Publications

2024

• Encoding the Latent Posterior of Bayesian Neural Networks for Uncertainty Quantification
  
  • Franchi Gianni
  • Bursuc Andrei
  • Aldea Emanuel
  • Dubuisson Séverine
  • Bloch Isabelle
  IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 2024, 46 (4), pp.2027-2040. Bayesian Neural Networks (BNNs) have long been considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior distribution of the network parameters, most BNN approaches are either limited to small networks or rely on constraining assumptions, e.g., parameter independence. These drawbacks have enabled prominence of simple, but computationally heavy approaches such as Deep Ensembles, whose training and testing costs increase linearly with the number of networks. In this work we aim for efficient deep BNNs amenable to complex computer vision architectures, e.g., ResNet-50 DeepLabv3+, and tasks, e.g., semantic segmentation and image classification, with fewer assumptions on the parameters. We achieve this by leveraging variational autoencoders (VAEs) to learn the interaction and the latent distribution of the parameters at each network layer. Our approach, called Latent-Posterior BNN (LP-BNN), is compatible with the recent BatchEnsemble method, leading to highly efficient (in terms of computation and memory during both training and testing) ensembles. LP-BNNs attain competitive results across multiple metrics in several challenging benchmarks for image classification, semantic segmentation, and out-of-distribution detection. (10.1109/TPAMI.2023.3328829)
  DOI : 10.1109/TPAMI.2023.3328829
• Unified two-scale Eulerian multi-fluid modeling of separated and dispersed two-phase flows
  
  • Loison Arthur
  , 2024. Liquid-gas two-phase flows are present in numerous industrial applications such as aerospace propulsion, nuclear hydraulics or bubble column reactors in the chemical industry.The simulation of such flows is of primary interest for their understanding and optimization.However, the dynamics of the interface separating the gas from the liquid can present a multiscale dynamics and thus makes simulations of industrial processes computationally too expensive.Some modelling efforts have been conducted on the development of cheaper multi-fluid models adapted to particular interface dynamics regime, e.g. in the separated regime where the fluids are separated by a single smooth surface or in the disperse regime where there are inclusions of one fluid carried by the other.Attempts of coupling between these models have showed some progress to simulate multiscale flows like atomization, but usually have physical or mathematical drawbacks.This thesis then pursues the goal of proposing a unified two-scale modelling framework with appropriate numerical methods adapted to this multiscale interface dynamics which goes from a separated to a disperse regime.The main contributions related to this modelling effort are :1- The combination of compressible multi-fluid models of the literature adapted to either the separated or the disperse regime into a unified two-scale multi-fluid model relying on Hamilton’s Stationary Action Principle;2- The local coupling of the models with an inter-scale mass transfer both regularizing the large-scale inter face and modelling mixed regime phenomena such as in primary break-up;3- Enhancing the small-scale models for the disperse regimes by adding the dynamics of geometrical quantities for oscillating droplets and pulsating bubbles, built as moments of a kinetic description.From the numerical perspective, finite-volume schemes and relaxation methods are used to solve the system of conservative laws of the models.Eventually, simulations with the open-source finite solver Josiepy demonstrates the regularization properties of the model on a set of well-chosen numerical setups leading to multi-scale interface dynamics.
• Gradient pulsed transient plasma for initiation of detonation
  
  • Lafaurie Victor
  • Shu Zhan
  • Vidal Pierre
  • Starikovskaia Svetlana
  Combustion and Flame, Elsevier, 2024, 261, pp.113311. The formation of a gradient of atomic oxygen is demonstrated by means of a nanosecond non-equilibrium plasma for a varying gap size plane-to-plane electrode. Using a flat high-voltage electrode in front of a rounded triangle a 2.9 to 5 cm gap is formed over a 9.8 cm span. ICCD imaging determined an adequate ground electrode shape and slope to create a gradient. The plasma is formed by three consecutive high voltage pulses of -30, -40 and -50 kV in 100 mbar of air. O-TALIF measurements confirm that atomic oxygen production changed with gap size within the same plasma. This setup will be used to test detonation initiation by Zel’dovich gradient mechanisms in stoichiometric H₂:O₂ mixtures. Novelty and Significance: A novel configuration of a nanosecond non-equilibrium discharge was developed to create a controllable gradient of atomic oxygen. This was achieved by using varying gap plane-to-plane electrodes to generate an electric field of varying strength along the length of the gap. This setup will be tested in combustible mixtures to initiate a detonation wave using a gradient mechanism of Zel’dovich. (10.1016/j.combustflame.2024.113311)
  DOI : 10.1016/j.combustflame.2024.113311
• Study of the breathing mode development in Hall thrusters using hybrid simulations
  
  • Petronio Federico
  • Alvarez Laguna Alejandro
  • Bourdon Anne
  • Chabert Pascal
  Journal of Applied Physics, American Institute of Physics, 2024, 135 (7). We use a 2.5D hybrid simulation to study the breathing mode (BM) dynamics in Hall thrusters (HTs). This involves a 1D Euler fluid simulation for neutral dynamics in the axial direction, coupled with a 2D axial–azimuthal Particle-in-Cell (PIC) simulation for charged species. The simulation also includes an out-of-plane virtual dimension for wall losses. This setup allows us to replicate the BM’s macroscopic features observed in experiments. A comprehensive analysis of plasma parameters in BM’s phases divides it into two growth and two decay sub-phases. Examining 1D axial profiles of electron temperature, gas and plasma densities, and particle creation rate shows that an increase in electron temperature alone cannot sustain ionization. Ionization seems to be influenced by the spatial correlation between electron and gas densities and the ionization rate coefficient. Investigating ion back-flow reveals its impact on modulating neutral flux entering the ionization region. The hybrid simulation’s outcomes let us assess the usual 0D predator–prey model’s validity and identify its limitations. The ionization and ion convection term approximations hold, but the gas convective term approximation does not. Introducing an alternative gas convective term approximation involving constant density ejection from the ionization region constructs an unstable BM model consistent with simulation results. In addition, this paper explores how varying the imposed voltage and mass flow rate impacts the BM. The BM frequency increases with imposed voltage, aligning with theoretical predictions. The mass flow rate variation has a limited effect on BM frequency, following the theoretical model’s trend. (10.1063/5.0188859)
  DOI : 10.1063/5.0188859
• Pinning of crack fronts by hard and soft inclusions: A phase field study
  
  • Henry Hervé
  Physical Review E, American Physical Society (APS), 2024, 109 (2), pp.025002. Through tridimensonal numerical simulations of cracks propagating in material with an elastic moduli heterogeneity, it is shown that the presence of a simple inclusion can dramatically affect the propagation of the crack. Both the presence of soft and hard inclusions can lead to the arrest of a crack front. Here the mechanism leading to the arrest of the crack are described and shown to depend on the nature of the inclusion. This is also the case in regimes where the presence of the inclusion leads to a slowdown of the crack. (10.1103/PhysRevE.109.025002)
  DOI : 10.1103/PhysRevE.109.025002
• A coupled VOF/embedded boundary method to model two-phase flows on arbitrary solid surfaces
  
  • Tavares Mathilde
  • Josserand Christophe
  • Limare Alexandre
  • Lopez-Herrera José-Maria
  • Popinet Stéphane
  Computers and Fluids, Elsevier, 2024. We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the two-phase flow and an embedded boundary method to sharply resolve arbitrary solid geometries. Coupling these approaches consistently is not trivial and we present in detail a quad/octree spatial discretization for solving the corresponding partial differential equations. Modelling contact angle dynamics is a complex physical and numerical problem. We present a Navier-slip boundary condition compatible with the present cut cell method, validated through a Taylor-Couette test case. To impose the boundary condition when the fluid-fluid interface intersects a solid surface, a geometrical contact angle approach is developed. Our method is validated for several test cases including the spreading of a droplet on a cylinder, and the equilibrium shape of a droplet on a flat or tilted plane in 2D and 3D. The temporal evolution and convergence of the droplet spreading on a flat plane is also discussed for the moving contact line given the boundary condition (Dirichlet or Navier) used. The ability of our numerical methodology to resolve contact line statics and dynamics for different solid geometries is thus demonstrated.
• PHARE: Parallel hybrid particle-in-cell code with patch-based adaptive mesh refinement
  
  • Aunai Nicolas
  • Smets Roch
  • Ciardi Andrea
  • Deegan Philip
  • Jeandet Alexis
  • Payet Thibault
  • Guyot Nathan
  • Darrieumerlou Loic
  Computer Physics Communications, Elsevier, 2024, 295, pp.108966. Modeling multi-scale collisionless magnetized processes constitutes an important numerical challenge. By treating electrons as a fluid and ions kinetically, the so-called hybrid Particle-In-Cell (PIC) codes represent a promising intermediary between fully kinetic codes, limited to model small scales and short durations, and magnetohydrodynamic codes used large scale. However, simulating processes at scales significantly larger than typical ion particle dynamics while resolving sub-ion dissipative current sheets remain extremely difficult. This paper presents a new hybrid PIC code with patch-based adaptive mesh refinement. Here, hybrid PIC equations are solved on a hierarchy of an arbitrary number of Cartesian meshes of incrementally finer resolution dynamically mapping regions of interest, and with a refined time stepping. This paper presents how the hybrid PIC algorithm is adapted to evolve such mesh hierarchy and the validation of the code on a uniform mesh, fixed refined mesh and dynamically refined mesh. (10.1016/j.cpc.2023.108966)
  DOI : 10.1016/j.cpc.2023.108966
• Acceleration of an interplanetary shock through the magnetosheath: a global hybrid simulation
  
  • Moissard C.
  • Savoini P.
  • Fontaine D.
  • Modolo Ronan
  Frontiers in Astronomy and Space Sciences, Frontiers Media, 2024, 11, pp.1330397. According to most observations and simulations, interplanetary shocks slow down when they propagate through the magnetosheath. In this article, we present results from a self-consistent global hybrid PIC simulation of an interplanetary shock which, by contrast, accelerates as it propagates through the magnetosheath. In this simulation, the solar wind upstream of the interplanetary shock is set up with an Alfvén Mach number M A = 4.5 and the interplanetary magnetic field (IMF) is set up to be almost parallel to the y direction in GSE coordinate system. The ‘planet’ is modelled as a magnetic dipole with no tilt: the dipole is in the GSE’s z direction. In the ecliptic plane (Oxy), which contains the interplanetary magnetic field (IMF), the magnetic field lines are piling up against the magnetopause, and the velocity of the interplanetary shock decreases from 779 ± 48 km/s in the solar wind down to 607 ± 48 km/s in the magnetosheath. By contrast, in the noon-meridian plane (Oxz), which is perpendicular to the IMF, the velocity of the interplanetary shock in the magnetosheath can reach values up to 904 ± 48 km/s. This study suggests that interplanetary shocks can accelerate as they propagate through the magnetosheath. This finding, reported here for the first time, could have important implications for space weather, as it corresponds to the case where an interplanetary shock catches up with a low Alfvén Mach number solar transient such as an interplanetary coronal mass ejection. (10.3389/fspas.2024.1330397)
  DOI : 10.3389/fspas.2024.1330397
• Abundance of G-Quadruplex Forming Sequences in the Hepatitis Delta Virus Genomes
  
  • Brázda Václav
  • Valková Natália
  • Dobrovolná Michaela
  • Mergny Jean-Louis
  ACS Omega, ACS Publications, 2024, 9, pp.4096-4101. Hepatitis Delta virus (HDV) is a unique and highly unusual RNA satellite virus that depends on the presence of the hepatitis B virus (HBV) to be infectious. Its single-stranded RNA genome is very compact and variable, consisting of eight major genotypes distributed unequally on various continents. The significance of noncanonical secondary structures in DNA or RNA, such as G-quadruplexes (G4s), is becoming more evident especially for transcription, replication, and translation. G4s are formed from guanine-rich sequences and have been found in most eukaryotic and prokaryotic genomes, as well as viruses. In this study, we analyzed the G-quadruplex propensity of HDV genomes using G4Hunter. In contrast to the HBV virus, which has a G4 density similar to that of the human genome, the HDV virus possesses a significantly higher number of potential quadruplex-forming sequences (PQS) with a density more than four times higher than that of the human genome. This observation suggests a crucial role for G-quadruplexes in HDV, particularly because the tracks with the potential to form G-quadruplexes are well conserved. Furthermore, the high prevalence of the G-quadruplex-forming sequence could represent a promising therapeutic target to control HDV replication. (10.1021/acsomega.3c09288)
  DOI : 10.1021/acsomega.3c09288
• Limitation strategies for high-order discontinuous Galerkin schemes applied to an Eulerian model of polydisperse sprays
  
  • Ait-Ameur Katia
  • Essadki Mohamed
  • Massot Marc
  • Pichard Teddy
  , 2024. In this paper, we tackle the modeling and numerical simulation of polydisperse sprays. Starting from a kinetic description for point particles, we focus on an Eulerian high-order geometric method of moment (GeoMOM) in size and consider a system of partial differential equations on a vector of successive fractional size moments of order 0 to N/2, N > 2, over a compact size interval. These moments correspond to physical quantities, which can be interpreted in terms of the geometry of the interface at small scale. There exists a stumbling block for the usual approaches using high-order moment methods resolved with high-order numerical methods: the transport algorithm does not naturally preserve the moment space. Indeed, reconstruction of moments by polynomials inside computational cells can create N-dimensional vectors which can fail to be moment vectors. We thus propose a new approach, as well as an algorithm, which is arbitrarily high-order in space and time with limited numerical diffusion, including at the boundaries of the state space, where a specific study is proposed. It allows to accurately describe the advection process and naturally preserves the moment space, at a reasonable computational cost. We show that such an approach is competitive compared to second order finite volume schemes, where limiters generate numerical diffusion and clipping at extrema. An accuracy study assesses the order of the method as well as the low level of numerical diffusion on structured meshes. We focus in this paper on cartesian meshes and 2D test cases are presented where the accuracy and efficiency of the approach are assessed.
• InfraParis: A multi-modal and multi-task autonomous driving dataset
  
  • Franchi Gianni
  • Hariat Marwane
  • Yu Xuanlong
  • Belkhir Nacim
  • Manzanera Antoine
  • Filliat David
  , 2024. Current deep neural networks (DNNs) for autonomous driving computer vision are typically trained on specific datasets that only involve a single type of data and urban scenes. Consequently, these models struggle to handle new objects, noise, nighttime conditions, and diverse scenarios, which is essential for safety-critical applications. Despite ongoing efforts to enhance the resilience of computer vision DNNs, progress has been sluggish, partly due to the absence of benchmarks featuring multiple modalities. We introduce a novel and versatile dataset named InfraParis that supports multiple tasks across three modalities: RGB, depth, and infrared. We assess various state-of-the-art baseline techniques, encompassing models for the tasks of semantic segmentation, object detection, and depth estimation. More visualizations and the download link for InfraParis are available at https://ensta-u2is.github.io/infraParis (10.1109/WACV57701.2024.00295)
  DOI : 10.1109/WACV57701.2024.00295
• Learning to Generate Training Datasets for Robust Semantic Segmentation
  
  • Hariat Marwane
  • Laurent Olivier
  • Kazmierczak Rémi
  • Bursuc Andrei
  • Yao Angela
  • Franchi Gianni
  , 2024. Semantic segmentation techniques have shown significant progress in recent years, but their robustness to real-world perturbations and data samples not seen during training remains a challenge, particularly in safety-critical applications. In this paper, we propose a novel approach to improve the robustness of semantic segmentation techniques by leveraging the synergy between label-to-image generators and image-to-label segmentation models. Specifically, we design and train Robusta, a novel robust conditional generative adversarial network to generate realistic and plausible perturbed or outlier images that can be used to train reliable segmentation models. We conduct in-depth studies of the proposed generative model, assess the performance and robustness of the downstream segmentation network, and demonstrate that our approach can significantly enhance the robustness of semantic segmentation techniques in the face of real-world perturbations, distribution shifts, and out-of-distribution samples. Our results suggest that this approach could be valuable in safety-critical applications, where the reliability of semantic segmentation techniques is of utmost importance and comes with a limited computational budget in inference. We will release our code shortly. (10.1109/wacv57701.2024.00385)
  DOI : 10.1109/wacv57701.2024.00385
• Analytical model of a Hall thruster
  
  • Lafleur Trevor
  • Chabert Pascal
  Physics of Plasmas, American Institute of Physics, 2024, 31 (9), pp.093507. Hall thrusters are one of the most successful and prevalent electric propulsion systems for spacecraft in use today. However, they are also complex devices and their unique E×B configuration makes modeling of the underlying plasma discharge challenging. In this work, a steady-state model of a Hall thruster is developed and a complete analytical solution presented that is shown to be in reasonable agreement with experimental measurements. A characterization of the discharge shows that the peak plasma density and ionization rate nearly coincide and both occur upstream of the peak electric field. The peak locations also shift as the thruster operating conditions are varied. Three key similarity parameters emerge that govern the plasma discharge and which are connected via a thruster current–voltage relation: a normalized discharge current, a normalized discharge voltage, and an amalgamated parameter, α¯, that contains all system geometric and magnetic field information. For a given normalized discharge voltage, the similarity parameter α¯ must lie within a certain range to enable high thruster performance. When applied to a krypton thruster, the model shows that both the propellant mass flow rate and the magnetic field strength must be simultaneously adjusted to achieve similar efficiency to a xenon thruster (for the same thruster geometry, discharge voltage, and power level). (10.1063/5.0220130)
  DOI : 10.1063/5.0220130
• Long-term performance of innovation systems in East Asian developing countries: A structural analysis
  
  • Lebert Didier
  , 2024. To measure the performance of East Asian developing countries’ innovation systems, we adopt a product space approach by considering the import and export flows linking each country to its trading partners over the long term (1980-2018). We apply economic dominance theory to construct and analyze this space. Using an extension of Pavitt’s (1984) taxonomy proposed by Castellacci (2008), we classify manufactured goods into categories distinguished by the technological intensity required for their development, production, and diffusion. We propose indices of economic complexity to position countries in relation to each other, to identify significant developments, and to infer the capacity of a national innovation system to deepen a country’s insertion into the global value chain based on the mastery of complex technologies. In this way, we identify three groups of countries: those whose current innovation system favors moving up the value chain, those caught in the middle-income trap and struggling to renew their innovation system, and those without a clearly structured innovation system.
• The linear sampling method for data generated by small random scatterers
  
  • Garnier Josselin
  • Haddar Houssem
  • Montanelli Hadrien
  SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2024, 17 (4), pp.2142-2173. (10.1137/24M1650417)
  DOI : 10.1137/24M1650417