arXiv subjects

Eusebio Valero

Publications and source records attributed to Eusebio Valero.

At least 19 recordsLinked to original sources

arXiv2026

Mesh Adaptation on Hybrid Unstructured Meshes for Immersed Boundary Methods

In this work, we describe a new preprocessing tool for mesh adaptation on hybrid unstructured meshes with a target application on immersed boundary methods. The tool has as input an unstructured, hybrid, and conforming mesh generated by an external mesh generation software, and the main goal is to refine this mesh around immersed geometries in such a way that the CFD solver using the immersed boundary method can simulate flow problems in an accurate and efficient manner. The input background mesh can be made of different types of elements, like tetrahedra, hexahedra, prisms, and pyramids, which, unlike Cartesian meshes, permit for a more flexible mesh. Hybrid unstructured meshes enable one to use the immersed boundary technology in a new class of flow problems where the full geometry is decomposed into a fixed geometry part and a changing geometry part. A body-fitted mesh is generated for the fixed geometry while for the changing one is used the immersed boundary method. We simulate several flow problems to test the new meshes, including subsonic flow past a cylinder and subsonic flow past an NACA0012 airfoil, both using finite volume and discontinuous Galerkin methods and solving the Navier--Stokes equations. As an industrial example of our mesh generation, we consider the simulation of a multi-element airfoil: in this case, a mesh generation software generates an unstructured conforming background mesh for the slat and main airfoil, while the flap is placed as immersed geometry in this body-fitted mesh. As accurate and efficient results are sought, this mesh is refined around the flap and then the subsonic flow at high-lift flow conditions is simulated with a finite volume method coupled with an immersed boundary method and using the Reynolds--averaged Navier--Stokes equations. The reported numerical simulations are in good agreement with experimental data.

physics.flu-dyn↗

arXiv2026

HORSES3D-GPU: A high-order discontinuous Galerkin solver for multi-GPU systems

We present the GPU acceleration and large-scale performance assessment of HORSES3D, an open-source high-order discontinuous Galerkin solver for computational fluid dynamics. The solver is ported to NVIDIA GPU architectures using OpenACC directives, preserving the original Fortran code structure while enabling GPU-resident execution of the main computational kernels. The implementation exploits the element-local structure of discontinuous Galerkin spectral element methods by mapping element-level loops to GPU gangs and nodal operations to vector-level parallelism. The GPU version is verified using the method of manufactured solutions and validated on canonical turbulent-flow benchmarks. Its performance is assessed on the MareNostrum 5 accelerated partition using NVIDIA H100 GPUs. Taylor-Green vortex benchmarks show that solver efficiency improves with polynomial order and that near-ideal strong and weak scaling is obtained when the workload exceeds approximately 16,000 to 20,000 elements per GPU. The solver is further evaluated on the High-Lift Common Research Model wing-body configuration, which involves a complex geometry, realistic boundary conditions, and unstructured meshes with up to 20.8 million hexahedral elements. Simulations with polynomial orders up to $P=7$ reach approximately $10.7 \times 10^9$ degrees of freedom and scale efficiently to 2,048 GPUs. The results demonstrate that HORSES3D preserves its performance characteristics for industrially relevant configurations and can exploit modern GPU-based supercomputers for billion-degree-of-freedom high-order CFD simulations.

math.NA↗

arXiv2026

Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs

Kolmogorov Arnold networks (KAN) have recently been introduced as a (deep) neural network architecture whose trainable parameters adapt the activation functions, instead of the coefficients of the affine transformations at the core of traditional architectures such as deep multilayer perceptrons (MLPs). This architecture builds on the Kolmogorov-Arnold theorem, which endows it with universal approximation properties. While the advent of KANs has been received with excitement, there is a current debate about the possible KAN supremacy over deep multilayer perceptrons (MLPs) for classic fields such as symbolic regression, generic-purpose machine learning, natural language processing or computer vision. Here we assess the performance of KANs --and its nuanced comparison against MLPs and graph neural networks (GNNs)-- in the realm of fluid dynamics surrogate modelling. To that aim, we consider the task of predicting the surface pressure distribution over subsonic and transonic airfoils, a canonical task in aerodynamics. Our results show that KAN models show good performance in predicting the whole pressure coefficients and is able to interpolate across Mach numbers and angles of attack, however its performance is comparable --marginally inferior-- to a suitably trained MLP, where best performance is achieved by a GNN at the expense or requiring lengthier training. While the optimal KAN model have typically much lower complexity than MLP and GNN --hence resulting in faster training--, we find that KANs suffer from training instabilities, and their performance is highly dependent on a proper hyperparameter optimisation.

cs.LG↗

arXiv2026

FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes

Computational fluid dynamics (CFD) provides high-fidelity simulations of fluid flows but remains computationally expensive for many-query applications. In recent years deep learning (DL) has been used to construct data-driven fluid-dynamic surrogate models. In this work we consider a different learning paradigm and embrace generative modelling as a framework for constructing scalable fluid-dynamics surrogate models. We introduce FluidFlow, a generative model based on conditional flow-matching, a recent alternative to diffusion models that learns deterministic transport maps between noise and data distributions. FluidFlow is specifically designed to operate directly on CFD data defined on both structured and unstructured meshes alike, without the needs to perform any mesh interpolation pre-processing and preserving geometric fidelity. We assess the capabilities of FluidFlow using two different core neural network architectures, a U-Net and diffusion transformer (DiT), and condition their learning on physically meaningful parameters. The methodology is validated on two benchmark problems of increasing complexity: prediction of pressure coefficients along an airfoil boundary across different operating conditions, and prediction of pressure and friction coefficients over a full three-dimensional aircraft geometry discretized on a large unstructured mesh. In both cases, FluidFlow outperform strong multilayer perceptron baselines, achieving significantly lower error metrics and improved generalisation across operating conditions. Notably, the transformer-based architecture enables scalable learning on large unstructured datasets while maintaining high predictive accuracy. These results demonstrate that flow-matching generative models provide an effective and flexible framework for surrogate modelling in fluid dynamics, with potential for realistic engineering and scientific applications.

cs.LG↗

arXiv2026

On the Role of Consistency Between Physics and Data in Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have gained significant attention as a surrogate modeling strategy for partial differential equations (PDEs), particularly in regimes where labeled data are scarce and physical constraints can be leveraged to regularize the learning process. In practice, however, PINNs are frequently trained using experimental or numerical data that are not fully consistent with the governing equations due to measurement noise, discretization errors, or modeling assumptions. The implications of such data-to-PDE inconsistencies on the accuracy and convergence of PINNs remain insufficiently understood. In this work, we systematically analyze how data inconsistency fundamentally limits the attainable accuracy of PINNs. We introduce the concept of a consistency barrier, defined as an intrinsic lower bound on the error that arises from mismatches between the fidelity of the data and the exact enforcement of the PDE residual. To isolate and quantify this effect, we consider the 1D viscous Burgers equation with a manufactured analytical solution, which enables full control over data fidelity and residual errors. PINNs are trained using datasets of progressively increasing numerical accuracy, as well as perfectly consistent analytical data. Results show that while the inclusion of the PDE residual allows PINNs to partially mitigate low-fidelity data and recover the dominant physical structure, the training process ultimately saturates at an error level dictated by the data inconsistency. When high-fidelity numerical data are employed, PINN solutions become indistinguishable from those trained on analytical data, indicating that the consistency barrier is effectively removed. These findings clarify the interplay between data quality and physics enforcement in PINNs providing practical guidance for the construction and interpretation of physics-informed surrogate models.

cs.LG↗

arXiv2025

Reliable Statistical Guarantees for Conformal Predictors with Small Datasets

Surrogate models (including deep neural networks and other machine learning algorithms in supervised learning) are capable of approximating arbitrarily complex, high-dimensional input-output problems in science and engineering, but require a thorough data-agnostic uncertainty quantification analysis before these can be deployed for any safety-critical application. The standard approach for data-agnostic uncertainty quantification is to use conformal prediction (CP), a well-established framework to build uncertainty models with proven statistical guarantees that do not assume any shape for the error distribution of the surrogate model. However, since the classic statistical guarantee offered by CP is given in terms of bounds for the marginal coverage, for small calibration set sizes (which are frequent in realistic surrogate modelling that aims to quantify error at different regions), the potentially strong dispersion of the coverage distribution around its average negatively impacts the relevance of the uncertainty model's statistical guarantee, often obtaining coverages below the expected value, resulting in a less applicable framework. After providing a gentle presentation of uncertainty quantification for surrogate models for machine learning practitioners, in this paper we bridge the gap by proposing a new statistical guarantee that offers probabilistic information for the coverage of a single conformal predictor. We show that the proposed framework converges to the standard solution offered by CP for large calibration set sizes and, unlike the classic guarantee, still offers relevant information about the coverage of a conformal predictor for small data sizes. We validate the methodology in a suite of examples, and implement an open access software solution that can be used alongside common conformal prediction libraries to obtain uncertainty models that fulfil the new guarantee.

cs.LG↗

arXiv2025

Can Explicit Subgrid Models Enhance Implicit LES Simulations? A Very High-Order Solver Perspective

High-order discontinuous Galerkin (DG) methods offer excellent accuracy for turbulent-flow simulations and are increasingly attractive on GPU-oriented architectures, where high polynomial orders can improve arithmetic intensity. However, very high-order under-resolved simulations remain sensitive to the balance between numerical and modeled dissipation. We investigate how explicit Vreman subgrid-scale (SGS) modeling interacts with dissipation from split-form stabilization and Riemann solvers in a DGSEM framework. Using the three-dimensional Taylor-Green vortex at Re=1600 and in the inviscid limit, we assess kinetic-energy dissipation, spectral accuracy, and stability across well-resolved, under-resolved viscous, and strongly under-resolved regimes, comparing lower- and very high-order configurations at similar degrees of freedom. The usefulness of explicit SGS modeling depends strongly on resolution, polynomial order, and the numerical dissipation already present. In the well-resolved cases considered, Vreman modeling does not improve accuracy because its active wavenumber range overlaps with the scheme's inherent dissipation. At similar degrees of freedom, lower-order simulations introduce stronger damping near the smallest resolved scales, whereas very high-order simulations preserve more spectral content but are more susceptible to high-wavenumber energy accumulation when dissipation is insufficient. Under stronger under-resolution, a weak SGS contribution can control this accumulation, while excessive SGS dissipation degrades intermediate scales. These results identify regimes in which explicit SGS modeling is beneficial, neutral, or detrimental, and provide practical guidance for selecting dissipation mechanisms in very high-order DG turbulence simulations suited to modern GPU architectures.

physics.flu-dyn↗

arXiv2025

A Certifiable Machine Learning-Based Pipeline to Predict Fatigue Life of Aircraft Structures

Fatigue life prediction is essential in both the design and operational phases of any aircraft, and in this sense safety in the aerospace industry requires early detection of fatigue cracks to prevent in-flight failures. Robust and precise fatigue life predictors are thus essential to ensure safety. Traditional engineering methods, while reliable, are time consuming and involve complex workflows, including steps such as conducting several Finite Element Method (FEM) simulations, deriving the expected loading spectrum, and applying cycle counting techniques like peak-valley or rainflow counting. These steps often require collaboration between multiple teams and tools, added to the computational time and effort required to achieve fatigue life predictions. Machine learning (ML) offers a promising complement to traditional fatigue life estimation methods, enabling faster iterations and generalization, providing quick estimates that guide decisions alongside conventional simulations. In this paper, we present a ML-based pipeline that aims to estimate the fatigue life of different aircraft wing locations given the flight parameters of the different missions that the aircraft will be operating throughout its operational life. We validate the pipeline in a realistic use case of fatigue life estimation, yielding accurate predictions alongside a thorough statistical validation and uncertainty quantification. Our pipeline constitutes a complement to traditional methodologies by reducing the amount of costly simulations and, thereby, lowering the required computational and human resources.

cs.LG↗

arXiv2025

Transfer learning-enhanced deep reinforcement learning for aerodynamic airfoil optimisation subject to structural constraints

The main objective of this paper is to introduce a transfer learning-enhanced deep reinforcement learning (DRL) methodology that is able to optimise the geometry of any airfoil based on concomitant aerodynamic and structural integrity criteria. To showcase the method, we aim to maximise the lift-to-drag ratio $C_L/C_D$ while preserving the structural integrity of the airfoil -- as modelled by its maximum thickness -- and train the DRL agent using a list of different transfer learning (TL) strategies. The performance of the DRL agent is compared with Particle Swarm Optimisation (PSO), a traditional gradient-free optimisation method. Results indicate that DRL agents are able to perform purely aerodynamic and hybrid aerodynamic/structural shape optimisation, that the DRL approach outperforms PSO in terms of computational efficiency and aerodynamic improvement, and that the TL-enhanced DRL agent achieves performance comparable to the DRL one, while further saving substantial computational resources.

cs.LG↗

arXiv2024

EigenHearts: Cardiac Diseases Classification Using EigenFaces Approach

In the realm of cardiovascular medicine, medical imaging plays a crucial role in accurately classifying cardiac diseases and making precise diagnoses. However, the field faces significant challenges when integrating data science techniques, as a significant volume of images is required for these techniques. As a consequence, it is necessary to investigate different avenues to overcome this challenge. In this contribution, we offer an innovative tool to conquer this limitation. In particular, we delve into the application of a well recognized method known as the EigenFaces approach to classify cardiac diseases. This approach was originally motivated for efficiently representing pictures of faces using principal component analysis, which provides a set of eigenvectors (aka eigenfaces), explaining the variation between face images. As this approach proven to be efficient for face recognition, it motivated us to explore its efficiency on more complicated data bases. In particular, we integrate this approach, with convolutional neural networks (CNNs) to classify echocardiography images taken from mice in five distinct cardiac conditions (healthy, diabetic cardiomyopathy, myocardial infarction, obesity and TAC hypertension). Performing a preprocessing step inspired from the eigenfaces approach on the echocardiography datasets, yields sets of pod modes, which we will call eigenhearts. To demonstrate the proposed approach, we compare two testcases: (i) supplying the CNN with the original images directly, (ii) supplying the CNN with images projected into the obtained pod modes. The results show a substantial and noteworthy enhancement when employing SVD for pre-processing, with classification accuracy increasing by approximately 50%.

eess.IV↗

arXiv2024

A Novel Data Augmentation Tool for Enhancing Machine Learning Classification: A New Application of the Higher Order Dynamic Mode Decomposition for Improved Cardiac Disease Identification

In this work, a data-driven, modal decomposition method, the higher order dynamic mode decomposition (HODMD), is combined with a convolutional neural network (CNN) in order to improve the classification accuracy of several cardiac diseases using echocardiography images. The HODMD algorithm is used first as feature extraction technique for the echocardiography datasets, taken from both healthy mice and mice afflicted by different cardiac diseases (Diabetic Cardiomyopathy, Obesity, TAC Hypertrophy and Myocardial Infarction). A total number of 130 echocardiography datasets are used in this work. The dominant features related to each cardiac disease were identified and represented by the HODMD algorithm as a set of DMD modes, which then are used as the input to the CNN. In a way, the database dimension was augmented, hence HODMD has been used, for the first time to the authors knowledge, for data augmentation in the machine learning framework. Six sets of the original echocardiography databases were hold out to be used as unseen data to test the performance of the CNN. In order to demonstrate the efficiency of the HODMD technique, two testcases are studied: the CNN is first trained using the original echocardiography images only, and second training the CNN using a combination of the original images and the DMD modes. The classification performance of the designed trained CNN shows that combining the original images with the DMD modes improves the results in all the testcases, as it improves the accuracy by up to 22%. These results show the great potential of using the HODMD algorithm as a data augmentation technique.

eess.IV↗

arXiv2024

Towards certification: A complete statistical validation pipeline for supervised learning in industry

Methods of Machine and Deep Learning are gradually being integrated into industrial operations, albeit at different speeds for different types of industries. The aerospace and aeronautical industries have recently developed a roadmap for concepts of design assurance and integration of neural network-related technologies in the aeronautical sector. This paper aims to contribute to this paradigm of AI-based certification in the context of supervised learning, by outlining a complete validation pipeline that integrates deep learning, optimization and statistical methods. This pipeline is composed by a directed graphical model of ten steps. Each of these steps is addressed by a merging key concepts from different contributing disciplines (from machine learning or optimization to statistics) and adapting them to an industrial scenario, as well as by developing computationally efficient algorithmic solutions. We illustrate the application of this pipeline in a realistic supervised problem arising in aerostructural design: predicting the likelikood of different stress-related failure modes during different airflight maneuvers based on a (large) set of features characterising the aircraft internal loads and geometric parameters.

cs.LG↗

arXiv2024

A comparison of h- and p-refinement to capture wind turbine wakes

This paper investigates a critical aspect of wind energy research - the development of wind turbine wake and its significant impact on wind farm efficiency. The study focuses on the exploration and comparison of two mesh refinement strategies, h- and p-refinement, in their ability to accurately compute the development of wind turbine wake. The h-refinement method refines the mesh by reducing the size of the elements, while the p-refinement method increases the polynomial degree of the elements, potentially reducing the error exponentially for smooth flows. A comprehensive comparison of these methods is presented that evaluates their effectiveness, computational efficiency, and suitability for various scenarios in wind energy. The findings of this research could potentially guide future studies and applications in wind turbine wake modeling, thus contributing to the optimization of wind farms using high-order h/p methods. This study fills a gap in the literature by thoroughly investigating the application of these methods in the context of wind turbine wake development.

physics.flu-dyn↗

arXiv2024

pyLOM: A HPC open source reduced order model suite for fluid dynamics applications

This paper describes the numerical implementation in a high-performance computing environment of an open-source library for model order reduction in fluid dynamics. This library, called pyLOM, contains the algorithms of proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD), as well as, efficient SVD and matrix-matrix multiplication, all of them tailored for supercomputers. The library is profiled in detail under the MareNostrum IV supercomputer. The bottleneck is found to be in the QR factorization, which has been solved by an efficient binary tree communications pattern. Strong and weak scalability benchmarks reveal that the serial part (i.e., the part of the code that cannot be parallelized) of these algorithms is under 10% for the strong scaling and under 0.7% for the weak scaling. Using pyLOM, a POD of a dataset containing 1.14 x 108 gridpoints and 1808 snapshots that takes 6.3Tb of memory can be computed in 81.08 seconds using 10368 CPUs. Additioally, the algorithms are validated using the datasets of a flow around a circular cylinder at ReD = 100 and ReD = 1 x 104, as well as the flow in the Stanford diffuser at Reh = 1 x 104.

physics.flu-dyn↗

arXiv2024

Implementation of Immersed Boundaries via Volume Penalization in the Industrial Aeronautical Computational Fluid Dynamics Solver CODA

We present the implementation and validation of an immersed boundary volume penalization method in the computational fluid dynamics solver CODA (from ONERA, DLR, and Airbus). Our goal is to model and simulate turbulent fluid flows in complex 3D aerodynamic configurations through the numerical solution of the Reynolds--averaged Navier--Stokes equations using the Spalart--Allmaras turbulent model. To do that, an immersed boundary method has been implemented in CODA and an efficient preprocessing tool for the construction of unstructured hexahedral meshes with adaptive mesh refinement around immersed geometries has been developed. We report several numerical examples, including subsonic flow past the NACA0012 airfoil, transonic flow past the RAE2822 airfoil, subsonic flow past the MDA30P30N multi-element airfoil, and subsonic flow around the NASA high-lift CRM aircraft. These simulations have been performed in the CODA solver with a second-order finite volume scheme as spatial discretization and an implicit backward Euler scheme based on the matrix-free GMRES block-Jacobi iterative method. The reported numerical simulations are in good agreement with their corresponding experimental data. These encouraging results allow us to conclude that the implemented immersed boundary method is efficient, flexible, and accurate and can therefore be used for aeronautical applications in industry.

physics.flu-dyn↗

arXiv2023

An unsupervised machine-learning-based shock sensor for high-order supersonic flow solvers

We present a novel unsupervised machine-learning sock sensor based on Gaussian Mixture Models (GMMs). The proposed GMM sensor demonstrates remarkable accuracy in detecting shocks and is robust across diverse test cases with significantly less parameter tuning than other options. We compare the GMM-based sensor with state-of-the-art alternatives. All methods are integrated into a high-order compressible discontinuous Galerkin solver, where two stabilization approaches are coupled to the sensor to provide examples of possible applications. The Sedov blast and double Mach reflection cases demonstrate that our proposed sensor can enhance hybrid sub-cell flux-differencing formulations by providing accurate information of the nodes that require low-order blending. Besides, supersonic test cases including high Reynolds numbers showcase the sensor performance when used to introduce entropy-stable artificial viscosity to capture shocks, demonstrating the same effectiveness as fine-tuned state-of-the-art sensors. The adaptive nature and ability to function without extensive training datasets make this GMM-based sensor suitable for complex geometries and varied flow configurations. Our study reveals the potential of unsupervised machine-learning methods, exemplified by this GMM sensor, to improve the robustness and efficiency of advanced CFD codes.

cs.LG↗

arXiv2023

The impact of harmonic inflow variations on the size and dynamics of the separated flow over a bump

The separated flow over a wall-mounted bump geometry under harmonic oscillations of the inflow stream is investigated by direct numerical simulations. The bump geometry gives rise to streamwise pressure gradients similar to those encountered on the suction side of low-pressure turbine (LPT) blades. Under steady inflow conditions, the separated-flow laminar-to-turbulent transition is initiated by self-sustained vortex shedding due to Kelvin-Helmholtz (KH) instability. In LPTs, the dynamics are further complicated by the passage of the wakes shed by the previous stage of blades. The wake-passing effect is modeled here by introducing a harmonic variation of the inflow conditions. Three inflow oscillation frequencies and three amplitudes are considered. The frequencies are comparable to the wake-passing frequencies in practical LPTs. The amplitudes range from 1% to 10% of the inflow total pressure. The dynamics of the separated flow are studied by isolating the flow components that are respectively coherent with and uncorrelated to the inflow oscillation. Three scenarios are identified. The first one is analogous to the steady inflow case. In the second one, the KH vortex shedding is replaced during a part of the inflow period by the formation and release of a large vortex cluster. The third scenario consists solely of the periodic formation and release of the vortex cluster; it leads to a consistent reduction of the separated flow length over all the period compared to the steady inflow case and would be the most desirable flow condition in a practical application.

physics.flu-dyn↗

arXiv2023

A flux-differencing formulation with Gauss nodes

In this work, we propose an extension of telescopic derivative operators for the DGSEM with Gauss nodes, and we prove that this formulation is equivalent to its usual matrix counterpart. Among other possible applications, this allows extending the stabilization methods already developed for Gauss-Lobatto nodes to Gauss nodes, also ensuring properties such as entropy stability while retaining their improved accuracy.

math.NA↗