Publications

2019

• Derivation of a two-phase flow model with two-scale kinematics and surface tension by means of variational calculus
  
  • Cordesse Pierre
  • Kokh Samuel
  • Di Battista Ruben
  • Massot Marc
  , 2019. The present paper proposes a definition of a two-phase interface that relies on a probability density function. This definition enables to introduce a scale separation in the definition this interface and to define fields that characterize the geometry of the interface. Relying on these fields, we propose a two-phase flow model that is able to account for small and large scale separation of the interface description by means of supplementary convected geometric variables. The model accounts for two-scale kinematics and two-scale surface tension. At large scale, the flow and the full geometry of the interface may be retrieved thanks to the bulk variables and the volume fraction, while at small scale the interface dynamics is accurately recovered through the interfacial area density fluctuation and the mean curvature.
• Exploring different approaches for the simulation of multi-scale atomization process
  
  • Remigi Alberto
  • Di Battista Ruben
  • Demoulin F. X
  • Duret Benjamin
  • Massot Marc
  • Menard Thibaut
  • Deneuville Hugo
  , 2019. A big effort has been made in the last decades to try to numerically simulate multiphase flows and specifically the atomization process. This has become a key topic for aeronautical application, as the combustion process must be optimized in order to reduce pollutant emission. Despite this effort, there is not a global approach capable of simulating the entire atomization process, starting from the nozzle up to the disperse phase region. The first part of this work deals with the design of a simple configuration able to reproduce high Weber and Reynolds numbers of industrial interest, on which DNS computation can be performed. The second part introduces the comparison of the DNS experiments results with the ones of simulations performed with two reduced order models. The comparison addresses the topology (liquid core length, penetration study), the first and the second order statistics in the diffuse interface zone, in order to have for the first time a common test case to evaluate advantages and effects of different modelling strategies.
• Optimisation topologique en mécanique de contact par la méthode des lignes de niveaux
  
  • Desai Jeet
  • Allaire G.
  • Jouve F
  • Nardoni Chiara
  , 2019. Nous nous intéressons à l'optimisation topologique en mécanique du contact par la méthode des lignes de niveau. Nous considérons une structure linéaire élastique contrainte unilatéralement par des supports rigides et possédant une interface en auto-contact. Le contact est modélisé par les conditions aux limites de Signorini et la friction par la loi de Coulomb. En pénalisant les conditions aux limites, le problème non linéaire obtenu est traité numériquement à l'aide des méthodes de point fixe et de Newton-Raphson. La compliance élastique de la structure est minimisée sous une contrainte de volume. Mots clés-optimisation topologique; contact; ligne de niveau; adaptation de maillage.
• Optimisation de trajectoire pour le procédé de fabrication Laser Powder Bed Fusion (LPBF)
  
  • Boissier M
  • Allaire G.
  • Tournier Christophe
  , 2019. Le procédé de fabrication additive par fusion laser sur lit de poudre (LPBF) est un procédé couche par couche consistant à faire fusionner de la poudre au passage d’un laser. Malgré les nombreux avantages qu’elle présente, cette méthode de fabrication induit des défauts dans la pièce. Le choix des trajectoires du laser est alors primordial. En effet, la qualité et la vitesse de fabrication en sont toutes deux tributaires. On s’intéressera ici à l’utilisation et l’adaptation des outils classiques d’optimisation de forme pour l’optimisation des trajectoires de lasage.
• Adaptation à deux niveaux pour le solveur Adaptive Multipreconditioned FETI
  
  • Bovet Christophe
  • Parret-Fréaud Augustin
  • Gosselet Pierre
  • Spillane Nicole
  , 2019. Nous présentons l’une des dernières évolutions de la méthode de décomposition de domaine multipréconditionnée et adaptative AMPFETI, qui vise à résoudre des problèmes de très grandes tailles et de complexités industrielles. Dans AMPFETI, chaque agrégat de sous-domaines propose une direction de recherche. Ce préconditionnement multiple fournit la robustesse nécessaire pour résoudre les systèmes mal conditionnés induits par exemple par une forte hétérogénéité du matériau. Le critère d’adaptation permet de sélectionner uniquement les directions de recherche qui contribuent réellement à la convergence du solveur itératif. L’évolution présentée est l’ajout d’un second niveau d’adaptation dans le sens où les agrégats de multipreconditionnement évoluent pour accélérer encore la convergence. Les performances du solveur AMPFETI sur des cas industriels seront également présentées.
• Different Measure Approximations for Efficient Constrained Multi-Objective Optimization under Uncertainty
  
  • Rivier Mickael
  • Congedo Pietro Marco
  , 2019.
• On Representer Theorems and Convex Regularization
  
  • Boyer Claire
  • Chambolle Antonin
  • de Castro Yohann
  • Duval Vincent
  • de Gournay Frédéric
  • Weiss Pierre
  SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2019, 29 (2), pp.1260–1281. We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and elements of the extreme rays of the regularizer level sets. An extension to a broader class of quasi-convex regularizers is also discussed. As a side result, we characterize the minimizers of the total gradient variation, which was still an unresolved problem. (10.1137/18M1200750)
  DOI : 10.1137/18M1200750
• Vibration isolation system with a compact damping system for power recycling mirrors of KAGRA
  
  • Akiyama Y
  • Akutsu T
  • Ando M.
  • Arai K
  • Arai Y
  • Araki S.
  • Araya A.
  • Aritomi N
  • Asada H
  • Aso Y
  • Bae S
  • Baiotti L
  • Barton M
  • Cannon K
  • Capocasa E.
  • Chen C-S
  • Chiu T-W
  • Cho K.
  • Chu Y-K
  • Craig K
  • Dattilo V
  • Doi K
  • Enomoto Y
  • Flaminio R.
  • Fujii Y
  • Fujimoto M-K
  • Fukunaga M
  • Fukushima M
  • Furuhata T
  • Haino S
  • Hasegawa K
  • Hashimoto Y.
  • Hashino K
  • Hayama K
  • Hirayama T
  • Hirose E
  • Hsieh B
  • Huang C-Z
  • Ikenoue B
  • Inoue Y
  • Ioka K
  • Itoh Y
  • Izumi K.
  • Kaji T
  • Kajita T
  • Kakizaki M.
  • Kamiizumi M
  • Kanbara S
  • Kanda N
  • Kanemura S
  • Kang G
  • Kasuya J
  • Kawai N.
  • Kawasaki T
  • Kim C
  • Kim W
  • Kim J
  • Kimura N
  • Kirii S
  • Kitaoka Y
  • Kitazawa H.
  • Kojima Y.
  • Kokeyama K
  • Komori K
  • Kong A
  • Kotake K.
  • Kozu R
  • Kumar R.
  • Kuo H-S
  • Kuroki S
  • Kuroyanagi S
  • Lee H.
  • Leonardi M
  • Lin C-y
  • Lin F-L
  • Liu G.
  • Marchio M
  • Matsui T.
  • Michimura Y
  • Mio N
  • Miyakawa O
  • Miyamoto A
  • Miyoki S
  • Morii W
  • Morisaki S
  • Moriwaki Y
  • Musha M
  • Nagano S
  • Nagano K
  • Nakamura K.
  • Nakamura T.
  • Nakano H
  • Nakano M
  • Narikawa T
  • Nguyen Quynh L
  • Ni W-T
  • Nishizawa A
  • Obuchi Y
  • Oh J
  • Oh S
  • Ohashi M.
  • Ohishi N
  • Ohkawa M
  • Okutomi K
  • Ono K
  • Oohara K
  • Ooi C
  • Pan S-S
  • Paoletti F
  • Park J
  • Passaquieti R
  • Peña Arellano F
  • Sago N
  • Saito S
  • Saito Y.
  • Sakai K
  • Sakai Y
  • Sasai M
  • Sato S
  • Sato T
  • Sekiguchi T
  • Sekiguchi Y
  • Shibata M
  • Shimoda T
  • Shinkai H
  • Shishido T
  • Shoda A
  • Someya N
  • Somiya K
  • Son E
  • Suemasa A
  • Suzuki T.
  • Tagoshi H
  • Tahara H
  • Takahashi H.
  • Takahashi R
  • Takeda H
  • Tanaka H
  • Tanaka K.
  • Tanaka T.
  • Tanioka S
  • Tapia San Martin E
  • Tomaru T
  • Tomura T
  • Travasso F
  • Tsubono K
  • Tsuchida S
  • Uchikata N
  • Uchiyama T
  • Uehara T
  • Ueno K
  • Uraguchi F
  • Ushiba T
  • van Putten M
  • Vocca H
  • Wakamatsu T
  • Watanabe Y.
  • Xu W-R
  • Yamada T.
  • Yamamoto K.
  • Yamamoto S
  • Yamamoto T.
  • Yokogawa K
  • Yokoyama J
  • Yokozawa T
  • Yoshioka T
  • Yuzurihara H
  • Zeidler S
  • Zhu Z-H
  Classical and Quantum Gravity, IOP Publishing, 2019, 36 (9), pp.095015. (10.1088/1361-6382/ab0fcb)
  DOI : 10.1088/1361-6382/ab0fcb
• Efficient sequential experimental design for surrogate modeling of nested codes
  
  • Sophie Marque-Pucheu
  • Garnier Josselin
  • Perrin Guillaume
  ESAIM: Probability and Statistics, EDP Sciences, 2019.
• Irreducible convex paving for decomposition of multidimensional martingale transport plans
  
  • de March Hadrien
  • Touzi Nizar
  The Annals of Probability, Institute of Mathematical Statistics, 2019, 47 (3). (10.1214/18-AOP1295)
  DOI : 10.1214/18-AOP1295
• Quantification of gemcitabine intravenous drugs by direct measurement in chemotherapy plastic bags using a handheld Raman spectrometer
  
  • Lê Laetitia
  • Berge Marion
  • Tfayli Ali
  • Baillet-Guffroy Arlette
  • Prognon Patrice
  • Dowek Antoine
  • Caudron Eric
  Talanta, Elsevier, 2019, 196, pp.376-380. (10.1016/j.talanta.2018.11.062)
  DOI : 10.1016/j.talanta.2018.11.062
• Impact of charged species transport coefficients on self-bias voltage in an electrically asymmetric RF discharge
  
  • Orlac'H Jean-Maxime
  • Novikova Tatiana
  • Giovangigli Vincent
  • Johnson Erik
  • Roca Pere
  Plasma Sources Science and Technology, IOP Publishing, 2019, 28 (5), pp.055003. In this paper, we use a fluid model to simulate the excitation of a hydrogen radio-frequency discharge, and employ tailored voltage waveforms to assess the effect of charged species transport properties. Results of the fluid simulation are compared with experimental data and previous results obtained with a hybrid model. Several expressions for electron and ion transport coefficients are compared, and their impact on the self-bias potential is studied. The self-bias is shown to be insensitive to the choice of electron transport coefficients, while remarkably sensitive to variations in ion mobility. Besides, our results show that fluid models can be competitive with hybrid models, provided self-consistent ion transport models and rate constants are used. (10.1088/1361-6595/ab067d)
  DOI : 10.1088/1361-6595/ab067d
• A Tale of a Principal and Many, Many Agents
  
  • Elie Romuald
  • Mastrolia Thibaut
  • Possamaï Dylan
  Mathematics of Operations Research, INFORMS, 2019, 44 (2), pp.440-467. In this paper, we investigate a moral hazard problem in finite time with lump-sum and continuous payments, involving infinitely many agents with mean-field type interactions, hired by one principal. By reinterpreting the mean-field game faced by each agent in terms of a mean-field forward-backward stochastic differential equation (FBSDE), we are able to rewrite the principal’s problem as a control problem of the McKean-Vlasov stochastic differential equations. We review one general approach to tackling it, introduced recently using dynamic programming and Hamilton-Jacobi-Bellman (HJB for short) equations, and mention a second one based on the stochastic Pontryagin maximum principle. We solve completely and explicitly the problem in special cases, going beyond the usual linear-quadratic framework. We finally show in our examples that the optimal contract in the N-players’ model converges to the mean-field optimal contract when the number of agents goes to +∞. (10.1287/moor.2018.0931)
  DOI : 10.1287/moor.2018.0931
• Emergence of turbulent epochs in oil prices
  
  • Garnier Josselin
  • Solna Knut
  Chaos, Solitons & Fractals, Elsevier, 2019, 122, pp.281-292. (10.1016/j.chaos.2019.03.016)
  DOI : 10.1016/j.chaos.2019.03.016
• Modeling and computing the adjustment of IM in pricing/hedging derivatives
  
  • Agarwal Ankush
  • Bourgey Florian
  • Gobet Emmanuel
  • Lopez-Salas Jose
  • de Marco Stefano
  • Noubiagain Fanny
  • Zhou Alexandre
  , 2019.
• Disentangling and quantifying market participant volatility contributions
  
  • Rambaldi Marcello
  • Bacry Emmanuel
  • Muzy Jean-François
  Quantitative Finance, Taylor & Francis (Routledge), 2019, 19 (10), pp.1613-1625. (10.1080/14697688.2019.1591631)
  DOI : 10.1080/14697688.2019.1591631
• Modeling Ovarian Folliculogenesis: Morphogenesis and Population Dynamics
  
  • Bonnet Celine
  • Chahour Keltoum
  • Clement Frederique
  • Postel Marie
  • Robin Frédérique
  • Yvinec Romain
  , 2019.
• Dynamics and control of a periodically forced microalgae culture
  
  • Martínez Carlos
  • Mairet Francis
  • Martinon Pierre
  • Bernard Olivier
  IFAC-PapersOnLine, Elsevier, 2019, 52, pp.922-927. Microalgae cultivation with wastewater is a promising way of reducing the energetic needs for wastewater treatment and the costs of biofuel production. However, the very turbid medium is not favorable for the development of microalgae. Indeed, light, the key element for photosynthesis, rapidly vanishes along depth due to absorption and scattering. Therefore it is crucial to understand the effects of the depth on turbid cultures. In this work, we study theoretically the long-term behavior of a continuous culture of microalgae exposed to a periodic source of light. By allowing periodic variations of the depth and the hydraulic retention time, we show that the microalgae population is forced to a periodic regime. Finally, we address numerically the problem of determining the optimal variations of the depth and the hydraulic retention time for maximizing the productivity of the culture in the periodic regime. (10.1016/j.ifacol.2019.06.180)
  DOI : 10.1016/j.ifacol.2019.06.180
• On Kernel Derivative Approximation with Random Fourier Features
  
  • Szabó Zoltán
  • Sriperumbudur Bharath K
  , 2019. Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood theoretically on their optimality and limitations of their performance. Only recently, precise statistical-computational trade-offs have been established for RFFs in the approximation of kernel values, kernel ridge regression, kernel PCA and SVM classification. Our goal is to spark the investigation of optimality of RFF-based approximations in tasks involving not only function values but derivatives, which naturally lead to optimization problems with kernel derivatives. Particularly, in this paper, we focus on the approximation quality of RFFs for kernel derivatives and prove that the existing finite-sample guarantees can be improved exponentially in terms of the domain where they hold, using recent tools from unbounded empirical process theory. Our result implies that the same approximation guarantee is attainable for kernel derivatives using RFF as achieved for kernel values.
• A very simple proof of the LSI for high temperature spin systems
  
  • Bauerschmidt Roland
  • Bodineau Thierry
  Journal of Functional Analysis, Elsevier, 2019, 276 (8). We present a very simple proof that the $O(n)$ model satisfies a uniform logarithmic Sobolev inequality (LSI) if the positive definite coupling matrix has largest eigenvalue less than $n$. This condition applies in particular to the SK spin glass model at inverse temperature $\beta < 1/4$. It is the first result of rapid relaxation for the SK model and requires significant cancellations between the ferromagnetic and anti-ferromagnetic spin couplings that cannot be obtained by existing methods to prove Log-Sobolev inequalities. The proof also applies to more general bounded and unbounded spin systems. It uses a single step of zero range renormalisation and Bakry--Emery theory for the renormalised measure.
• Dealing with missing data in model-based clustering through a MNAR model
  
  • Biernacki Christophe
  • Celeux Gilles
  • Josse Julie
  • Laporte Fabien
  , 2019. Since the 90s, model-based clustering is largely used to classify data. Nowadays, with the increase of available data, missing values are more frequent. Traditional ways to deal with them consist to obtain a filled data set, either by discarding missing values or by imputing them. In the first case some information is lost; in the second case the final clustering purpose is not taken into account through the imputation step. Thus both solutions risk to blur the clustering estimation result. Alternatively, we defend the need to embed the missingness mechanism directly within the clustering modeling step. There exists three types of missing data: missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). In all situations, logistic regression is proposed as a natural and flexible candidate model. In particular, its flexibility property allows to design some meaningful parsimonious variants, as dependency on missing values or dependency on the cluster label. In this unified context, standard model selection criteria can be used to select between such different missing data mechanisms, simultaneously with the number of clusters. Practical interest of our proposal is illustrated on data derived from medical studies suffering from many missing data.
• The extrinsic geometry of dynamical systems tracking nonlinear matrix projections
  
  • Feppon Florian
  • Lermusiaux Pierre F J
  , 2019. A generalization of the concepts of extrinsic curvature and Weingarten endomorphism is introduced to study a class of nonlinear maps over embedded matrix manifolds. These (nonlinear) oblique projections, generalize (nonlinear) orthogonal projections, i.e. applications mapping a point to its closest neighbor on a matrix manifold. Examples of such maps include the truncated SVD, the polar decomposition, and functions mapping symmetric and non-symmetric matrices to their linear eigenprojectors. This paper specifically investigates how oblique projections provide their image manifolds with a canonical extrinsic differential structure, over which a generalization of the Weingarten identity is available. By diagonalization of the corresponding Weingarten endomorphism, the manifold principal curvatures are explicitly characterized, which then enables us to (i) derive explicit formulas for the differential of oblique projections and (ii) study the global stability of a governing generic Ordinary Differential Equation (ODE) computing their values. This methodology, exploited for the truncated SVD in [22], is generalized to non-Euclidean settings, and applied to the four other maps mentioned above and their image manifolds: respectively, the Stiefel, the isospectral, the Grassmann manifolds, and the manifold of fixed rank (non-orthogonal) linear projectors. In all cases studied, the oblique projection of a target matrix is surprisingly the unique stable equilibrium point of the above gradient flow. Three numerical applications concerned with ODEs tracking dominant eigenspaces involving possibly multiple eigenvalues finally showcase the results.
• Existence and uniqueness for anisotropic and crystalline mean curvature flows
  
  • Chambolle Antonin
  • Morini Massimiliano
  • Novaga Matteo
  • Ponsiglione Marcello
  Journal of the American Mathematical Society, American Mathematical Society, 2019, pp.1. An existence and uniqueness result, up to fattening, for crystalline mean curvature flows with forcing and arbitrary (convex) mobilities, is proven. This is achieved by introducing a new notion of solution to the corresponding level set formulation. Such a solution satisfies the comparison principle and a stability property with respect to the approximation by suitably regularized problems. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets. The approach accounts for the possible presence of a time-dependent bounded forcing term, with spatial Lipschitz continuity. As a by-product of the analysis, the problem of the convergence of the Almgren-Taylor-Wang minimizing movements scheme to a unique (up to fattening) "flat flow" in the case of general, possibly crystalline, anisotropies is settled. (10.1090/jams/919)
  DOI : 10.1090/jams/919
• Low-rank model with covariates for count data analysis
  
  • Robin Geneviève
  • Josse Julie
  • Moulines Éric
  • Sardy Sylvain
  Journal of Multivariate Analysis, Elsevier, 2019, 173. Count data are collected in many scientific and engineering tasks including image processing, single-cell RNA sequencing and ecological studies. Such data sets often contain missing values, for example because some ecological sites cannot be reached in a certain year. In addition, in many instances, side information is also available, for example covariates about ecological sites or species. Low-rank methods are popular to denoise and impute count data, and benefit from a substantial theoretical background. Extensions accounting for covariates have been proposed, but to the best of our knowledge their theoretical and empirical properties have not been thoroughly studied, and few softwares are available for practitioners. We propose a complete methodology called LORI (Low-Rank Interaction), including a Poisson model, an algorithm, and automatic selection of the regularization parameter, to analyze count tables with covariates. We also derive an upper bound on the estimation error. We provide a simulation study with synthetic data, revealing empirically that LORI improves on state of the art methods in terms of estimation and imputation of the missing values. We illustrate how the method can be interpreted through visual displays with the analysis of a well-know plant abundance data set, and show that the LORI outputs are consistent with known results. Finally we demonstrate the relevance of the methodology by analyzing a waterbirds abundance table from the French national agency for wildlife and hunting management (ONCFS). The method is available in the R package lori on the Comprehensive Archive Network (CRAN).
• Quasi-Regression Monte-Carlo scheme for semi-linear PDEs and BSDEs with large scale parallelization on GPUs
  
  • Gobet Emmanuel
  • López-Salas José Germán
  • Vázquez Carlos
  Archives of Computational Methods in Engineering, Springer Verlag, 2019, 27 (3), pp.889-921. In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations (BSDEs), and we analyze the convergence of the proposed method. The algorithm also approximates the solution to the related semi-linear parabolic partial differential equation (PDE) obtained through the well known Feynman-Kac representation. For the sake of enriching the algorithm with high order convergence a weighted approximation of the solution is computed and appropriate conditions on the parameters of the method are inferred. With the challenge of tackling problems in high dimensions we propose suitable projections of the solution and efficient parallelizations of the algorithm taking advantage of powerful many core processors such as graphics processing units (GPUs). (10.1007/s11831-019-09335-x)
  DOI : 10.1007/s11831-019-09335-x