensional datasets, separating physical parameters, spatial coordinates, and temporal evolution into distinct modal components. This decomposition enables the application of dedicated approximation operators to each mode. Gaussian Process Regression is employed to interpolate and extrapolate parametric and spatial modal matrices, enabling database completion and resolution enhancement, while recurrent neural networks are applied to the temporal mode to forecast system evolution. This decoupled operator-learning strategy preserves the intrinsic tensor structure while providing a flexible non-intrusive reduced-order modelling framework. The proposed methodology is validated on a database of unsteady laminar flow simulations with varying Reynolds numbers and angles of attack. Accurate reconstruction of unseen flow configurations and temporal prediction are achieved, with relative root mean square errors consistently below 2\% compared to high-fidelity simulations. The framework provides a scalable and mathematically structured alternative to conventional surrogate modelling approaches for high-dimensional parametric dynamical systems.

physics.flu-dyn↗

arXiv2026

Reduced-order modeling of a viscoelastic turbulent jet with hybrid machine learning models

Adding flexible polymers to a Newtonian solvent confers complex properties to the resulting solution. The additional complexity substantially increases the computational cost of numerical simulations, which often makes them prohibitively expensive. Here, we propose hybrid reduced-order models to accelerate simulations of viscoelastic turbulent jets. The model combines modal decompositions with deep networks: we use proper orthogonal decomposition to obtain a compact representation of the data, and a neural network is trained to predict the mode coefficients in the low-dimensional space. Results show that the hybrid model effectively captures the long-term behavior of the viscoelastic jet, that we demonstrate by computing relevant statistics of the jet. While small models are capable of predicting large-scale dynamics more than one-step at a time, thus facilitating greater accelerations, larger models are mandatory for forecasting smaller-scale dynamics, with skip connections the most effective strategy for deeper and generalizable models. The proposed methodology underpins the potential of hybrid approaches for compact and robust reduced-order models of viscoelastic turbulent jets.

physics.flu-dyn↗

arXiv2026

Coherent structures in Newtonian and viscoelastic turbulent planar jets

The addition of a small amount of long-chain polymers confers viscoelastic properties to Newtonian flows. The resulting non-Newtonian solution now exhibits different dynamics, such as enhanced mixing at low Reynolds, where elastic instabilities can trigger elastic turbulence even though inertial turbulence is absent. Here, we study this phenomenon in viscoelastic planar jets and, in particular, we do it from the perspective of coherent structures to understand how elastic turbulence is triggered and sustained, which remain barely explored in this setup. We introduce the spatio-temporal Koopman decomposition for extracting the dominant flow patterns, and we compare them with those from Newtonian planar jets at high Reynolds number. Global flow structures are similar between jets, with low-frequency streaks and high-frequency wave packets dominating the turbulent dynamics. However, structures are strikingly different in the near field, where elasticity-driven streaks affect the dynamics in the potential core of the viscoelastic planar jet, modifying the bulk flow and interacting with the flow instability. The analysis of the polymer field reveals stretched polymer filaments and centre-mode structures, which support the implication of the near-field streaks on sustaining elastic turbulence in three-dimensional viscoelastic planar jets.

physics.flu-dyn↗

arXiv2026

A temporal deep learning framework for calibration of low-cost air quality sensors

Low-cost air quality sensors (LCS) provide a practical alternative to expensive regulatory-grade instruments, making dense urban monitoring networks possible. Yet their adoption is limited by calibration challenges, including sensor drift, environmental cross-sensitivity, and variability in performance from device to device. This work presents a deep learning framework for calibrating LCS measurements of PM$_{2.5}$, PM$_{10}$, and NO$_2$ using a Long Short-Term Memory (LSTM) network, trained on co-located reference data from the OxAria network in Oxford, UK. Unlike the Random Forest (RF) baseline, which treats each observation independently, the proposed approach captures temporal dependencies and delayed environmental effects through sequence-based learning, achieving higher $R^2$ values across training, validation, and test sets for all three pollutants. A feature set is constructed combining time-lagged parameters, harmonic encodings, and interaction terms to improve generalization on unseen temporal windows. Validation of unseen calibrated values against the Equivalence Spreadsheet Tool 3.1 demonstrates regulatory compliance with expanded uncertainties of 22.11% for NO$_2$, 12.42% for PM$_{10}$, and 9.1% for PM$_{2.5}$.

cs.LG↗

arXiv2026

Clustering the Flow: A Data-Driven Framework for Pattern Discovery in Fluid Dynamics

Clustering techniques offer a powerful framework for analyzing complex flow dynamics and reducing computational costs in large-scale simulations. In this work, we propose a novel clustering-based approach using Vector Quantization Principal Component Analysis (VQPCA) to identify structural sensitivity zones, namely the regions where the fluid flow is more receptive to changes. To the authors knowledge, this is the first application of VQPCA to a fluid dynamics problem for the identification of flow patterns and dynamically relevant regions. As a fully data-driven technique, it does not rely on adjoint methods; therefore, this approach has the advantage of having low computational cost, since it depends exclusively on data from the direct problem. The VQPCA technique demonstrates its ability to extract dominant flow features by clustering the flow field into regions characterized by their intrinsic dynamics. To assess the validity of this method, it is used to investigate the wake behind a circular cylinder, revealing similarities to previously established structural sensitivity regions. The robustness of the approach is further assessed through validation and calibration in different operating conditions in this flow scenario. As an extension of the analysis, we address the complex dynamics of two planar synthetic jets, where the clustering insights can lead to develop flow control strategies. These results highlight the potential of clustering-based methods as practical and effective tools to analyze and optimize fluid flows.

physics.flu-dyn↗

arXiv2026

Agentic Exploration of PDE Spaces using Latent Foundation Models for Parameterized Simulations

Flow physics and more broadly physical phenomena governed by partial differential equations (PDEs), are inherently continuous, high-dimensional and often chaotic in nature. Traditionally, researchers have explored these rich spatiotemporal PDE solution spaces using laboratory experiments and/or computationally expensive numerical simulations. This severely limits automated and large-scale exploration, unlike domains such as drug discovery or materials science, where discrete, tokenizable representations naturally interface with large language models. We address this by coupling multi-agent LLMs with latent foundation models (LFMs), a generative model over parametrised simulations, that learns explicit, compact and disentangled latent representations of flow fields, enabling continuous exploration across governing PDE parameters and boundary conditions. The LFM serves as an on-demand surrogate simulator, allowing agents to query arbitrary parameter configurations at negligible cost. A hierarchical agent architecture orchestrates exploration through a closed loop of hypothesis, experimentation, analysis and verification, with a tool-modular interface requiring no user support. Applied to flow past tandem cylinders at Re = 500, the framework autonomously evaluates over 1,600 parameter-location pairs and discovers divergent scaling laws: a regime-dependent two-mode structure for minimum displacement thickness and a robust linear scaling for maximum momentum thickness, with both landscapes exhibiting a dual-extrema structure that emerges at the near-wake to co-shedding regime transition. The coupling of the learned physical representations with agentic reasoning establishes a general paradigm for automated scientific discovery in PDE-governed systems.

cs.AI↗

arXiv2026

CardioMOD-Net: A Modal Decomposition-Neural Network Framework for Diagnosis and Prognosis of HFpEF from Echocardiography Cine Loops

Introduction: Heart failure with preserved ejection fraction (HFpEF) arises from diverse comorbidities and progresses through prolonged subclinical stages, making early diagnosis and prognosis difficult. Current echocardiography-based Artificial Intelligence (AI) models focus primarily on binary HFpEF detection in humans and do not provide comorbidity-specific phenotyping or temporal estimates of disease progression towards decompensation. We aimed to develop a unified AI framework, CardioMOD-Net, to perform multiclass diagnosis and continuous prediction of HFpEF onset directly from standard echocardiography cine loops in preclinical models. Methods: Mouse echocardiography videos from four groups were used: control (CTL), hyperglycaemic (HG), obesity (OB), and systemic arterial hypertension (SAH). Two-dimensional parasternal long-axis cine loops were decomposed using Higher Order Dynamic Mode Decomposition (HODMD) to extract temporal features for downstream analysis. A shared latent representation supported Vision Transformers, one for a classifier for diagnosis and another for a regression module for predicting the age at HFpEF onset. Results: Overall diagnostic accuracy across the four groups was 65%, with all classes exceeding 50% accuracy. Misclassifications primarily reflected early-stage overlap between OB or SAH and CTL. The prognostic module achieved a root-mean-square error of 21.72 weeks for time-to-HFpEF prediction, with OB and SAH showing the most accurate estimates. Predicted HFpEF onset closely matched true distributions in all groups. Discussion: This unified framework demonstrates that multiclass phenotyping and continuous HFpEF onset prediction can be obtained from a single cine loop, even under small-data conditions. The approach offers a foundation for integrating diagnostic and prognostic modelling in preclinical HFpEF research.

cs.CV↗

arXiv2025

A Critical Assessment of Pattern Comparisons Between POD and Autoencoders in Intraventricular Flows

Understanding intraventricular hemodynamics requires compact and physically interpretable representations of the underlying flow structures, as characteristic flow patterns are closely associated with cardiovascular conditions and can support early detection of cardiac deterioration. Conventional visualization of velocity or pressure fields, however, provides limited insight into the coherent mechanisms driving these dynamics. Reduced-order modeling techniques, like Proper Orthogonal Decomposition (POD) and Autoencoder (AE) architectures, offer powerful alternatives to extract dominant flow features from complex datasets. This study systematically compares POD with several AE variants (Linear, Nonlinear, Convolutional, and Variational) using left ventricular flow fields obtained from computational fluid dynamics simulations. We show that, for a suitably chosen latent dimension, AEs produce modes that become nearly orthogonal and qualitatively resemble POD modes that capture a given percentage of kinetic energy. As the number of latent modes increases, AE modes progressively lose orthogonality, leading to linear dependence, spatial redundancy, and the appearance of repeated modes with substantial high-frequency content. This degradation reduces interpretability and introduces noise-like components into AE-based reduced-order models, potentially complicating their integration with physics-based formulations or neural-network surrogates. The extent of interpretability loss varies across the AEs, with nonlinear, convolutional, and variational models exhibiting distinct behaviors in orthogonality preservation and feature localization. Overall, the results indicate that AEs can reproduce POD-like coherent structures under specific latent-space configurations, while highlighting the need for careful mode selection to ensure physically meaningful representations of cardiac flow dynamics.

physics.flu-dyn↗

arXiv2025

Heart Failure Prediction using Modal Decomposition and Masked Autoencoders for Scarce Echocardiography Databases

Heart diseases remain the leading cause of mortality worldwide, implying approximately 18 million deaths according to the WHO. In particular, heart failures (HF) press the healthcare industry to develop systems for their early, rapid, and effective prediction. This work presents an automatic system based on a novel framework which combines Modal Decomposition and Masked Autoencoders (MAE) to extend the application from heart disease classification to the more challenging and specific task of heart failure time prediction, not previously addressed to the best of authors' knowledge. This system comprises two stages. The first one transforms the data from a database of echocardiography video sequences into a large collection of annotated images compatible with the training phase of machine learning-based frameworks and deep learning-based ones. This stage includes the use of the Higher Order Dynamic Mode Decomposition (HODMD) algorithm for both data augmentation and feature extraction. The second stage builds and trains a Vision Transformer (ViT). MAEs based on a combined scheme of self-supervised (SSL) and supervised learning, so far barely explored in the literature about heart failure prediction, are adopted to effectively train the ViT from scratch, even with scarce databases. The designed neural network analyses in real-time images from echocardiography sequences to estimate the time of happening a heart failure. This approach demonstrates to improve prediction accuracy from scarce databases and to be superior to several established ViT and Convolutional Neural Network (CNN) architectures. The source code will be incorporated into the next version release of the ModelFLOWs-app software (https://github.com/modelflows/ModelFLOWs-app).

eess.IV↗

arXiv2025

Generative Urban Flow Modeling: From Geometry to Airflow with Graph Diffusion

Urban wind flow modeling and simulation play an important role in air quality assessment and sustainable city planning. A key challenge for modeling and simulation is handling the complex geometries of the urban landscape. Low order models are limited in capturing the effects of geometry, while high-fidelity Computational Fluid Dynamics (CFD) simulations are prohibitively expensive, especially across multiple geometries or wind conditions. Here, we propose a generative diffusion framework for synthesizing steady-state urban wind fields over unstructured meshes that requires only geometry information. The framework combines a hierarchical graph neural network with score-based diffusion modeling to generate accurate and diverse velocity fields without requiring temporal rollouts or dense measurements. Trained across multiple mesh slices and wind angles, the model generalizes to unseen geometries, recovers key flow structures such as wakes and recirculation zones, and offers uncertainty-aware predictions. Ablation studies confirm robustness to mesh variation and performance under different inference regimes. This work develops is the first step towards foundation models for the built environment that can help urban planners rapidly evaluate design decisions under densification and climate uncertainty.

cs.LG↗

arXiv2025

The coherent structures of EVP Fluid Flow Past a Circular Cylinder

This study investigates the impact of elasticity and plasticity on two-dimensional flow past a circular cylinder at Reynolds number $Re = 100$. Ten direct numerical simulations were performed using the Saramito-Herschel-Bulkley model to represent viscoelastic and elastoviscoplastic (EVP) fluids. The flow evolves from a periodic von Kármán vortex street to chaotic-like regimes. Proper Orthogonal Decomposition (POD) and Higher Order Dynamic Mode Decomposition (HODMD) are applied to extract dominant flow structures and their temporal dynamics. For viscoelastic fluids, increasing the Weissenberg number $Wi$ elongates the recirculation bubble and shifts it downstream, resulting in more intricate but still periodic behavior. In EVP fluids, seven cases explore variations in Bingham number Bn, solvent viscosity ratio $β_s$, and power law index n, aiming to qualitatively assess their influence rather than determine critical thresholds. Results indicate that stronger plastic effects, especially with n>1, lead to increased flow complexity. Three dynamic regimes are identified: (i) periodic; (ii) transitional, with elongated recirculation and disrupted periodicity; and (iii) fully complex, with breakdown of recirculation. Overall, the study highlights the interplay between inertia, elasticity, and yield stress in non-Newtonian flows past obstacles and identifies key parameters driving the transition from periodic to complex regimes.

physics.flu-dyn↗

arXiv2025

Characterizing Intraventricular Flow Patterns via Modal Decomposition Techniques in Idealized Left Ventricle Models

Understanding the formation, propagation, and breakdown of the main vortex ring (VR) is essential for characterizing left ventricular (LV) hemodynamics, as its dynamics have been linked to the onset and progression of cardiovascular diseases. In this study, two idealized LV geometries, a semi-ellipsoidal chamber and a more rounded configuration, are analyzed using computational fluid dynamics (CFD) simulations under physiological conditions, with the aim of investigating the fluid mechanisms that govern VR evolution during diastole. Modal decomposition techniques, specifically proper orthogonal decomposition (POD) and higher order dynamic mode decomposition (HODMD), are employed to identify dominant coherent structures and track their temporal behavior. To the authors' knowledge, this is the first time such an analysis is conducted with the explicit goal of unraveling the physics of vortex ring dynamics in idealized ventricular chambers. The comparative approach reveals that geometric morphology plays a central role in modulating the flow: in one case, early interaction between the VR and the ventricular wall, driven by the chamber's shape, triggers strong nonlinear interactions and a more intricate dynamic evolution. In the other, the vortex ring propagates more freely toward the apex before dissipating, resulting in a more organized flow pattern and simpler spectral content. These findings advance the understanding of flow-based indicators relevant to early diagnosis and treatment planning in cardiovascular disease. Moreover, they illustrate how the choice of ventricular geometry can influence not only the simulated hemodynamics, but also the effectiveness of data-driven analysis tools, depending on the clinical context under study.

physics.flu-dyn↗

arXiv2025

Efficient Reduced Order Modeling Based on HODMD to Predict Intraventricular Flow Dynamics

Accurate and efficient modeling of cardiac blood flow is crucial for advancing data-driven tools in cardiovascular research and clinical applications. Recently, the accuracy and availability of computational fluid dynamics (CFD) methodologies for simulating intraventricular flow have increased. However, these methods remain complex and computationally costly. This study presents a reduced order model (ROM) based on higher order dynamic mode decomposition (HODMD). The proposed approach enables accurate reconstruction and long term prediction of left ventricle flow fields. The method is tested on two idealized ventricular geometries exhibiting distinct flow regimes to assess its robustness under different hemodynamic conditions. By leveraging a small number of training snapshots and focusing on the dominant periodic components representing the physics of the system, the HODMD-based model accurately reconstructs the flow field over entire cardiac cycles and provides reliable long-term predictions beyond the training window. The reconstruction and prediction errors remain below 5\% for the first geometry and below 10\% for the second, even when using as few as the first 3 cycles of simulated data, representing the transitory regime. Additionally, the approach reduces computational costs with a speed-up factor of at least $10^{5}$ compared to full-order simulations, enabling fast surrogate modeling of complex cardiac flows. These results highlight the potential of spectrally-constrained HODMD as a robust and interpretable ROM for simulating intraventricular hemodynamics. This approach shows promise for integration in real-time analysis and patient specific models.

physics.flu-dyn↗