Publications

2021

• A random walk model that accounts for space occupation and movements of a large herbivore
  
  • Berthelot Geoffroy C.B.
  • Saïd Sonia
  • Bansaye Vincent
  Scientific Reports, Nature Publishing Group, 2021, 11 (1). Abstract Animal movement has been identified as a key feature in understanding animal behavior, distribution and habitat use and foraging strategies among others. Large datasets of invididual locations often remain unused or used only in part due to the lack of practical models that can directly infer the desired features from raw GPS locations and the complexity of existing approaches. Some of them being disputed for their lack of biological justifications in their design. We propose a simple model of individual movement with explicit parameters, based on a two-dimensional biased and correlated random walk with three forces related to advection (correlation), attraction (bias) and immobility of the animal. These forces can be directly estimated using individual data. We demonstrate the approach by using GPS data of 5 red deer with a high frequency sampling. The results show that a simple random walk template can account for the spatial complexity of wild animals. The practical design of the model is also verified for detecting spatial feature abnormalities and for providing estimates of density and abundance of wild animals. Integrating even more additional features of animal movement, such as individuals’ interactions or environmental repellents, could help to better understand the spatial behavior of wild animals. (10.1038/s41598-021-93387-2)
  DOI : 10.1038/s41598-021-93387-2
• A Phase Transition for Large Values of Bifurcating Autoregressive Models
  
  • Bansaye Vincent
  • Bitseki Penda Siméon Valère
  Journal of Theoretical Probability, Springer, 2021. We describe the asymptotic behavior of the number Z(n)[a(n), infinity) of individuals with a large value in a stable bifurcating autoregressive process, where a(n) -> infinity. The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of Z(n)[a(n), infinity) is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process. (10.1007/s10959-020-01033-w)
  DOI : 10.1007/s10959-020-01033-w
• Polynomial surrogates for Bayesian traveltime tomography
  
  • Sochala Pierre
  • Gesret Alexandrine
  • Le Maitre Olivier
  GEM - International Journal on Geomathematics, Springer, 2021, 12 (1). This paper tackles the issue of the computational load encountered in seismic imaging by Bayesian traveltime inversion. In Bayesian inference, the exploration of the posterior distribution of the velocity model parameters requires extensive sampling. The computational cost of this sampling step can be prohibitive when the first arrival traveltime prediction involves the resolution of an expensive number of forward models based on the eikonal equation. We propose to rely on polynomial chaos surrogates of the traveltimes between sources and receivers to alleviate the computational burden of solving the eikonal equation during the sampling stage. In an offline stage, the approach builds a functional approximation of the traveltimes from a set of solutions of the eikonal equation corresponding to a few values of the velocity model parameters selected in their prior range. These surrogates then substitute the eikonal-based predictions in the posterior evaluation, enabling very efficient extensive sampling of Bayesian posterior, for instance, by a Markov Chain Monte Carlo (MCMC) algorithm. We demonstrate the potential of the approach using numerical experiments on the inference of two-dimensional domains with layered velocity models and different acquisition geometries (microseismic and seismic refraction contexts). The results show that, in our experiments, the number of eikonal model evaluations required to construct accurate surrogates of the traveltimes is low. Further, an accurate and complete characterization of the posterior distribution of the velocity model is possible, thanks to the generation of large sample sets at a low cost. Finally, we discuss the extension of the current approach to more realistic velocity models and operational situations. (10.1007/s13137-021-00184-0)
  DOI : 10.1007/s13137-021-00184-0
• Monotone finite difference discretization of degenerate elliptic partial differential equations using Voronoi's first reduction
  
  • Bonnet Guillaume
  , 2021. In this thesis, we show how Voronoi's first reduction may be used in order to build monotone finite difference discretizations on Cartesian grids of some degenerate elliptic differential operators. We recommend a specific, second-order consistent discretization of two- and three-dimensional linear anisotropic differential operators involving both a first- and a second-order term. We prove the quasi-optimality of this construction. We study some properties on the regularity and the compactness of Voronoi's first reduction in dimension four. We design a method allowing to efficiently approximate Randers distances and associated optimal transport distances, using a large deviations principle. We discretize the Pucci and Monge-Ampère operators. The resulting discretizations are written as maxima of discrete operators; in dimension two, we show that these maxima admit closed-form formulae, reducing the numerical cost of their evaluation. We study the well-posedness, and in some cases the convergence, of a numerical scheme for the second boundary value problem for the Monge-Ampère equation. We present a numerical application to the far-field refractor problem in nonimaging optics.
• A machine learning-based methodology for multi-parametric solution of chemical processes operation optimization under uncertainty
  
  • Shokry Ahmed
  • Medina-González Sergio
  • Baraldi Piero
  • Zio Enrico
  • Moulines Eric
  • Espuña Antonio
  Chemical Engineering Journal, Elsevier, 2021, 425, pp.131632. (10.1016/j.cej.2021.131632)
  DOI : 10.1016/j.cej.2021.131632
• Quantitative large population approximations for stochastic models with interaction or varying environment
  
  • Muñoz-Hernández Felipe
  , 2021. This thesis focuses on the study of stochastic population models composed of individuals interacting between them or with the environment.In a first part, we consider cross-diffusion systems for two species. We develop a duality approach which allows to obtain quantitative stability estimates. We also introduce a stochastic individual-based model on a discrete space. The individuals follow random walks and they are sensitives to the number of individuals of the other species on the same site, with a linear dependence in their rates of motion. We stablish the convergence in law of the stochastic model towards the cross-diffusion systems when the number of individuals per site is greater than the square of the number of sites, assuming small initial conditions.In a second part, we obtain an explicit rate of convergence for some systems of mean-field interacting diffusions with logistic binary branching towards the solutions of non-local self-diffusion systems with logistic mass growth, that describe their large population approximations. The proof relies on a coupling argument for binary branching diffusions based on optimal transport, which allows us to approximate the trajectory of the interacting branching population by a system of independent particles with suitably distributed random space-time births.Finally, in a third part, we consider the reduced tree associated with birth and death processes in varying environments that gives the genealogical structure of the population. We describe geometrically this object by using the lookdown construction introduced by Kurtz and Rodrigues. By introducing a suitable coupling and distance, we approximate the genealogy in the large population regime.
• Synthèse sur la détection des produits issus des nouvelles technologies génomiques (NGT) appliquées aux plantes. Paris, Paris, le 26 novembre 2021
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Demeneix Barbara
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Khalife Jamal
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémy
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2021, pp.29 p.. Synthèse sur la détection des produits issus des nouvelles technologies génomiques (NGT) appliquées aux plantes La question du statut réglementaire des NGT (New Genomic Techniques), qui ont été définies comme techniques de modification du génome « apparues » depuis 2001 , est actuellement débattue en Europe. Ces techniques n’existaient pas, ou étaient peu développées lors de l’adoption des directives et règlements européens qui encadrent actuellement les organismes génétiquement modifiés (OGM). A l’époque le législateur européen avait choisi de réglementer les techniques de transgénèse et d’exempter les méthodes de mutagénèse notamment sur la base d’une expérience d’usage n’ayant révélé aucun problème particulier. Certaines NGT pouvant être utilisées pour induire une mutagenèse, ciblée ou non , la question de leur soumission à la réglementation européenne en vigueur fait l’objet de discussions juridiques et politiques depuis quelques années. Les données scientifiques relatives à ces technologies (définitions, méthodes et résultats) doivent permettre de guider ces discussions.
• Dual Optimization for convex constrained objectives without the gradient-Lipschitz assumptions
  
  • Gaïffas Stéphane
  • Bompaire Martin
  • Bacry Emmanuel
  , 2021.
• Existence and uniqueness of generalized solutions to hyperbolic systems with linear fluxes and stiff sources
  
  • Pichard Teddy
  • Aguillon Nina
  • Després Bruno
  • Godlewski Edwige
  • Ndjinga Michael
  Journal of Hyperbolic Differential Equations, World Scientific Publishing, 2021, 18 (3), pp.653-700. Motivated by the modelling of boiling two-phase flows, we study systems of balance laws with a source term defined as a discontinuous function of the unknown. Due to this discontinuous source term, the classical theory of partial differential equations (PDE) is not sufficient here. Restricting to a simpler system with linear fluxes, a notion of generalized solution is developed. An important point in the construction of a solution is that the curve along which the source jumps, which we call the boiling curve, must never be tangent to the characteristics. This leads to exhibit sufficient conditions which ensure the existence and uniqueness of a solution in two different situations: first when the initial data is smooth and such that the boiling curve is either overcharacteristic or (10.1142/S021989162150020X)
  DOI : 10.1142/S021989162150020X
• Bayesian calibration and assessment of gas-surface interaction models and experiments in atmospheric entry plasmas
  
  • del Val Anabel
  , 2021. The investigation of gas-surface interaction phenomena for atmospheric entry vehicles relies on the development of predictive theoretical models and the capabilities of current experimental facilities. However, due to the complexity of the physics and the various phenomena that need to be investigated in ground-testing facilities, both numerical and experimental processes generate data subjected to uncertainties. Nevertheless, it remains a common practice in the field of aerothermodynamics to resort to calibration and validation methods that are not apt for rigorous uncertainty treatment. This thesis investigates the process of scientific inference and its ramifications for selected gas-surface interaction experiments. Its main contributions are the improvement and re-formulation of model calibrations as statistical inverse problems with the consequent extension of current databases for catalysis and ablation. The model calibrations are posed using the Bayesian formalism where a complete characterization of the posterior probability distributions of selected parameters are computed. The first part of the thesis presents a review of the theoretical models, experiments and numerical codes used to study catalysis and ablation in the context of the von Karman Institute's Plasmatron wind tunnel. This part ends with a summary on the potential uncertainty sources present in both theoretical-numerical and experimental data. Subsequently, the methods used to deal with these uncertainty sources are introduced in detail. The second part of the thesis presents the various original contributions of this thesis. For catalytic materials, an optimal likelihood framework for Bayesian calibration is proposed. This methodology offers a complete uncertainty characterization of catalytic parameters with a decrease of 20\% in the standard deviation with respect to previous works. Building on this framework, a testing strategy which produces the most informative catalysis experiments to date is proposed. Experiments and consequent stochastic analyses are performed, enriching existing catalysis experimental databases for ceramic matrix composites with accurate uncertainty estimations. The last contribution deals with the re-formulation of the inference problem for nitridation reaction efficiencies of a graphite ablative material from plasma wind tunnel data. This is the first contribution in the literature where different measurements of the same flowfield are used jointly to assess their consistency and the resulting ablation parameters. An Arrhenius law is calibrated using all available data, extending the range of conditions to lower surface temperatures where no account of reliable experimental data is found. Epistemic uncertainties affecting the model definition and ablative wall conditions are gauged through various hypothesis testing studies. The final account on the nitridation reaction efficiency uncertainties is given by averaging the results obtained under the different models. This thesis highlights the fact that the process of scientific inference can also carry deep assumptions about the nature of the problem and it can impact how researchers reach conclusions about their work. Ultimately, this thesis contributes to the early efforts of introducing accurate and rigorous uncertainty quantification techniques in atmospheric entry research. The methodologies here presented go in line with developing predictive models with estimated confidence levels.
• Exponential convergence to a steady-state for a population genetics model with sexual reproduction and selection
  
  • Raoul Gaël
  , 2021. We are interested in the dynamics of a population structured by a phenotypic trait. Individuals reproduce sexually, which is represented by a non-linear integral operator. This operator is combined to a multiplicative operator representing selection. When the strength of selection is small, we show that the dynamics of the population is governed by a simple macroscopic differential equation, and that solutions converge exponentially to steady-states that are locally unique. The analysis is based on Wasserstein distance inequalities using a uniform lower bound on distributions. These inequalities are coupled to tail estimates to show the stability of the steady-states.
• Kinetic derivation of Cahn-Hilliard fluid models
  
  • Giovangigli Vincent
  Physical Review E, American Physical Society (APS), 2021, 104. A compressible Cahn-Hilliard fluid model is derived from the kinetic theory of dense gas mixtures. The fluid model involves a van der Waals and Cahn-Hilliard gradient energy, a generalized Korteweg's tensor, a generalized Dunn and Serrin heat flux, and Cahn-Hilliard-type diffusive fluxes. Starting from the BBGKY hierarchy for gas mixtures, a Chapman-Enskog method is used-with a proper scaling of the generalized Boltzmann equations-as well as higher-order Taylor expansions of pair distribution functions. A Euler and van der Waals model is obtained at zeroth order, while the Cahn-Hilliard fluid model is obtained at first order, involving viscous, heat, and diffusive fluxes. The Cahn-Hilliard extra terms are associated with intermolecular forces and pair interaction potentials. (10.1103/physreve.104.054109)
  DOI : 10.1103/physreve.104.054109
• Weak Langmuir turbulence in disordered multimode optical fibers
  
  • Baudin Kilian
  • Garnier Josselin
  • Fusaro Adrien
  • Berti Nicolas
  • Millot Guy
  • Picozzi Antonio
  , 2021.
• A generative model for fBm with deep ReLU neural networks
  
  • Allouche Michaël
  • Girard Stéphane
  • Gobet Emmanuel
  , 2021.
• Comments on the cosmic convergence of nonexpansive maps
  
  • Gutiérrez Armando W.
  • Karlsson Anders
  Journal of Fixed Point Theory and Applications, Springer Verlag, 2021, 23 (4). This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of $\ell^{1}$. We also point out some inaccurate assertions appearing in the literature on this topic. (10.1007/s11784-021-00896-8)
  DOI : 10.1007/s11784-021-00896-8
• Optimal ecological transition path of a credit portfolio distribution, based on Multidate Monge-Kantorovich formulation
  
  • Gobet Emmanuel
  • Lage Clara
  , 2021.
• Mixture of Conditional Gaussian Graphical Models for unlabelled heterogeneous populations in the presence of co-factors
  
  • Lartigue Thomas
  • Durrleman Stanley
  • Allassonnière Stéphanie
  SN Computer Science, Springer, 2021, 2 (466). Conditional correlation networks, within Gaussian Graphical Models (GGM), are widely used to describe the direct interactions between the components of a random vector. In the case of an unlabelled Heterogeneous population, Expectation Maximisation (EM) algorithms for Mixtures of GGM have been proposed to estimate both each sub-population's graph and the class labels. However, we argue that, with most real data, class affiliation cannot be described with a Mixture of Gaussian, which mostly groups data points according to their geometrical proximity. In particular, there often exists external co-features whose values affect the features' average value, scattering across the feature space data points belonging to the same sub-population. Additionally, if the co-features' effect on the features is Heterogeneous, then the estimation of this effect cannot be separated from the sub-population identification. In this article, we propose a Mixture of Conditional GGM (CGGM) that subtracts the heterogeneous effects of the co-features to regroup the data points into sub-population corresponding clusters. We develop a penalised EM algorithm to estimate graph-sparse model parameters. We demonstrate on synthetic and real data how this method fulfils its goal and succeeds in identifying the sub-populations where the Mixtures of GGM are disrupted by the effect of the co-features. (10.1007/s42979-021-00865-5)
  DOI : 10.1007/s42979-021-00865-5
• Optimal Auction Duration: A Price Formation Viewpoint
  
  • Paul Jusselin
  • Thibaut Mastrolia
  • Mathieu Rosenbaum
  Operations Research, INFORMS, 2021, 69 (6), pp.1734-1745. Optimal Auction Duration in Financial Markets In the considered auction market, market makers fill the order book during a given time period while some other investors send market orders. The clearing price is set to maximize the exchanged volume at the clearing time according to the supply and demand of each market participant. The error made between this clearing price and the efficient price is derived as a function of the auction duration. We study the impact of the behavior of market takers on this error to minimize their transaction costs. We compute the optimal duration of the auctions for 77 stocks traded on Euronext and compare the quality of the price formation process under this optimal value to the case of a continuous limit order book. Continuous limit order books are usually found to be suboptimal. Order of magnitude of optimal auction durations is from 2–10 minutes. (10.1287/opre.2021.2113)
  DOI : 10.1287/opre.2021.2113
• Design of multiobjective optimization algorithms and theoretical analysis of evolution strategies
  
  • Toure Cheikh Saliou
  , 2021. This work is dedicated to zero-order black-box optimization, where only a sequence of function evaluations is available for the update of the optimization algorithm. Evolutionary algorithms are commonly used to solve this type of problems. Among them, evolution strategies like CMA-ES are state-of-the-art optimization algorithms for zero-order black-box optimization problems with a continuous search space. Particular aspects of the CMA-ES are the recombination mechanism and the non-elitist selection scheme, that are crucial to deal with local irregularities and multimodality. A multiobjective CMA-ES (with recombination) is then particularly in demand for real world applications, to tackle multiobjective problems with local Pareto fronts.We design that type of multiobjective optimizers. More specifically, a new multiobjective indicator called Uncrowded Hypervolume Improvement (UHVI) is created, along with a framework of multiobjective optimizers called Sofomore. By instantiating Sofomore with CMA-ES, COMO-CMA-ES is obtained. The COMO-CMA-ES algorithm is experimented on bi-objective functions that we analyze in details in this thesis, that are the bi-objective convex quadratic problems. Interestingly, linear convergence results are empirically observed, which is the optimal linear behavior we can get since CMA-ES converges linearly on strictly convex-quadratic functions. A Python package called pycomocma and a Matlab interface are developed in this work for COMO-CMA-ES and the Sofomore framework.On a theoretical perspective, we analyze global linear convergence of evolution strategies with recombination that include well-known optimization algorithms, on a wide class of functions that are the scaling-invariant functions. Our main condition for convergence is that the expected logarithm of the step-size must increase on nontrivial linear functions. We analyze thoroughly the class of scaling-invariant functions and emphasize similar properties that they share with the positively homogeneous functions.
• Factored couplings in multi-marginal optimal transport via difference of convex programming
  
  • Tran Huy Quang
  • Janati Hicham
  • Redko Ievgen
  • Flamary Rémi
  • Courty Nicolas
  , 2021. Optimal transport (OT) theory underlies many emerging machine learning (ML) methods nowadays solving a wide range of tasks such as generative modeling, transfer learning and information retrieval. These latter works, however, usually build upon a traditional OT setup with two distributions, while leaving a more general multi-marginal OT formulation somewhat unexplored. In this paper, we study the multi-marginal OT (MMOT) problem and unify several popular OT methods under its umbrella by promoting structural information on the coupling. We show that incorporating such structural information into MMOT results in an instance of a different of convex (DC) programming problem allowing us to solve it numerically. Despite high computational cost of the latter procedure, the solutions provided by DC optimization are usually as qualitative as those obtained using currently employed optimization schemes.
• VP17.02: Description and clinical validation of a real‐time AI diagnostic companion for fetal ultrasound examination
  
  • Stirnemann Julien J.
  • Besson Rémi
  • Spaggiari Emmanuel
  • Bourgon Nicolas
  • Rojo Sandra
  • Logé Frédéric
  • Saint Paul Hélène Peyro
  • Allassonnière Stéphanie
  • Le Pennec Erwan
  • Ville Yves
  , 2021, 58 (S1), pp.169-170. (10.1002/uog.24291)
  DOI : 10.1002/uog.24291
• Système de guidage d’un utilisateur par un signal sonore, et procédé de guidage correspondant
  
  • Alouges François
  • Ferrand Sylvain
  • Le Borgne Philippe
  , 2021. La présente invention concerne un système de guidage d’un utilisateur, comprenant un terminal informatique portable et un dispositif audio stéréophonique , destiné à être associé à la tête de l’utilisateur , communiquant l’un avec l’autre sans fil. Le dispositif audio est équipé de capteurs inertiels et d’un moteur de rendu binaural. Le terminal informatique portable comprend un logiciel apte à générer des données d’instructions de guidage qui associent une description d’au moins un signal sonore à diffuser, et une indication relative à la position virtuelle de ce ou ces signaux sonores. Le moteur de rendu binaural génère un signal sonore spatialisé, diffusé à l’utilisateur par le dispositif audio , en fonction des données d’instructions de guidage, transmises par le terminal informatique portable par communication sans fil, et de données de données des capteurs inertiels.
• Semi-relaxed Gromov Wasserstein divergence with applications on graphs
  
  • Vincent-Cuaz Cédric
  • Flamary Rémi
  • Corneli Marco
  • Vayer Titouan
  • Courty Nicolas
  , 2021. Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), has proven to be successful in handling the specific nature of the associated objects. More specifically, through the nodes connectivity relations, GW operates on graphs, seen as probability measures over specific spaces. At the core of OT is the idea of conservation of mass, which imposes a coupling between all the nodes from the two considered graphs. We argue in this paper that this property can be detrimental for tasks such as graph dictionary or partition learning, and we relax it by proposing a new semi-relaxed Gromov-Wasserstein divergence. Aside from immediate computational benefits, we discuss its properties, and show that it can lead to an efficient graph dictionary learning algorithm. We empirically demonstrate its relevance for complex tasks on graphs such as partitioning, clustering and completion.
• Topology optimization in quasi-static plasticity with hardening using a level-set method
  
  • Desai Jeet
  • Allaire Grégoire
  • Jouve François
  • Mang Chetra
  Structural and Multidisciplinary Optimization, Springer Verlag, 2021, 64. We study topology optimization in quasi-static plasticity with linear kinematic and linear isotropic hardening using a level-set method. We consider the primal variational formulation for the plasticity problem. This formulation is subjected to penalization and regularization, resulting in an approximate problem that is shape-dierentiable. The shape derivative for the approximate problem is computed using the adjoint method. Thanks to the proposed penalization and regularization, the time discretization of the adjoint problem is proved to be well-posed. For comparison purposes, the shape derivative for the original problem is computed in a formal manner. Finally, shape and topology optimization is performed numerically using the level-set method, and 2D and 3D case studies are presented. Shapes are captured exactly using a body-tted mesh at every iteration of the optimization algorithm. (10.1007/s00158-021-03034-7)
  DOI : 10.1007/s00158-021-03034-7
• Recycling Krylov subspace strategies for sequences of sampled stochastic elliptic equations
  
  • Venkovic Nicolas
  • Mycek Paul
  • Giraud Luc
  • Le Maitre Olivier
  , 2021. We are interested in the quantification of uncertainties in discretized elliptic partial differential equations with a random coefficient field. In sampling-based approaches, this relies on solving large numbers of symmetric positive definite (SPD) linear systems with different matrices. In particular, we consider the case in which these operators are sampled by Markov chain Monte Carlo, which leads to sequences of correlated matrices. We investigate recycling Krylov subspace strategies for the iterative solution of sequences of linear systems formed with such matrices. The linear systems are solved using initialized conjugate gradient (Init-CG) methods, where approximate eigenvectors of the previously sampled operator are used to set an initial guess, and deflated conjugate gradient (Def-CG) methods, where the Krylov subspace is augmented with these vectors. The following aspects of eigenvector approximation, and their effect on deflation and initialization, are investigated in this context: (i) projection technique, and (ii) refreshing strategy of the eigen-search space. Our numerical experiments show that, when not using a preconditioner, these aspects only impact convergence behaviors of Def-CG at the early stages of the sampling sequence. Second, unlike sequences with multiple right-hand sides and a constant operator, our experiments with multiple matrices show that, even for highly correlated matrices, Init-CG does not reproduce the convergence behavior of Def-CG. Finally, the limits of deflation used as a means to compensate for the inefficiency of block-Jacobi (bJ) preconditioners are investigated. For small systems, using a bJ preconditioner while deflating with at least as many approximate eigenvectors as the number of bJ blocks achieves similar convergence behaviors to PCG with a constant algebraic multigrid (AMG) preconditioner. For larger systems, although the effect of deflation is improved when using the right refreshing strategy of the eigen-search space, the combination of deflation with bJ preconditioners does not scale as well as using PCG with a constant AMG preconditioner based on the median realization of the coefficient field.