Publications

2018

• Robust optimization of turbine cascades for Organic Rankine Cycles operating with siloxane MDM
  
  • Razaaly Nassim
  • Gori Giulio
  • Le Maitre Olivier
  • Iaccarino Gianluca
  • Congedo Pietro Marco
  , 2018, pp.2015-214. This work presents the application of a robust optimization approach to improve the efficiency of an Organic Rankine Cycle (ORC) cascade subject to uncertain operating conditions. The optimization algorithm is based on the minimization of a high quantile of a random cost function. The system under consideration employs siloxane MDM (Oc-tamethyltrisiloxane) as a working fluid. The thermodynamic behavior of MDM requires the utilization of complex Equations-of-State (EoS) that rely on material-dependent parameters. Discussed here are the aleatory uncertainties affecting both the cascade operating conditions and the fluid model parameters. An uncertainty quantification framework is used to forward propagate the considered uncertainties to some performance estima-tors. The performances of the robust blade design are compared against performances characterizing the optimal design obtained using a deterministic optimization approach. Results show that the quantile-based approach yields to a significant improvement in cascade performance in variable operating conditions.
• Large-scale space definition for the DG-VMS method based on energy transfer analyses
  
  • Naddei Fabio
  • de La Llave Plata Marta
  • Lamballais Eric
  • Couaillier Vincent
  • Massot Marc
  • Ihme Matthias
  , 2018. A-priori analyses to study the effect of the large-scale space definition in the variational multiscale simulation (VMS) approach to LES are carried out in the context of a modal discontinuous Galerkin (DG) method. A numerically consistent framework is introduced to derive the expression of the ideal subgrid-scale (SGS) energy transfer, which takes into account the different terms involved in the DG discretization. Based on the insight gained from this study, a locally adaptive modeling strategy able to adjust the definition of the large-scale space to the local resolution requirements of the flow is proposed.
• Robust optimization of ORC turbine cascades operating with siloxane MDM
  
  • Razaaly Nassim
  • Gori Giulio
  • Le Maitre Olivier
  • Iaccarino Gianluca
  • Congedo Pietro Marco
  , 2018. This work presents the application of a robust optimization approach to improve the efficiency of an Organic Rankine Cycle (ORC) cascade subject to uncertain operating conditions. The optimization algorithm is based on the minimization of a high quantile of a random cost function. The system under consideration employs siloxane MDM (Oc-tamethyltrisiloxane) as a working fluid. The thermodynamic behavior of MDM requires the utilization of complex Equations-of-State (EoS) that rely on material-dependent parameters. Discussed here are the aleatory uncertainties affecting both the cascade operating conditions and the fluid model parameters. An uncertainty quantification framework is used to forward propagate the considered uncertainties to some performance estima-tors. The performances of the robust blade design are compared against performances characterizing the optimal design obtained using a deterministic optimization approach. Results show that the quantile-based approach yields to a significant improvement in cascade performance in variable operating conditions.
• Eulerian modeling and simulation of two-phase flows in solid rocket motors taking into account size polydispersion and droplet trajectory crossing
  
  • Dupif Valentin
  , 2018. The massive amount of aluminum oxide particles carried in the internal flow of solid rocket motors significantly influences their behavior.The objective of this PhD thesis is to improve the two-phase flow Eulerian models available in the semi-industrial CFD code for energeticsCEDRE at ONERA by introducing the possibility of a local velocity dispersion in addition to the size dispersion already taken into accountin the code, while keeping the well-posed characteristics of the system of equations. Such a new feature enables the model to treat anisotropicparticle trajectory crossings, which is a key issue of Eulerian models for droplets of moderately large inertia.In addition to the design and detailed analysis of a class of models based on moment methods, the conducted work focuses on the resolution ofthe system of equations for industrial configurations. To do so, a new class of accurate and realizable numerical schemes for the transport ofthe particles in both the physical and the phase space is proposed. It ensures the robustness of the simulation despite the presence of varioussingularities (including shocks, -shocks, zero pressure area and vacuum...), while keeping a second order accuracy for regular solutions. Thesedevelopments are conducted in two and three dimensions, including the two dimensional axisymmetric framework, in the context of generalunstructured meshes.The ability of the numerical schemes to maintain a high level of accuracy in any condition is a key aspect in an industrial simulation of theinternal flow of solid rocket motors. In order to assess this, the in-house code SIERRA, originally designed at ONERA in the 90’s for solidrocket simulation purpose, has been rewritten, restructured and augmented in order to compare two generations of models and numericalschemes, to provide a basis for the integration of the features developed in CEDRE. The obtained results assess the efficiency of the chosennumerical strategy and confirm the need to introduce a new specific boundary condition in the context of axisymmetric simulations. Inparticular, it is shown that the model and numerical scheme can have an impact in the context of the simulation of the internal flow ofsolid rocket motors and their instabilities. Through our approach, the shed light on the links between fundamental aspects of modeling andnumerical schemes and their consequences on the applications.
• Day-ahead probabilistic forecast of solar irradiance: a Stochastic Differential Equation approach
  
  • Badosa Jordi
  • Gobet Emmanuel
  • Grangereau Maxime
  • Kim Daeyoung
  , 2018.
• Tropical cellular automata : why urban fires propagate according to polyhedral balls
  
  • Gaubert Stephane
  • Jones Daniel
  , 2018. In order to analyse the propagation of fire in urban areas, we study a deterministic percolation model on a regular grid in which fire propagates from a point to a bounded neighbourhood of this point, with time constants depending on the jump. Using discrete geometry methods, we obtain an explicit formula for the propagation speed. In particular, we show that for a large time horizon, the wave front is close to the boundary of a ball with respect to a polyhedral weak-Minkowski seminorm, which can be determined analytically from the time constants. We illustrate the model by simulations on data from the Kobe fire following the 1995 Southern Hyogo Prefecture Earthquake, indicating that this deterministic model gives an accurate account of actual urban fires.
• Block sparse linear models for learning structured dynamical systems in aeronautics
  
  • Rommel Cédric
  • Bonnans Joseph Frédéric
  • Gregorutti Baptiste
  • Martinon Pierre
  , 2018. This paper addresses an aircraft dynamical system identification problem, with the goal of using the learned models for trajectory optimization purposes. Our approach is based on multi-task regression. We present in this setting a new class of estimators that we call Block sparse Lasso, which conserves a certain structure between the tasks and some groups of variables, while promoting sparsity within these groups. An implementation leading to consistent feature selection is suggested, allowing to obtain accurate models, which are suitable for trajectory optimization. An additional regularizer is also proposed to help in recovering hidden representations of the initial dynamical system. We illustrate our method with numerical results based on real flight data from 25 medium haul aircraft, totaling 8 million observations.
• Quantifying the Closeness to a Set of Random Curves via the Mean Marginal Likelihood
  
  • Rommel Cédric
  • Bonnans Frédéric
  • Gregorutti Baptiste
  • Martinon Pierre
  , 2018. In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.
• Horofunction Compactifications of Symmetric Spaces
  
  • Haettel Thomas
  • Schilling Anna-Sofie
  • Wienhard Anna
  • Walsh Cormac
  , 2018. We consider horofunction compactifications of symmetric spaces with respect to invariant Finsler metrics. We show that any (generalized) Satake compactification can be realized as a horofunction compactification with respect to a polyhedral Finsler metric.
• Mathematical modelling of multi-phase flow using entropy symmetrization
  
  • Cordesse Pierre
  • Massot Marc
  • Murrone Angelo
  , 2018. Jet atomizations play a crucial role in many applications such as in cryogenic combustion chambers, thus must be thoroughly studied to understand its impact on high frequencies instabilities. Since direct numerical simulations of these two-phase flows in a real configuration of an engine are still out of reach, predictive numerical tools must be developed using reduced-order models. However great care must be taken on the choices of these models in order to both have sound mathematics properties and lead to predictive simulations after a validation process. The contribution of this work is three-fold. First, we present an original fully Eulerian modelling strategy. It relies on the coupling of a hierarchy of diffuse interface models with a Eulerian kinetic-based moment method (KBMM). Special attention will be given to the description of various disequilibrium level for the diffuse interface model, which describes the separated and mixed zone. A member of the KBMM hierarchy will accurately describe the polydisperse evaporating spray generated through atomization. Second, to cope with the strong discontinuities encountered in jet atomization, a robust and accurate numerical method using multi-slope MUSCL technique will be applied. The extension of the proposed strategy to the various levels of the diffuse interface models will be discussed. Third, relying on the previous two points, large eddy simulations of a jet atomization in a cryogenic combustion chamber in subcritical conditions are presented using various levels of modelling. Numerical results of jet atomization on the test bench MASCOTTE (ONERA). should eventually be obtained.
• Efficient optimization under uncertainty within the SABBa framework
  
  • Rivier Mickael
  • Congedo Pietro Marco
  , 2018.
• Efficient clustering based training set generation for systems of solvers
  
  • Sanson Francois
  • Eggels Anne
  • Le Maitre Olivier
  • Crommelin Daan J. A.
  • Congedo Pietro Marco
  , 2018.
• Robust Optimization of a Supersonic ORC Turbine Cascade: a Quantile-based Approach
  
  • Razaaly Nassim
  • Persico Giacomo
  • Gori Giulio
  • Congedo Pietro Marco
  , 2018.
• Stochastic FISTA algiorithms : so fast ?
  
  • Fort Gersende
  • Risser Laurent
  • Atchadé Yves
  • Moulines Éric
  , 2018.
• ON THE APPROXIMATION OF SBD FUNCTIONS AND SOME APPLICATIONS
  
  • Crismale Vito
  , 2018. Three density theorems for three suitable subspaces of SBD functions, in the strong BD topology, are proven. The spaces are SBD, SBD p ∞ , where the absolutely continuous part of the symmetric gradient is in L p , with p > 1, and SBD p , whose functions are in SBD p ∞ and the jump set has finite H n−1-measure. This generalises on the one hand the density result [12] by Chambolle and, on the other hand, extends in some sense the three approximation theorems in [27] by De Philippis, Fusco, Pratelli for SBV , SBV p ∞ , SBV p spaces, obtaining also more regularity for the absolutely continuous part of the approximating functions. As application, the sharp version of two Γ-convergence results for energies defined on SBD 2 is derived.
• On a Wasserstein-type distance between solutions to stochastic differential equations
  
  • Bion-Nadal Jocelyne
  • Talay Denis
  , 2018. In this paper we introduce a Wasserstein-type distance on the set of the probability distributions of strong solutions to stochastic differential equations. This new distance is defined by restricting the set of possible coupling measures. We prove that it may also be defined by means of the value function of a stochastic control problem whose Hamilton–Jacobi– Bellman equation has a smooth solution, which allows one to deduce a priori estimates or to obtain numerical evaluations. We exhibit an optimal coupling measure and characterizes it as a weak solution to an explicit stochastic differential equation, and we finally describe procedures to approximate this optimal coupling measure. A notable application concerns the following modeling issue: given an exact diffusion model, how to select a simplified diffusion model within a class of admissible models under the constraint that the probability distribution of the exact model is preserved as much as possible?
• Approximation of a Brittle Fracture Energy with a Constraint of Non-Interpenetration
  
  • Chambolle Antonin
  • Conti Sergio
  • Francfort Gilles A
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2018, 228 (3), pp.867–889. Linear fracture mechanics (or at least the initiation part of that theory) can be framed in a variational context as a minimization problem over a SBD type space. The corresponding functional can in turn be approximated in the sense of Γ-convergence by a sequence of functionals involving a phase field as well as the displacement field. We show that a similar approximation persists if additionally imposing a non-interpenetration constraint in the minimization, namely that only nonnegative normal jumps should be permissible. 2010 Mathematics subject classification: 26A45 (10.1007/s00205-017-1207-z)
  DOI : 10.1007/s00205-017-1207-z
• Component Mapping Automation for Parametric Component Reduced Basis Techniques (RB-Component)
  
  • Chakir Rachida
  • Dapogny Charles
  • Japhet Caroline
  • Maday Yvon
  • Montavon Jean-Baptiste
  • Pantz Olivier
  • Patera Anthony T.
  ESAIM: Proceedings and Surveys, EDP Sciences, 2018, 63, pp.208-227. The aim of this paper is to develop some techniques for automation of the mappings (between working and reference domains) required by reduced basis methods: the development of geometry mappings is indeed often a substantial impediment to the implementation of reduced basis techniques, especially in the context of the reduced basis element method (RBEM) and the reduced basis component method (RBCM). In the RBCM context, the geometry mappings are applied at the level of components. The methods have been tested on various cases to understand the limits of the approach and try to foresee and overcome the possible failures. (10.1051/proc/201863208)
  DOI : 10.1051/proc/201863208
• Transmission eigenvalues with artificial background for explicit material index identification
  
  • Audibert Lorenzo
  • Chesnel Lucas
  • Haddar Houssem
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2018, 356 (6), pp.626-631. We are interested in the problem of retrieving information on the refractive index $n$ of a penetrable inclusion embedded in a reference medium from farfield data associated with incident plane waves. Our approach relies on the use of transmission eigenvalues (TEs) that carry information on $n$ and that can be determined from the knowledge of the farfield operator $F$. In this note, we explain how to modify $F$ into a farfield operator $F^{art}=F-\tilde{F}$, where $\tilde{F}$ is computed numerically, corresponding to well chosen artificial background and for which the associated TEs provide more accessible information on $n$. (10.1016/j.crma.2018.04.015)
  DOI : 10.1016/j.crma.2018.04.015
• Algèbre de groupe en caractéristique 1 et distances invariantes sur un groupe fini
  
  • Castella Dominique Pierre
  • Gaubert Stephane
  Mathematische Zeitschrift, Springer, 2018, 289, pp.695-709. Les distances et plus généralement les métriques invariantes sur un groupe fini, utilisées en particulier en statistique, sont étroitement liées aux idempotents de l'algèbre du groupe sur le semi-corps idempotent des réels min-plus. Comme dans le cas classique, les idempotents centraux (qui correspondent aux distances bi-invariantes) sont donnés par les caractères de représentations linéaires de ce groupe. Nous montrons que ces caractères s'obtiennent encore à partir de caractères irréductibles et que plus généralement les idempotents admettent une décomposition unique en somme d'idempotents minimaux. Nous déterminons de façon explicite les idempotents minimaux et nous donnons de même la construction des caractères irréductibles à partir des classes de conjugaison du groupe. Ce travail conduit en particulier à la mise en valeur d'une famille finie de métriques invariantes, à valeurs entières, engendrant toutes les autres : ce sont les métriques de Cayley associées aux sous-groupes monogènes. Les distances usuelles sur $ S_n $ s'interprètent alors facilement dans cette construction. Ces résultats se généralisent en partie aux groupes infinis. (10.1007/s00209-017-1971-3)
  DOI : 10.1007/s00209-017-1971-3
• Phase field approximations of branched transportation problems
  
  • Ferrari Luca Alberto Davide
  • Rossmanith Carolin
  • Wirth Benedikt
  , 2018. In branched transportation problems mass has to be transported from a given initial distribution to a given final distribution, where the cost of the transport is proportional to the transport distance, but subadditive in the transported mass. As a consequence, mass transport is cheaper the more mass is transported together, which leads to the emergence of hierarchically branching transport networks. We here consider transport costs that are piecewise affine in the transported mass with N affine segments, in which case the resulting network can be interpreted as a street network composed of N different types of streets. In two spatial dimensions we propose a phase field approximation of this street network using N phase fields and a function approximating the mass flux through the network. We prove the corresponding Γ-convergence and show some numerical simulation results.
• Application de la multirésolution adaptative à la simulation numérique d'écoulements incompressibles
  
  • N'Guessan Marc-Arthur
  • Massot Marc
  • Tenaud Christian
  • Series Laurent
  , 2018.
• Infinite-Task Learning with Vector-Valued RKHSs
  
  • Brault Romain
  • Lambert Alex
  • Szabo Zoltan
  • Sangnier Maxime
  • d'Alché-Buc Florence
  , 2018. Machine learning has witnessed the tremendous success of solving tasks depending on a hyperparameter. While multi-task learning is celebrated for its capacity to solve jointly a finite number of tasks, learning a continuum of tasks for various loss functions is still a challenge. A promising approach, called Parametric Task Learning, has paved the way in the case of piecewise-linear loss functions. We propose a generic approach, called Infinite-Task Learning, to solve jointly a continuum of tasks via vector-valued RKHSs. We provide generalization guarantees to the suggested scheme and illustrate its efficiency in cost-sensitive classification, quantile regression and density level set estimation.
• HIGH-DIMENSIONAL ROBUST REGRESSION AND OUTLIERS DETECTION WITH SLOPE
  
  • Virouleau Alain
  • Guilloux Agathe
  • Gaïffas Stéphane
  • Bogdan Malgorzata
  , 2018. The problems of outliers detection and robust regression in a high-dimensional setting are fundamental in statistics, and have numerous applications. Following a recent set of works providing methods for simultaneous robust regression and outliers detection, we consider in this paper a model of linear regression with individual intercepts , in a high-dimensional setting. We introduce a new procedure for simultaneous estimation of the linear regression coefficients and intercepts, using two dedicated sorted-1 penalizations, also called SLOPE [5]. We develop a complete theory for this problem: first, we provide sharp upper bounds on the statistical estimation error of both the vector of individual intercepts and regression coefficients. Second, we give an asymptotic control on the False Discovery Rate (FDR) and statistical power for support selection of the individual intercepts. As a consequence, this paper is the first to introduce a procedure with guaranteed FDR and statistical power control for outliers detection under the mean-shift model. Numerical illustrations, with a comparison to recent alternative approaches, are provided on both simulated and several real-world datasets. Experiments are conducted using an open-source software written in Python and C++.
• Fractional-order variational numerical methods for tomographic reconstruction of binary images
  
  • Bergounioux Maïtine
  • Le Pennec Erwann
  • Trélat Emmanuel
  , 2018. The aim of this article is to provide and compare several numerical methods for the tomographic reconstruction of blurred and noised binary images, based on one single snapshot taken from an axially symmetric 3D object. This problem is motivated by a physical experiment of the CEA, where a single radiography is taken during the implosion process of some dense such object and is strongly blurred and noised. In a previous article [3] we have provided a refined functional analysis of the Radon operator restricted to axisymmetric functions and proved that it enjoys strong regularity properties in fractional order Hilbert spaces. Based on that theoretical study, we provide here the details of the numerical solving of a minimization problem settled in suitable fractional order Hilbert spaces, using a numerical approximation of the fractional Laplacian and some adapted Newton-like methods. The resulting procedure happens to be very efficient, both for the execution time and for the quality of the reconstruction. We compare this approach with two other numerical approaches: the first one uses the Fourier transform, and the second uses a wavelet reconstruction sofware.