Publications

2019

• Energy Management for Microgrids: a Reinforcement Learning Approach
  
  • Levent Tanguy
  • Preux Philippe
  • Le Pennec Erwan
  • Badosa Jordi
  • Henri Gonzague
  • Bonnassieux Yvan
  , 2019, pp.1-5. This paper presents a framework based on reinforcement learning for energy management and economic dispatch of an islanded microgrid without any forecasting module. The architecture of the algorithm is divided in two parts: a learning phase trained by a reinforcement learning (RL) algorithm on a small dataset and the testing phase based on a decision tree induced from the trained RL. An advantage of this approach is to create an autonomous agent, able to react in real-time, considering only the past. This framework was tested on real data acquired at Ecole Polytechnique in France over a long period of time, with a large diversity in the type of days considered. It showed near optimal, efficient and stable results in each situation. (10.1109/ISGTEurope.2019.8905538)
  DOI : 10.1109/ISGTEurope.2019.8905538
• Adiabatic control of quantum systems
  
  • Augier Nicolas
  , 2019. The main purpose of the thesis is to study the links between the singularities of the spectrum of a controlled quantum Hamiltonian and the controllability issues of the associated Schr"odinger equation.The principal issue that is developed is how to control a parameter-dependent family of quantum systems with a common control input. This problem of ensemble controllability is linked to the design of a robust control strategy when a parameter (a resonance frequency or a control field inhomogeneity for instance) is unknown, and is an important issue for experimentalists.Thanks to the study one-parametric families of Hamiltonians and their generic singularities, we give an explicit control strategy for the ensemble controllability problem when geometric conditions on the spectrum of the Hamiltonian are satisfied. The result is based on adiabatic approximation theory and on the presence of curves of conical eigenvalue intersections of the controlled Hamiltonian. The proposed technique works for systems evolving both in finite-dimensional and infinite-dimensional Hilbert spaces. Then we study the problem of ensemble controllability under less restrictive hypotheses on the spectrum, namely the presence of non-conical singularities. Under generic conditions such non-conical singularities are not present for single systems, but appear for one-parametric families of systems.For the study of a single system, we focus on a class of curves in the space of controls, called the non-mixing curves (defined in cite{Bos}), that can optimize the adiabatic dynamics near conical and non-conical intersections. They are linked to the geometry of the eigenspaces of the controlled Hamiltonian and the adiabatic approximation holds with higher precision along them.We propose to study the compatibility of the adiabatic approximation with the rotating wave approximation. Such approximations are usually done in cascade by physicists. My work shows that this is justified for finite dimensional quantum systems only under certain conditions on the time scales. We also study ensemble control issues in this case.
• A law of large numbers for branching Markov processes by the ergodicity of ancestral lineages
  
  • Marguet Aline
  ESAIM: Probability and Statistics, EDP Sciences, 2019, 23, pp.638–661. We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event occurs, the trait of a descendant at birth depends on the trait of the mother. We prove a law of large numbers for the empirical distribution of ancestral trajectories. It ensures that the empirical measure converges to the mean value of the spine which is a time-inhomogeneous Markov process describing the trait of a typical individual along its ancestral lineage. Our approach relies on ergodicity arguments for this time-inhomogeneous Markov process. We apply this technique on the example of a size-structured population with exponential growth in varying environment. (10.1051/ps/2018029)
  DOI : 10.1051/ps/2018029
• Statistical models and stochastic algorithms for the analysis of longitudinal Riemanian manifold valued data with multiple dynamic
  
  • Chevallier Juliette
  , 2019. Beyond transversal studies, temporal evolution of phenomena is a field of growing interest. For the purpose of understanding a phenomenon, it appears more suitable to compare the evolution of its markers over time than to do so at a given stage. The follow-up of neurodegenerative disorders is carried out via the monitoring of cognitive scores over time. The same applies for chemotherapy monitoring: rather than tumors aspect or size, oncologists asses that a given treatment is efficient from the moment it results in a decrease of tumor volume. The study of longitudinal data is not restricted to medical applications and proves successful in various fields of application such as computer vision, automatic detection of facial emotions, social sciences, etc.Mixed effects models have proved their efficiency in the study of longitudinal data sets, especially for medical purposes. Recent works (Schiratti et al., 2015, 2017) allowed the study of complex data, such as anatomical data. The underlying idea is to model the temporal progression of a given phenomenon by continuous trajectories in a space of measurements, which is assumed to be a Riemannian manifold. Then, both a group-representative trajectory and inter-individual variability are estimated. However, these works assume an unidirectional dynamic and fail to encompass situations like multiple sclerosis or chemotherapy monitoring. Indeed, such diseases follow a chronic course, with phases of worsening, stabilization and improvement, inducing changes in the global dynamic.The thesis is devoted to the development of methodological tools and algorithms suited for the analysis of longitudinal data arising from phenomena that undergo multiple dynamics and to apply them to chemotherapy monitoring. We propose a nonlinear mixed effects model which allows to estimate a representative piecewise-geodesic trajectory of the global progression and together with spacial and temporal inter-individual variability. Particular attention is paid to estimation of the correlation between the different phases of the evolution. This model provides a generic and coherent framework for studying longitudinal manifold-valued data.Estimation is formulated as a well-defined maximum a posteriori problem which we prove to be consistent under mild assumptions. Numerically, due to the non-linearity of the proposed model, the estimation of the parameters is performed through a stochastic version of the EM algorithm, namely the Markov chain Monte-Carlo stochastic approximation EM (MCMC-SAEM). The convergence of the SAEM algorithm toward local maxima of the observed likelihood has been proved and its numerical efficiency has been demonstrated. However, despite appealing features, the limit position of this algorithm can strongly depend on its starting position. To cope with this issue, we propose a new version of the SAEM in which we do not sample from the exact distribution in the expectation phase of the procedure. We first prove the convergence of this algorithm toward local maxima of the observed likelihood. Then, with the thought of the simulated annealing, we propose an instantiation of this general procedure to favor convergence toward global maxima: the tempering-SAEM.
• Variational approximation of size-mass energies for k-dimensional currents
  
  • Chambolle Antonin
  • Ferrari Luca Alberto Davide
  • Merlet Benoît
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2019, 25 (2019) (43), pp.39. In this paper we produce a $Γ$-convergence result for a class of energies $F k ε,a$ modeled on the Ambrosio-Tortorelli functional. For the choice k = 1 we show that $F 1 ε,a Γ$-converges to a branched transportation energy whose cost per unit length is a function $f n−1 a$ depending on a parameter $a > 0$ and on the codimension n − 1. The limit cost f a (m) is bounded from below by 1 + m so that the limit functional controls the mass and the length of the limit object. In the limit a ↓ 0 we recover the Steiner energy. We then generalize the approach to any dimension and codimension. The limit objects are now k-currents with prescribed boundary, the limit functional controls both their masses and sizes. In the limit $a ↓ 0$, we recover the Plateau energy defined on k-currents, $k < n$. The energies $F k ε,a$ then can be used for the numerical treatment of the k-Plateau problem. (10.1051/cocv/2018027)
  DOI : 10.1051/cocv/2018027
• Viscosity solutions of path-dependent PDEs with randomized time
  
  • Ren Zhenjie
  • Rosestolato Mauro
  , 2019. We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a slight modification of the definition introduced in [8]. With the new definition, we prove the two important results till now missing in the literature, namely, a general stability result and a comparison result for semicontinuous sub-/super-solutions. As an application, we prove the existence of viscosity solutions using the Perron method. Moreover, we connect viscosity solutions of path-dependent PDEs with viscosity solutions of partial differential equations on Hilbert spaces.
• Second order backward SDE with random terminal time
  
  • Lin Yiqing
  • Ren Zhenjie
  • Touzi Nizar
  • Yang Junjian
  , 2019. Backward stochastic differential equations extend the martingale representation theorem to the nonlinear setting. This can be seen as path-dependent counterpart of the extension from the heat equation to fully nonlinear parabolic equations in the Markov setting. This paper extends such a nonlinear representation to the context where the random variable of interest is measurable with respect to the information at a finite stopping time. We provide a complete wellposedness theory which covers the semilinear case (backward SDE), the semilinear case with obstacle (reflected backward SDE), and the fully nonlinear case (second order backward SDE).
• Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks
  
  • Hu Kaitong
  • Ren Zhenjie
  • Siska David
  • Szpruch Lukasz
  , 2019. We present a probabilistic analysis of the long-time behaviour of the nonlocal, diffusive equations with a gradient flow structure in 2-Wasserstein metric, namely, the Mean-Field Langevin Dynamics (MFLD). Our work is motivated by a desire to provide a theoretical underpinning for the convergence of stochastic gradient type algorithms widely used for non-convex learning tasks such as training of deep neural networks. The key insight is that the certain class of the finite dimensional non-convex problems becomes convex when lifted to infinite dimensional space of measures. We leverage this observation and show that the corresponding energy functional defined on the space of probability measures has a unique minimiser which can be characterised by a first order condition using the notion of linear functional derivative. Next, we show that the flow of marginal laws induced by the MFLD converges to the stationary distribution which is exactly the minimiser of the energy functional. We show that this convergence is exponential under conditions that are satisfied for highly regularised learning tasks. At the heart of our analysis is a pathwise perspective on Otto calculus used in gradient flow literature which is of independent interest. Our proof of convergence to stationary probability measure is novel and it relies on a generalisation of LaSalle's invariance principle. Importantly we do not assume that interaction potential of MFLD is of convolution type nor that has any particular symmetric structure. This is critical for applications. Finally, we show that the error between finite dimensional optimisation problem and its infinite dimensional limit is of order one over the number of parameters.
• Nonlinear predictable representation and L1-solutions of second-order backward SDEs
  
  • Ren Zhenjie
  • Touzi Nizar
  • Yang Junjian
  , 2019. The theory of backward SDEs extends the predictable representation property of Brownian motion to the nonlinear framework, thus providing a path-dependent analog of fully nonlinear parabolic PDEs. In this paper, we consider backward SDEs, their reflected version, and their second-order extension, in the context where the final data and the generator satisfy L1-type of integrability condition. Our main objective is to provide the corresponding existence and uniqueness results for general Lipschitz generators. The uniqueness holds in the so-called Doob class of processes, simultaneously under an appropriate class of measures. We emphasize that the previous literature only deals with backward SDEs, and requires either that the generator is separable in (y,z), see Peng [Pen97], or strictly sublinear in the gradient variable z, see [BDHPS03], or that the final data satisfies an LlnL-integrability condition, see [HT18]. We by-pass these conditions by defining L1-integrability under the nonlinear expectation operator induced by the previously mentioned class of measures.
• Accelerated Monte-Carlo methods for Piecewise Deterministic Markov Processes for a faster reliability assessment of power generation systems within the PyCATSHOO toolbox
  
  • Galtier Thomas
  , 2019. This thesis deals with the reliability assessment of nuclear or hydraulic power plants, which are built and exploited by the company EDF (Électricité de France). As the failures of such systems are associated to major human and environmental consequences, for both safety and regulatory reasons, EDF must ensure that the probability of failure of its power generation systems is low enough. The failure of a system occurs when the physical variables characterizing the system (temperature, pression, water level) enter a critical region. Typically, these physical variables can enter a critical region only when a sufficient number of the basic components within the system are damaged. So, in order to assess the probability of having a system failure, we have to jointly model the evolution of the physical variables and of the statuses of the components. To do so we use a model based on piecewise deterministic Markovian processes (PDMPs). This model allows to estimate the probability of failure of the system by simulation. Unfortunately the model is computationally intensive to run, and the classic Monte-carlo method, which needs a lot of simulations to estimate the probability of a rare event, is then too computationally intensive in our context. Methods requiering less simulations are needed, like for instance variance reduction methods. Among variance reduction methods, we distinguish importance sampling methods and splitting methods. The difficulty is that we need to use these methods on PDMPs, which raises a few issues. The theoretical foundations for the importance sampling methods with PDMPs are yet to be defined. Indeed these methods require to weight the simulations with likelihood ratios, and these likelihood ratios have not been properly defined so far for PDMP trajectories, which are degenerate processes. Also efficient biasing strategies (i.e. altered simulation processes yielding a small variance estimator) have not been proposed for PDMPs. This thesis presents how to build the likelihood ratios, it investigates the characteristics of the ideal optimal biasing strategy, and it presents a convenient and efficient way to specify practical biasing strategies for systems of reasonable size. Concerning particular filters methods, they tend to perform poorly on PDMPs with low jump rates and therefore they need to be adapted in order to be successfully applied to reliable power generation systems. Indeed in this context, splitting methods are sometimes less efficient than the naive Monte-Carlo method. This thesis investigates how it is possible to efficiently use these methods with PDMPs. Namely we propose an adaptation of the interacting particles system method (IPS) for PDMPs with low jump rates, and we investigate the convergence properties of the estimators of our methods. The efficiency of the method is tested on a reasonable size system showing a perfomance slightly better than or equivalent to the Monte-Carlo method. An additionnal result on the IPS method is also proposed in a general Markovian framework (beyond PDMPs). The IPS method takes as input certain potential functions that directly impact the variance of the estimator. In this PhD, we show that there are optimal potential functions for which the variance is minimized and we give their closed-form expressions.
• Development of a multiscale finite element method for incompressible flows in heterogeneous media
  
  • Feng Qingqing
  , 2019. The nuclear reactor core is a highly heterogeneous medium crowded with numerous solid obstacles and macroscopic thermohydraulic phenomena are directly affected by localized phenomena. However, modern computing resources are not powerful enough to carry out direct numerical simulations of the full core with the desired accuracy. This thesis is devoted to the development of Multiscale Finite Element Methods (MsFEMs) to simulate incompressible flows in heterogeneous media with reasonable computational costs. Navier-Stokes equations are approximated on the coarse mesh by a stabilized Galerkin method, where basis functions are solutions of local problems on fine meshes by taking precisely local geometries into account. Local problems are defined by Stokes or Oseen equations with appropriate boundary conditions and source terms. We propose several methods to improve the accuracy of MsFEMs, by enriching the approximation space of basis functions. In particular, we propose high-order MsFEMs where boundary conditions and source terms are chosen in spaces of polynomials whose degrees can vary. Numerical simulations show that high-order MsFEMs improve significantly the accuracy of the solution. A multiscale simulation chain is constructed to simulate successfully flows in two- and three-dimensional heterogeneous media.
• Non-Convex Optimization for Latent Data Models : Algorithms, Analysis and Applications
  
  • Karimi Belhal
  , 2019. Many problems in machine learning pertain to tackling the minimization of a possibly non-convex and non-smooth function defined on a Many problems in machine learning pertain to tackling the minimization of a possibly non-convex and non-smooth function defined on a Euclidean space.Examples include topic models, neural networks or sparse logistic regression.Optimization methods, used to solve those problems, have been widely studied in the literature for convex objective functions and are extensively used in practice.However, recent breakthroughs in statistical modeling, such as deep learning, coupled with an explosion of data samples, require improvements of non-convex optimization procedure for large datasets.This thesis is an attempt to address those two challenges by developing algorithms with cheaper updates, ideally independent of the number of samples, and improving the theoretical understanding of non-convex optimization that remains rather limited.In this manuscript, we are interested in the minimization of such objective functions for latent data models, ie, when the data is partially observed which includes the conventional sense of missing data but is much broader than that.In the first part, we consider the minimization of a (possibly) non-convex and non-smooth objective function using incremental and online updates.To that end, we propose several algorithms exploiting the latent structure to efficiently optimize the objective and illustrate our findings with numerous applications.In the second part, we focus on the maximization of non-convex likelihood using the EM algorithm and its stochastic variants.We analyze several faster and cheaper algorithms and propose two new variants aiming at speeding the convergence of the estimated parameters.
• Mean-field Langevin System, Optimal Control and Deep Neural Networks
  
  • Hu Kaitong
  • Kazeykina Anna
  • Ren Zhenjie
  , 2019. In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant measure of which is shown to be the optimal control of the initial problem under mild conditions. Therefore, this system of processes can be viewed as a continuous-time numerical algorithm for computing the optimal control. As an application, this result endorses the solvability of the stochastic gradient descent algorithm for a wide class of deep neural networks.
• Analytic expressions of the solutions of advection-diffusion problems in 1D with discontinuous coefficients
  
  • Lejay Antoine
  • Lenôtre Lionel
  • Pichot Géraldine
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2019, 79 (5), pp.1823-1849. In this article, we provide a method to compute analytic expressions of the resolvent kernel of differential operators of the diffusion type with discontinuous coefficients in one dimension. Then we apply it when the coefficients are piecewise constant. We also perform the Laplace inversion of the resolvent kernel to obtain expressions of the transition density functions or fundamental solutions. We show how these explicit formula are useful to simulate advection-diffusion problems using particle tracking techniques (10.1137/18M1164500)
  DOI : 10.1137/18M1164500
• Inside-outside duality with artificial backgrounds
  
  • Audibert Lorenzo
  • Chesnel Lucas
  • Haddar Houssem
  Inverse Problems, IOP Publishing, 2019, 35 (10), pp.104008. We use the inside-outside duality approach proposed by Kirsch-Lechleiter to identify transmission eigenvalues associated with artificial backgrounds. We prove that for well chosen artificial backgrounds, in particular for the ones with zero index of refraction at the inclusion location, one obtains a necessary and sufficient condition characterizing transmission eigenvalues via the spectrum of the modified far field operator. We also complement the existing literature with a convergence result for the invisible generalized incident field associated with the transmission eigenvalues. This work is based on several of the pioneering works of our dearest colleague and friend Armin Lechleiter and is dedicated to his memory.
• Approximation of curves with piecewise constant or piecewise linear functions
  
  • de Gournay Frédéric
  • Kahn Jonas
  • Lebrat Léo
  , 2019. In this paper we compute the Hausdorff distance between sets of continuous curves and sets of piecewise constant or linear discretizations. These sets are Sobolev balls given by the continuous or discrete L p-norm of the derivatives. We detail the suitable discretization or smoothing procedure which are preservative in the sense of these norms. Finally we exhibit the link between Eulerian numbers and the uniformly space knots B-spline used for smoothing.
• HRTF and panning evaluations for binaural audio guidance
  
  • Ferrand Sylvain
  • Alouges François
  • Aussal Matthieu
  , 2019. We develop a device to guide blind people using binaural sound obtained by HRTF convolutions and reproduced by headphones. We have obtained good results in terms of user experience, but for guidance precision, the contribution of HRTFs compared to panning remained to be demonstrated. In this study, we design different binaural filters and we ask the subjects to orient themselves in the direction of a sound source. We compare their performances with two HRTFs and two panning filters, both for static and continuously moving sound sources. We show that HRTFs filtering allows the user to orient him/herself more precisely towards a sound source compared to a panning both in the static and the dynamic cases.
• Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater topography
  
  • Chesnel Lucas
  • Nazarov Sergei
  • Taskinen Jari
  Asymptotic Analysis, IOS Press, 2019. We consider the propagation of surface water waves in a straight planar channel perturbed at the bottom by several thin curved tunnels and wells. We propose a method to construct non reflecting underwater topographies of this type at an arbitrary prescribed wave number. To proceed, we compute asymptotic expansions of the diffraction solutions with respect to the small parameter of the geometry taking into account the existence of boundary layer phenomena. We establish error estimates to validate the expansions using advances techniques of weighted spaces with detached asymptotics. In the process, we show the absence of trapped surface waves for perturbations small enough. This analysis furnishes asymptotic formulas for the scattering matrix and we use them to determine underwater topographies which are non-reflecting. Theoretical and numerical examples are given.
• On-ground risk estimation of reentering human-made space objects
  
  • Sanson Francois
  , 2019. Recent regulations impose the re-entry of human-made end-of-life space object with a rigorous assessment of the risk for human assets. The risk evaluation requires sequences of complex numerical simulations accounting for the multi-physics phenomena occurring during the reentry of a space object, e.g., fluid-structure interactions and heat transfer. Further, these simulations are inaccurate because they rely on overly simplified models and partial knowledge of the reentry conditions.In this thesis, we propose novel uncertainty quantification techniques to deal with some of the uncertainties characterizing the problem and apply them to predict the risk for human assets due to the reentry of a space object.First, we construct a system of solvers to predict both the controlled or uncontrolled reentry of space objects. Compared to the existing reentry software, our system naturally accommodates the uncertainty in the object breakup predictions. Moreover, the constitutive solvers are interfaced and coupled within a framework that allows a single user to perform parallel runs of the full system.Second, we present two original methods to propagate the uncertainties in reentry predictions using the system of solvers. First, we construct a surrogate model approximating the directed systems of solvers, using a system of Gaussian Processes (SoGP). We build this probabilistic surrogate by approximating each solver (or a group of solvers) of the directed system by a Gaussian Process (GP). We show that the predictive variance of the SoGP is composed of individual contributions from each GP.We use this decomposition of the variance decomposition to develop active learning strategies based on training datasets which are enriched parsimoniously to improve the prediction of the least reliable GP only. We assessed the performance of the SoGP on several analytical and industrial cases. The SoGP coupled with active learning strategies yielded systematically significant improvements.The second method aims at predicting the survivability of space objects. During a space reentry event, the object can break up and generate fragments. Some fragments disintegrate in the atmosphere while others survive to the ground. Assessing the survivability of a fragment implies determining whether it reaches the ground or not and if it does, the impact location and the risk associated. We propose an original formulation of the survivability assessment problem to efficiently estimate the risk. The proposed method involves the composition of a classifier (demise prediction) with a Gaussian Process (impact location prediction).Dedicated active learning strategies are designed to balance the prediction errors of the classifier and GP and allocate training samples adequately.Finally, we apply the methods developed in the thesis to the prediction of the controlled reentry of a rocket upper-stage. The problem involves a large number of uncertainties (38), including the initial orbit properties, the deorbiting conditions, the upper stage material characteristics, the atmosphere model parameters, and the fragment material uncertainties. Moreover, we use a probabilistic breakup model for the object breakup to account for the model uncertainties. With our methods, we estimate at a reasonable computational cost the statistics of the conditions at breakup, the survival probability of the fragments, the casualty area, and the human risk. Global sensitivity analyses of the breakup conditions and casualty area provide a ranking of the most critical uncertainties. This study demonstrates the capability of our surrogate simulator to produce a robust measure of on-ground risk for a realistic reentry scenario.
• Optimal Design of ORC Turbine Blades Under Geometric and Operational Uncertainties
  
  • Razaaly Nassim
  • Persico Giacomo
  • Congedo Pietro Marco
  , 2019. Typical energy sources for Organic Rankine Cycle (ORC) power systems feature variable heat load, hence turbine inlet/outlet thermodynamic conditions. The use of organic compounds with heavy molecular weight introduces uncertainties in the fluid thermodynamic modeling and complexity in the turbomachinery aerodynamics, with supersonic flows and strong shocks, which grow in relevance in the aforementioned off-design conditions. These features also depend strongly on the local blade shape, which can be influenced by the geometric tolerances of the blade manufacturing. This study presents a Robust Optimization (RO) analysis on a typical supersonic nozzle cascade for ORC applications under the combined effect of uncertainties associated to operating conditions and geometric tolerances: a classical formulation consisting in minimizing the mean of a well-suited performance function, constraining the average mass flow rate to be within a prescribed range is addressed, by means of a bi-level Gaussian Process (GP) surrogate-based approach. Influence of the operating conditions range and geometric variability are investigated considering several scenarios, in which the different effects act in combination or separated; results indicate that the combination of different classes of uncertainites has an impact on the robust-optimal blade shape and, in turn, in their response in the frame of uncertain scenarios.
• Detecting Sound Hard Cracks in Isotropic Inhomogeneities
  
  • Audibert Lorenzo
  • Chesnel Lucas
  • Haddar Houssem
  • Napal Kevish
  , 2019, pp.61-73. We consider the problem of detecting the presence of sound-hard cracks in a non homogeneous reference medium from the measurement of multi-static far field data. First, we provide a factorization of the far field operator in order to implement the Generalized Linear Sampling Method (GLSM). The justification of the analysis is also based on the study of a special interior transmission problem. This technique allows us to recover the support of the inhomogeneity of the medium but fails to locate cracks. In a second step, we consider a medium with a multiply connected inhomogeneity assuming that we know the far field data at one given frequency both before and after the appearance of cracks. Using the Differential Linear Sampling Method (DLSM), we explain how to identify the component(s) of the inhomogeneity where cracks have emerged. The theoretical justification of the procedure relies on the comparison of the solutions of the corresponding interior transmission problems without and with cracks. Finally we illustrate the GLSM and the DLSM providing numerical results in 2D. In particular, we show that our method is reliable for different scenarios simulating the appearance of cracks between two measurements campaigns.
• Shape Optimization of a Coupled Thermal Fluid-Structure Problem in a Level Set Mesh Evolution Framework
  
  • Feppon Florian
  • Allaire Grégoire
  • Bordeu Felipe
  • Cortial Julien
  • Dapogny Charles
  SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, Springer, 2019, 76 (3), pp.413–458. Hadamard's method of shape differentiation is applied to topology optimization of a weakly coupled three physics problem. The coupling is weak because the equations involved are solved consecutively, namely the steady state Navier-Stokes equations for the fluid domain, first, the convection diffusion equation for the whole domain, second, and the linear thermo-elasticity system in the solid domain, third. Shape sensitivities are derived in a fully Lagrangian setting which allows us to obtain shape derivatives of general objective functions. An emphasis is given on the derivation of the adjoint interface condition dual to the one of equality of the normal stresses at the fluid solid interface. The arguments allowing to obtain this surprising condition are specifically detailed on a simplified scalar problem. Numerical test cases are presented using the level set mesh evolution framework of [4]. It is demonstrated how the implementation enables to treat a variety of shape optimization problems. keywords. Topology and shape optimization, adjoint methods, fluid structure interaction, convective heat transfer, adaptive remeshing. (10.1007/s40324-018-00185-4)
  DOI : 10.1007/s40324-018-00185-4
• A microscopic view of the Fourier law
  
  • Bodineau Thierry
  • Gallagher Isabelle
  • Saint-Raymond Laure
  Comptes Rendus. Physique, Académie des sciences (Paris), 2019, 20, pp.402 - 418. (10.1016/j.crhy.2019.08.002)
  DOI : 10.1016/j.crhy.2019.08.002
• Contract Theory in a VUCA World
  
  • Hernández-Santibán͂ez Nicolás
  • Mastrolia Thibaut
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2019, 57 (4), pp.3072-3100. (10.1137/18M1184527)
  DOI : 10.1137/18M1184527
• Assessing the causes of diversification slowdowns: temperature‐dependent and diversity‐dependent models receive equivalent support
  
  • Condamine Fabien
  • Rolland Jonathan
  • Morlon Hélène
  Ecology Letters, Wiley, 2019, 22 (11), pp.1900-1912. (10.1111/ele.13382)
  DOI : 10.1111/ele.13382