Publications

2017

• Monte-Carlo acceleration: importance sampling and hybrid dynamic systems
  
  • Chraïbi Hassane
  • Dutfoy Anne
  • Galtier Thomas Antoine
  • Garnier Josselin
  , 2017. The reliability of a complex industrial system can rarely be assessed analytically. As system failure is often a rare event, crude Monte-Carlo methods are prohibitively expensive from a computational point of view. In order to reduce computation times, variance reduction methods such as importance sampling can be used. We propose an adaptation of this method for a class of multi-component dynamical systems. We address a system whose failure corresponds to a physical variable of the system (temperature, pressure, water level) entering a critical region. Such systems are common in hydraulic and nuclear industry. In these systems, the statuses of the components (on, off, or out-of-order) determine the dynamics of the physical variables, and is altered both by deterministic feedback mechanisms and random failures or repairs. In order to deal with this interplay between components status and physical variables we model trajectory using piecewise deterministic Markovian processes (PDMP). We show how to adapt the importance sampling method to PDMP, by introducing a reference measure on the trajectory space, and we present a biasing strategy for importance sampling. A simulation study compares our importance sampling method to the crude Monte-Carlo method for a three-component-system.
• Solving Generic Nonarchimedean Semidefinite Programs Using Stochastic Game Algorithms
  
  • Allamigeon Xavier
  • Gaubert Stephane
  • Skomra Mateusz
  , 2017.
• Binaural spatialization methods for indoor navigation
  
  • Ferrand Sylvain
  • Alouges François
  • Aussal Matthieu
  , 2017. The visually impaired people are able to follow sound sources with a remarkable accuracy. They often use this ability to follow a guide in everyday activities or for practicing sports, like running or cycling. On the same principle, it is possible to guide people with spatialized sound. We have thus developed a navigation device to guide with sounds using binaural synthesis techniques. In this device, we are using both localization information provided by a precise and low latency positioning system and heading data computed from an Inertial Measurement Unit. These positioning data are feeding an HRTF based binaural engine, producing spatialized sound in real-time and guiding the user along a way. The user follows the sound, quite naturally and without initial training. Experiments show that it is possible to guide a walker with enough precision.
• Méthode de décomposition de domaine multipréconditionnée et adaptative pour les problèmes mal conditionnés
  
  • Bovet Christophe
  • Parret-Fréaud Augustin
  • Spillane Nicole
  • Gosselet Pierre
  , 2017. Nous présentons la méthode de décomposition de domaine multipréconditionnée et adaptative AMPFETI, qui vise à résoudre des problèmes de très grandes tailles et de complexités industrielles. La méthode AMPFETI est robuste et particulièrement efficace pour résoudre des problèmes mal conditionnés impliquant par exemple de fortes hétérogénéités. Ce travail présente une amélioration de la méthode où la « granularité » du multipréconditionnement n’est plus systématiquement le sous-domaine. Cette récente amélioration rend accessibles des problèmes à un grand nombre de sous-domaines.
• TOPOLEV: Topological optimization using level-set method
  
  • Lachouette Damien
  • Conraux Philippe
  • Allaire Grégoire
  • Jouve François
  , 2017. Weight reduction is a very important issue in the industry, particularly in the industry of transport vehicles. To meet this objective, ESI has developed a disruptive and innovative optimization tool based on the technology of the level-set [[5], [6]]. Unlike existing methods (homogenization, and flavors : power law, SIMP etc. [[1], [8]]), the level-set representation allows an accurate sharp knowledge of the boundary location, thus we are able to have a large scope of geometrical constraints of the shape, or to include manu facturing constraints involving precise knowledge of the shape like casting or additive manufacturing processes.
• A bilevel optimization model for load balancing in mobile networks through price incentives
  
  • Eytard Jean Bernard
  • Akian Marianne
  • Bouhtou Mustapha
  • Gaubert Stephane
  , 2017, pp.1-8. We propose a model of incentives for data pricing in large mobile networks, in which an operator wishes to balance the number of connexions (active users) of different classes of users in the different cells and at different time instants, in order to ensure them a sufficient quality of service. We assume that each user has a given total demand per day for different types of applications, which he may assign to different time slots and locations, depending on his own mobility, on his preferences and on price discounts proposed by the operator. We show that this can be cast as a bilevel programming problem with a special structure allowing us to develop a polynomial time decomposition algorithm suitable for large networks. First, we determine the optimal number of connexions (which maximizes a measure of balance); next, we solve an inverse problem and determine the prices generating this traffic. Our results exploit a recently developed application of tropical geometry methods to mixed auction problems, as well as algorithms in discrete convexity (minimization of discrete convex functions in the sense of Murota). We finally present an application on real data provided by Orange and we show the efficiency of the model to reduce the peaks of congestion. (10.23919/WIOPT.2017.7959902)
  DOI : 10.23919/WIOPT.2017.7959902
• Optimisation de structures composées de cellules périodiques modulées orthotropes par la méthode d'homogénéisation
  
  • Geoffroy Perle
  , 2017. Nous proposons ici une méthode d’optimisation topologique basée sur la méthode d’homogénéisation afin d’obtenir des structures composées de cellules périodiques de densité variable. Une projection de nos solutions optimales permet d’envisager des applications à la fabrication additive.
• Développement d'un couplage "intriqué" entre thermomécanique et diffusion neutronique
  
  • Patricot Cyril
  • Allaire Grégoire
  • Fandeur Olivier
  , 2017. Ce papier s’intéresse à la simulation numérique de la diffusion neutronique, telle qu’elle peut avoir lieu dans un réacteur nucléaire, dans un milieu se dilatant thermiquement du fait de l’échauffement nucléaire. Plutôt que de coupler des outils distincts, le parti a été pris de développer un solveur commun aux disciplines couplées (approche dite intriquée), basé sur l’algorithme de Newton. Après un calcul analytique de la jacobienne du système complet, un cas d’application simple vise à montrer la justesse des développements et la pertinence de la méthode.
• Méthodes de décomposition de domaine robustes appliquées au calcul en régime linéaire et non linéaire de structures industrielles de grande taille
  
  • Parret-Fréaud Augustin
  • Marchand Basile
  • Bovet Christophe
  • Gosselet Pierre
  • Spillane Nicole
  • Rey Christian
  • Feyel Frédéric
  , 2017. Nous présentons de nouveaux développements destinés à améliorer la robustesse des approches de décomposition de domaine de type FETI en vue de permettre leur utilisation dans le contexte de problèmes industriels de grande taille. Ces méthodes, appelées AMPFETI, reposent sur l’usage d’une stratégie de multi-préconditionnement adaptatif au niveau du solveur itératif du problème d’interface. Leurs performances sont illustrées sur une étude d’extensibilité faible sur un problème hétérogène pathologique. Un cas d’application au calcul non linéaire d’une aube oligocristalline est présenté.
• General indifference pricing with small transaction costs
  
  • Possamaï Dylan
  • Royer Guillaume
  Asymptotic Analysis, IOS Press, 2017, 102 (3-4), pp.177-226. We study the utility indifference price of a European option in the context of small transaction costs. Considering the general setup allowing consumption and a general utility function at final time T, we obtain an asymptotic expansion of the utility indifference price as a function of the asymptotic expansions of the utility maximization problems with and without the European contingent claim. We use the tools developed in [54] and [48] based on homogenization and viscosity solutions to characterize these expansions. Finally we study more precisely the example of exponential utilities, in particular recovering under weaker assumptions the results of [6]. (10.3233/ASY-171415)
  DOI : 10.3233/ASY-171415
• Convergence of a Moran model to Eigen's quasispecies model
  
  • Dalmau Joseba
  Journal of Theoretical Biology, Elsevier, 2017, 420, pp.36-40. We prove that a Moran model converges in probability to Eigen's quasispecies model in the infinite population limit. We show further that the invariant probability measure of the Moran model converges to the unique stationary solution of Eigen's quasispecies model. (10.1016/j.jtbi.2017.02.035)
  DOI : 10.1016/j.jtbi.2017.02.035
• A First Finite Element Solver Shared By Neutron Diffusion, Heat Transfer And Mechanics
  
  • Patricot C.
  • Allaire G.
  • Fandeur O.
  , 2017. Nuclear reactor core simulations involve several physics, especially in accidental transients.Neutron transport is needed to compute the power distribution. Thermal-hydraulics drives the cooling of the core. Fuel mechanics and heat transfer describe fuel state (including temperature). Mechanics allows to take into account deformations of the core. A lot of works have been done on coupling techniques betweenthese physics, but are usually based on separated codes or solvers. In this paper, we present an alternative approach the development of a shared solver for the coupled physics. A multiphysics solver is proposed for a time-dependent coupling between neutron diusion, heat transfer and linear mechanics. It is based on the finite element method and the Newton algorithm. A very simple application is given and shows the rightness of the developments and the relevance of the solver.
• A First Finite Element Solver Shared by Neutron Diffusion,Heat Transfer and Mechanics
  
  • Patricot C.
  • Allaire G.
  • Fandeur O.
  , 2017.
• Moral hazard in welfare economics: on the advantage of Planner's advices to manage employees' actions.
  
  • Mastrolia Thibaut
  , 2017. In this paper, we study moral hazard problems in contract theory by adding an exogenous Planner to manage the actions of Agents hired by a Principal. We provide conditions ensuring that Pareto optima exist for the Agents using the scalarization method associated with the multi-objective optimization problem and we solve the problem of the Principal by finding optimal remunerations given to the Agents. We illustrate our study with a linear-quadratic model by comparing the results obtained when we add a Planner in the Principal/multi-Agents problem with the results obtained in the classical second-best case. More particularly in this example, we give necessary and sufficient conditions ensuring that Pareto optima are Nash equilibria and we prove that the Principal takes the benefit of the action of the Planner in some cases.
• Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures
  
  • Descombes Stéphane
  • Duarte Max
  • Dumont Thierry
  • Guillet Thomas
  • Louvet Violaine
  • Massot Marc
  SMAI Journal of Computational Mathematics, Société de Mathématiques Appliquées et Industrielles (SMAI), 2017, pp.1-23. A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high order time integrators with specific stability properties for each operator, this strategy yields high computational efficiency for large multidimensional computations on standard architectures such as powerful workstations. However, the data structure of the original implementation, based on trees of pointers, provides limited opportunities for efficiency enhancements, while posing serious challenges in terms of parallel programming and load balancing. The present contribution proposes a new implementation of the whole set of numerical methods including Radau5 and ROCK4, relying on a fully different data structure together with the use of a specific library, TBB, for shared-memory, task-based parallelism with work-stealing. The performance of our implementation is assessed in a series of test-cases of increasing difficulty in two and three dimensions on multi-core and many-core architectures, demonstrating high scalability. (10.5802/smai-jcm.19)
  DOI : 10.5802/smai-jcm.19
• Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations
  
  • Gobet Emmanuel
  • Turkedjiev P.
  Stochastic Processes and their Applications, Elsevier, 2017, 127 (4), pp.1171-1203. We design an importance sampling scheme for backward stochastic differential equations (BSDEs) that minimizes the conditional variance occurring in least-squares Monte Carlo (LSMC) algorithms. The Radon-Nikodym derivative depends on the solution of BSDE, and therefore it is computed adaptively within the LSMC procedure. To allow robust error estimates w.r.t. the unknown change of measure, we properly randomize the initial value of the forward process. We introduce novel methods to analyze the error: firstly, we establish norm stability results due to the random initialization; secondly, we develop refined concentration-of-measure techniques to capture the variance of reduction. Our theoretical results are supported by numerical experiments. (10.1016/j.spa.2016.07.011)
  DOI : 10.1016/j.spa.2016.07.011
• Mathematical modelling of the electric sense of fish: the role of multi-frequency measurements and movement
  
  • Garnier Josselin
  • Ammari Habib
  • Boulier Thomas
  • Wang Han
  Bioinspiration and Biomimetics, IOP Publishing, 2017, 12 (2). (10.1088/1748-3190/aa5296)
  DOI : 10.1088/1748-3190/aa5296
• Statistical Post-Processing of Weather Forecasts for the Renewable Energy Production by Eolian Devices
  
  • Lenôtre Lionel
  , 2017. This paper reviews different statistical methods dedicated to the post-processing of Numerical Weather Predictions and Ensemble Forecast. We focus on the application of the post-processing to problems linked to the production of electricity by eolian devices. The basic idea is to give a concise panorama of the methods commonly used nowadays. We pay a particular attention to the mathematics involved in the methods. We do not compare the methods and do not provide some preferences. Classification. 62-02; 62P12.
• Fast Boundary Element Method for acoustics with the Sparse Cardinal Sine Decomposition
  
  • Alouges François
  • Aussal Matthieu
  • Parolin Emile
  Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, Hermès / Paris : Lavoisier, 2017, 26 (4), pp.377-393. (10.1080/17797179.2017.1306832)
  DOI : 10.1080/17797179.2017.1306832
• Alternating block coordinate proximal forward-backward descent for nonconvex regularised problems with biconvex terms
  
  • Nikolova Mila
  • Tan Pauline
  , 2017. In this work we consider a broad class of smooth optimization problems composed of a biconvex data-fidelity terms and smooth, nonconvex regularisation terms. We propose a family of attractive schemes for solving this class of problems. It is based on the standard alternate proximal linearized forward-backward approach. Unlike the existing prox-based algorithms, our approach exploits the biconvex structure of the data term. Thus we use proximity operators with respect to convex functions only. The iterates are uniquely defined, independently of the form of regularization terms.
• Quantitative Performance Assessment of Multiobjective Optimizers: The Average Runtime Attainment Function
  
  • Brockhoff Dimo
  • Auger Anne
  • Hansen Nikolaus
  • Tušar Tea
  , 2017, 10173, pp.103-119. Numerical benchmarking of multiobjective optimization algorithms is an important task needed to understand and recommend algorithms. So far, two main approaches to assessing algorithm performance have been pursued: using set quality indicators, and the (empirical) attainment function and its higher-order moments as a generalization of empirical cumulative distributions of function values. Both approaches have their advantages but rely on the choice of a quality indicator and/or take into account only the location of the resulting solution sets and not when certain regions of the objective space are attained. In this paper, we propose the average runtime attainment function as a quantitative measure of the performance of a multiobjective algorithm. It estimates, for any point in the objective space, the expected runtime to find a solution that weakly dominates this point. After defining the average runtime attainment function and detailing the relation to the (empirical) attainment function, we illustrate how the average runtime attainment function plot displays algorithm performance (and differences in performance) for some algorithms that have been previously run on the biobjective bbob-biobj test suite of the COCO platform. (10.1007/978-3-319-54157-0_8)
  DOI : 10.1007/978-3-319-54157-0_8
• The operator approach to entropy games
  
  • Akian Marianne
  • Gaubert Stephane
  • Grand-Clément Julien
  • Guillaud Jérémie
  , 2017.
• Parallelized Stochastic Gradient Markov Chain Monte Carlo Algorithms for Non-Negative Matrix Factorization
  
  • Şimşekli Umut
  • Durmus Alain
  • Badeau Roland
  • Richard Gael
  • Moulines Éric
  • Cemgil Taylan
  , 2017. Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have become popular in modern data analysis problems due to their computational efficiency. Even though they have proved useful for many statistical models, the application of SG-MCMC to non- negative matrix factorization (NMF) models has not yet been extensively explored. In this study, we develop two parallel SG-MCMC algorithms for a broad range of NMF models. We exploit the conditional independence structure of the NMF models and utilize a stratified sub-sampling approach for enabling parallelization. We illustrate the proposed algorithms on an image restoration task and report encouraging results.
• Focusing Waves Through a Randomly Scattering Medium in the White-Noise Paraxial Regime
  
  • Garnier Josselin
  • Sølna Knut
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2017, 77 (2), pp.500 - 519. (10.1137/16M1087266)
  DOI : 10.1137/16M1087266
• Consensus Convergence with Stochastic Effects
  
  • Garnier Josselin
  • Papanicolaou George
  • Yang Tzu-Wei
  Vietnam Journal of Mathematics, Springer, 2017, 45 (1-2), pp.51 - 75. We consider a stochastic, continuous state and time opinion model where each agent’s opinion locally interacts with other agents’ opinions in the system, and there is also exogenous randomness. The interaction tends to create clusters of common opinion. By using linear stability analysis of the associated nonlinear Fokker–Planck equation that governs the empirical density of opinions in the limit of infinitely many agents, we can estimate the number of clusters, the time to cluster formation, and the critical strength of randomness so as to have cluster formation. We also discuss the cluster dynamics after their formation, the width and the effective diffusivity of the clusters. Finally, the long-term behavior of clusters is explored numerically. Extensive numerical simulations confirm our analytical findings. (10.1007/s10013-016-0190-2)
  DOI : 10.1007/s10013-016-0190-2