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Scalable Sparse Co-Kriging for Multi-Fidelity Data Fusion: An Application to Aerodynamics
Multi-fidelity Kriging surrogate modeling combines data of varying accuracy, such as experimental tests and numerical simulations, to improve predictive performance. Autoregressive models are commonly used to capture correlations across fidelity levels, offering interpretability compared to purely data-driven approaches. However, existing frameworks often suffer from high computational costs or rely on restrictive assumptions, such as requiring nested designs of experiments (DoEs). In an engineering context, the latter assumption implies that experimental tests must be conducted at the same input conditions as those used in numerical simulations. This requirement cannot always be met due to safety constraints in tests, which limit flexibility in data acquisition. In this work, we revisit the multi-fidelity Kriging approach and introduce a generalized co-Kriging framework that jointly models multiple fidelity levels through a correlation structure based on the autoregressive model. To ensure scalability, we extend sparse approximation techniques to the multi-fidelity setting, maintaining the efficiency of classical sparse Kriging while improving accuracy. We evaluate our framework on both nested and non-nested DoEs. On a large-scale multi-fidelity aerodynamic dataset that combines wind tunnel experiments with CFD simulations, the percentage of standardized residuals falling outside the confidence intervals is reduced by approximately 75% compared to standard sparse Kriging, highlighting the benefit of incorporating multi-fidelity information in complex engineering applications
Perspectives et défis des essais aérodynamiques dans les grands souffleries pour supporter le développement des futurs programmes aéronautiques et de défense
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Towards the use of formal methods in the certification of vision-based landing systems using high-dimensional ML algorithms
International audienceFormal methods show great promise for supporting the verification process within the avionics certification context. However, they remain intractable for high-dimensionalproblems. This paper summarizes the results of a CIFRE PhD thesis that paves the way for resolving this challeng
Divergence-Free Diffusion Models for Incompressible Fluid Flows
Generative diffusion models are extensively used in unsupervised and self-supervised machine learning with the aim to generate new samples from a probability distribution estimated with a set of known samples. They have demonstrated impressive results in replicating dense, real-world contents such as images, musical pieces, or human languages. This work investigates their application to the numerical simulation of incompressible fluid flows, with a view toward incorporating physical constraints such as incompressibility in the probabilistic forecasting framework enabled by generative networks. For that purpose, we explore different conditional, score-based diffusion models where the divergence-free constraint is imposed by the Leray spectral projector, and autoregressive conditioning is aimed at stabilizing the forecasted flow snapshots at distant time horizons. The proposed models are run on a benchmark turbulence problem, namely a Kolmogorov flow, which allows for a fairly detailed analytical and numerical treatment and thus simplifies the evaluation of the numerical methods used to simulate it. Numerical experiments of increasing complexity are performed in order to compare the advantages and limitations of the diffusion models we have implemented and appraise their performances, including: (i) in-distribution assessment over the same time horizons and for similar physical conditions as the ones seen during training; (ii) rollout predictions over time horizons unseen during training; and (iii) out-of-distribution tests for forecasting flows markedly different from those seen during training. In particular, these results illustrate the ability of diffusion models to reproduce the main statistical characteristics of Kolmogorov turbulence in scenarios departing from the ones they were trained on
Enhanced Surface Wave Propagation With a Highly Inductive Metasurface
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Un modèle de turbulence RANS à deux échelles dédié à la prévision des couches limites turbulentes soumises à de forts taux de turbulence extérieure
International audienceTurbulent boundary layers (TBLs) developing beneath a highly turbulent free stream are ubiquitous in turbomachinary flows and come along with a substantial increase in skin friction and wall heat transfer. A precise numerical prediction of this kind of flow is then of paramount importance in this context. Nevertheless, classical RANS (Reynolds-Averaged Navier-Stokes) turbulence models have shown to fail in this regard. The present paper presents the development process and rationale behind a multi-scale k − ω model designed to capture free-stream turbulence (FST) effects. Starting from an in-depth insight at the physical mechanisms characterising the development of TBLs under strong FST, in particular the scale separation and inactive character of the large scales, modelling guidelines are obtained. The multi-scale approach to turbulence modelling then appears to offer a sound framework for a faithful reproduction of the complex physics involved in the interaction between FST and TBLs as opposed to classical single-scale models. The two-scale k − ω model developed in this work is presented in detail and special attention is paid to how the experimental observations are transcribed in the model. Extensive testing of the two-scale model on various datasets about TBLs developing under strong FST environment is undertaken and it is shown that our modelling choices greatly improve the predictions when compared to a single-scale k − ω model
From leaf to barrier scale: A multisource data evaluation of a spontaneous vegetative barrier to prevent potentially toxic element dispersal
International audiencePotentially toxic elements (PTEs) may threaten both environmental and human health due to their persistence and their potential for widespread dispersal through wind and water erosion. Phytoremediation is often evaluated for soil contamination management although vegetation barriers have been less explored to reduce airborne dispersal of PTEs. The current study presents an approach to evaluate trapping capacity of woody species in vegetative barriers by combining field, laboratory measurements and airborne LiDAR point cloud to change scale from a single leaf to the entire vegetative barrier. To upscale leaf PTE concentration to plant and whole barrier estimation, allometric equations were used to evaluate accuracy of LiDAR HD above-ground volume estimation. This approach was tested on a spontaneous vegetative barrier surrounding PTE contaminated brownfields in Marseille (France). Although dense and overlapping shrub and tree canopies made measurements challenging, strong correlations were found between both methods (R 2 = 0.93 and 0.82 for Pinus halepensis and Pistacia lentiscus, respectively). Although PTE concentrations (As, Cd, Cu, Pb, Sb, Zn) in leaves were relatively low compared to those in soils (203 to 6592 times lower), the fraction attributed to atmospheric deposition represented a significant portion of leaf contamination, accounting for 22 % of total Pb and 44 % of total Sb. Similar efficiencies in trapping PTEs were observed between P. halepensis and P. lentiscus. The vegetative barrier, as a whole, can be considered as efficient to restrict contaminated particle dispersal in the studied context. This study underscores the accuracy of combining diverse data sources for robust assessment of nature-based solutions to mitigate contamination, moving beyond leaf-level trapping to a comprehensive barrier-scale evaluation
Optimization of explicit RKN schemes to minimize spurious reflections from shock wave propagation on non-uniform grids
International audienceThe propagation of shock waves on non-uniform grids appears, for example, in some impact problems of the fast dynamics type, where a finer mesh can typically be employed in regions of interest, leading to mesh ratios that can range from 10 to 20 or even more. Unfortunately, unwanted spurious reflections occur for this type of problem using (standard) explicit FE software. An optimized explicit time integration scheme is therefore built to minimize spurious wave reflections for shock wave propagation on non-uniform grids. Specifically, we consider RKN (Runge-Kutta-Nyström) time integration methods and optimize a parameter appearing in the RKN3 and RKN4 schemes by minimizing thestrain error that occurs when a shock wave passes through the mesh break. The effectiveness of the proposed approach is highlighted using some discrete indicators in a one-dimensional academic test case. Moreover, our method is compared to Hulbert and Chung’s and Noh and Bathe’s time-integration schemes using a two-dimensional test case of the literature. All schemes exhibited merits in mitigating spurious reflections of shock waves propagating on non-uniform grids. However, the proposed optimized RKN3 was the most efficient one
Évaluation de la contribution des particules d'alumine à la signature Infrarouge d'un jet de moteur-fusée
International audienceThe study focuses on the unresolved radiative contribution of alumina particles in IR signature of rocket engine plume. A sensitivity analysis is performed using Mie theory with multiple experimental values and models of the complex refractive index. Radiative transfer equations suggest that alumina particles radiation is dependent to the ratio of the particle absorption efficiency Q abs relative to its radius. Absorption index data can be several orders of magnitude different, resulting in a high uncertainty of the oxide radiative contribution. CFD simulations of the JAXA M-V 3rd stage are presented. IR Signature calculations are performed with two models of the complex refractive index using SHDOM solver. Computation is done over the 0.9 -10 µm spectral domain. Simulations reveal that the global contribution of alumina follow the trends formulated by the sensitivity analysis, with increasing emitted radiation with higher alumina absorption index. However, simulations suggest that the particle thermal inertia overwhelm the purely size-dependent particle effect
Closed-Form Solution of Skip Re-Entry Trajectories with Velocity-Dependent Aerodynamic Coefficients using Matched Asymptotic Expansions
International audienceAnalytical solutions to the planar atmospheric re-entry equations are derived using the Matched Asymptotic Expansions (MAE) method. In this approach, the exo-and endoatmospheric flight regimes are considered separately. The aerodynamic coefficients are modelled as affine functions of velocity at hypersonic speeds. A composite solution is obtained by integrating the solutions from each regime together; the adopted matching principle allows this solution to be applied to skip trajectories. The results are compared with those obtained using numerical ODE solvers to validate the accuracy of the solutions obtained and show the improvements over the case with constant aerodynamic coefficients