Publications

2020

• The polyhedral structure and complexity of multistage stochastic linear problem with general cost distribution
  
  • Forcier Maël
  • Gaubert Stephane
  • Leclère Vincent
  , 2020. By studying the intrinsic polyhedral structure of multistage stochastic linear problems (MSLP), we show that a MSLP with an arbitrary cost distribution is equivalent to a MSLP on a finite scenario tree. More precisely, we show that the expected cost-to-go function, at a given stage, is affine on each cell of a chamber complex i.e., on the common refinement of the complexes obtained by projecting the faces of a polyhedron. This chamber complex is independent of the cost distribution. Furthermore, we examine several important special cases of random cost distributions, exponential on a polyhedral cone, or uniform on a polytope, and obtain an explicit description of the supporting hyperplanes of the cost-to-go function, in terms of certain valuations attached to the cones of a normal fan. This leads to fixed-parameter tractability results, showing that MSLP can be solved in polynomial time when the number of stages together with certain characteristic dimensions are fixed.
• Topology optimization of thermal fluid-structure systems using body-fitted meshes and parallel computing
  
  • Feppon Florian
  • Allaire Grégoire
  • Dapogny Charles
  • Jolivet Pierre
  Journal of Computational Physics, Elsevier, 2020, 417, pp.109574. An efficient framework is described for the shape and topology optimization of realistic three-dimensional, weakly-coupled fluid-thermal-mechanical systems. At the theoretical level, the proposed methodology relies on the boundary variation of Hadamard for describing the sensitivity of functions with respect to the domain. From the numerical point of view, three key ingredients are used: (i) a level set based mesh evolution method allowing to describe large deformations of the shape while maintaining an adapted, high-quality mesh of the latter at every stage of the optimization process; (ii) an efficient constrained optimization algorithm which is very well adapted to the infinite-dimensional shape optimization context; (iii) efficient preconditioning techniques for the solution of large finite element systems in a reasonable computational time. The performance of our strategy is illustrated with two examples of coupled physics: respectively fluid-structure interaction and convective heat transfer. Before that, we perform three other test cases, involving a single physics (structural, thermal and aerodynamic design), for comparison purposes and for assessing our various tools: in particular, they prove the ability of the mesh evolution technique to capture very thin bodies or shells in 3D. (10.1016/j.jcp.2020.109574)
  DOI : 10.1016/j.jcp.2020.109574
• A bi-level energy management strategy for HEVs under probabilistic traffic conditions
  
  • Le Rhun Arthur
  • Bonnans Frédéric
  • de Nunzio Giovanni
  • Leroy Thomas
  • Martinon Pierre
  , 2020. This work proposes a new approach to optimize the consumption of a hybrid electric vehicle taking into account the traffic conditions. The method is based on a bi-level decomposition in order to make the implementation suitable for online use. The offline lower level computes cost maps thanks to a stochastic optimization that considers the influence of traffic, in terms of speed/acceleration probability distributions. At the online upper level, a deterministic optimization computes the ideal state of charge at the end of each road segment, using the computed cost maps. Since the high computational cost due to the uncertainty of traffic conditions has been managed at the lower level, the upper level is fast enough to be used online in the vehicle. Errors due to discretization and computation in the proposed algorithm have been studied. Finally, we present numerical simulations using actual traffic data, and compare the proposed bi-level method to a deterministic optimization with perfect information about traffic conditions. The solutions show a reasonable over-consumption compared with deterministic optimization, and manageable computational times for both the offline and online parts.
• Sparse Inverse Covariance Learning for CMA-ES with Graphical Lasso
  
  • Varelas Konstantinos
  • Auger Anne
  • Hansen Nikolaus
  , 2020. This paper introduces a variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), denoted as gl-CMA-ES, that utilizes the Graphical Lasso regularization. Our goal is to efficiently solve partially separable optimization problems of a certain class by performing stochastic search with a search model parameterized by a sparse precision , i.e. inverse covariance matrix. We illustrate the effect of the global weight of the l1 regularizer and investigate how Graphical Lasso with non equal weights can be combined with CMA-ES, allowing to learn the conditional dependency structure of problems with sparse Hessian matrices. For non-separable sparse problems, the proposed method with appropriately selected weights, outperforms CMA-ES and improves its scaling, while for dense problems it maintains the same performance.
• A Real-Time Indoor Localization Method with Low-Cost Microwave Doppler Radar Sensors and Particle Filter
  
  • Ferrand Sylvain
  • Alouges François
  • Aussal Matthieu
  , 2020, pp.467-474. (10.1007/978-3-030-58796-3_54)
  DOI : 10.1007/978-3-030-58796-3_54
• Efficient methodology for seismic fragility curves estimation by active learning on Support Vector Machines
  
  • Sainct Rémi
  • Feau Cyril
  • Martinez Jean-Marc
  • Garnier Josselin
  Structural Safety, Elsevier, 2020, 86, pp.101972. Fragility curves which express the failure probability of a structure as function of a loading intensity measure are nowadays widely used to facilitate the design and decision making of structures/infrastructures against seismic hazard (and possibly other natural hazards), with analysis procedures specified by Seismic Probabilistic Risk Assessment, Performance-Based Earthquake Engineering, and other frameworks. To avoid the use of parametric models (such as the lognormal model) to estimate fragility curves from a reduced number of numerical calculations, a methodology based on Support Vector Machines (SVMs) coupled with an active learning algorithm is proposed in this paper. In practice, input excitation is reduced to some relevant parameters and then SVMs are used for a binary classification of the structural responses relative to a limit threshold of exceedance. Since the output is not binary but a real-valued score, a probabilistic interpretation of the output is exploited to estimate very efficiently fragility curves as score functions or as functions of classical seismic intensity measures. (10.1016/j.strusafe.2020.101972)
  DOI : 10.1016/j.strusafe.2020.101972
• Fused Gromov-Wasserstein Distance for Structured Objects
  
  • Vayer Titouan
  • Chapel Laetitia
  • Flamary Rémi
  • Tavenard Romain
  • Courty Nicolas
  Algorithms, MDPI, 2020, 13 (9), pp.212. Optimal transport theory has recently found many applications in machine learning thanks to its capacity to meaningfully compare various machine learning objects that are viewed as distributions. The Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the elements of the objects, but treats them independently, whereas the Gromov–Wasserstein distance focuses on the relations between the elements, depicting the structure of the object, yet discarding its features. In this paper, we study the Fused Gromov-Wasserstein distance that extends the Wasserstein and Gromov–Wasserstein distances in order to encode simultaneously both the feature and structure information. We provide the mathematical framework for this distance in the continuous setting, prove its metric and interpolation properties, and provide a concentration result for the convergence of finite samples. We also illustrate and interpret its use in various applications, where structured objects are involved. (10.3390/a13090212)
  DOI : 10.3390/a13090212
• Doubly robust treatment effect estimation with missing attributes
  
  • Mayer Imke
  • Sverdrup Erik
  • Gauss Tobias
  • Moyer Jean-Denis
  • Wager Stefan
  • Josse Julie
  Annals of Applied Statistics, Institute of Mathematical Statistics, 2020, 14 (3), pp.1409-1431. Missing attributes are ubiquitous in causal inference, as they are in most applied statistical work. In this paper, we consider various sets of assumptions under which causal inference is possible despite missing attributes and discuss corresponding approaches to average treatment effect estimation, including generalized propensity score methods and multiple imputation. Across an extensive simulation study, we show that no single method systematically out-performs others. We find, however, that doubly robust modifications of standard methods for average treatment effect estimation with missing data repeatedly perform better than their non-doubly robust baselines; for example, doubly robust generalized propensity score methods beat inverse-weighting with the generalized propensity score. This finding is reinforced in an analysis of an observations study on the effect on mortality of tranexamic acid administration among patients with traumatic brain injury in the context of critical care management. Here, doubly robust estimators recover confidence intervals that are consistent with evidence from randomized trials, whereas non-doubly robust estimators do not. (10.1214/20-AOAS1356)
  DOI : 10.1214/20-AOAS1356
• Hierarchical matrix approximations for space-fractional diffusion equations
  
  • Boukaram Wajih
  • Lucchesi Marco
  • Turkiyyah George
  • Le Maitre Olivier
  • Knio Omar
  • Keyes David
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2020, 369, pp.113191. Space fractional diffusion models generally lead to dense discrete matrix operators, which lead to substantial computational challenges when the system size becomes large. For a state of size N , full representation of a fractional diffusion matrix would require O(N 2) memory storage requirement, with a similar estimate for matrix-vector products. In this work, we present H 2 matrix representation and algorithms that are amenable to efficient implementation on GPUs, and that can reduce the cost of storing these operators to O(N) asymp-totically. Matrix-vector multiplications can be performed in asymptotically linear time as well. Performance of the algorithms is assessed in light of 2D simulations of space fractional diffusion equation with constant diffusivity. Attention is focused on smooth particle approximation of the governing equations, which lead to discrete operators involving explicit radial kernels. The algorithms are first tested using the fundamental solution of the un-forced space fractional diffusion equation in an unbounded domain, and then for the steady, forced, fractional diffusion equation in a bounded domain. Both matrix-inverse and pseudo-transient solution approaches are considered in the latter case. Our experiments show that the construction of the fractional diffusion matrix, the matrix-vector multiplication, and the generation of an approximate inverse pre-conditioner all perform very well on a single GPU on 2D problems with N in the range 10 5-10 6. In addition, the tests also showed that, for the entire range of parameters and fractional orders considered, results obtained using the H 2 approximations were in close agreement with results obtained using dense operators, and exhibited the same spatial order of convergence. Overall, the present experiences showed that the H 2 matrix framework promises to provide practical means to handle large-scale space fractional diffusion models in several space dimensions, at a computational cost that is asymptotically similar to the cost of handling classical diffusion equations. (10.1016/j.cma.2020.113191)
  DOI : 10.1016/j.cma.2020.113191
• A mathematical approach to deal with nanoparticle polydispersity in surface enhanced Raman spectroscopy to quantify antineoplastic agents
  
  • Dowek Antoine
  • Lê Laetitia Minh Mai
  • Rohmer Tom
  • Legrand François-Xavier
  • Remita Hynd
  • Lampre Isabelle
  • Tfayli Ali
  • Lavielle Marc
  • Caudron Eric
  Talanta, Elsevier, 2020, 217, pp.121040. Antineoplastic agents are, for most of them, highly toxic drugs prepared at hospital following individualized prescription. To protect patients and healthcare workers, it is important to develop analytical tools able to identify and quantify such drugs on a wide concentration range. In this context, surface enhanced Raman spectroscopy (SERS) has been tested as a specific and sensitive technique. Despite the standardization of the nanoparticle synthesis, a polydispersity of nanoparticles in the suspension and a lack of reproducibility persist. This study focuses on the development of a new mathematical approach to deal with this nanoparticle polydispersity and its consequences on SERS signal variability through the feasibility of 5-fluorouracil (5FU) quantification using silver nanoparticles (AgNPs) and a handled Raman spectrophotometer. Variability has been maximized by synthetizing six different batches of AgNPs for an average size of 24.9 nm determined by transmission electron microscopy, with residual standard deviation of 17.0%. Regarding low performances of the standard multivariate data processing, an alternative approach based on the nearest neighbors were developed to quantify 5FU. By this approach, the predictive performance of the 5FU concentration was significantly improved. The mean absolute relative error (MARE) decreased from 16.8% with the traditional approach based on PLS regression to 6.30% with the nearest neighbors approach (p-value < 0.001). This study highlights the importance of developing mathematics adapted to SERS analysis which could be a step to overcome the spectral variability in SERS and thus participate in the development of this technique as an analytical tool in quality control to quantify molecules with good performances, particularly in the pharmaceutical field. (10.1016/j.talanta.2020.121040)
  DOI : 10.1016/j.talanta.2020.121040
• Identification d’une signature moléculaire d’hypercortisolisme par analyse du methylome du sang total
  
  • Armignacco Roberta
  • Lartigue Thomas
  • Jouinot Anne
  • Septier Amandine
  • Neou Mario
  • Gaspar Cassandra
  • Perlemoine Karine
  • Bouys Lucas
  • Braun Leah
  • Riester Anne
  • Allassonnière Stéphanie
  • Zennaro Maria Christina
  • Reincke Martin
  • Bertherat Jérôme
  • Beuschlein Felix
  • Assié Guillaume
  Annales d'Endocrinologie = Annals of Endocrinology, Société française d'endocrinologie [1939-....], 2020, 81 (4), pp.180. (10.1016/j.ando.2020.07.117)
  DOI : 10.1016/j.ando.2020.07.117
• Adaptive predictive-questionnaire by approximate dynamic-programming
  
  • Logé Frédéric
  • Le Pennec Erwan
  • Amadou-Boubacar Habiboulaye
  , 2020. (10.18420/muc2020-ws111-264)
  DOI : 10.18420/muc2020-ws111-264
• Apparent diffusion coefficient measured by diffusion MRI of moving and deforming domains
  
  • Mekkaoui Imen
  • Pousin Jerome
  • Hesthaven Jan
  • Li Jing-Rebecca
  Journal of Magnetic Resonance, Elsevier, 2020, 318, pp.106809. The modeling of the diffusion MRI signal from moving and deforming organs such as the heart is challenging due to significant motion and deformation of the imaged medium during the signal acquisition. Recently, a mathematical formulation of the Bloch-Torrey equation, describing the complex transverse magnetization due to diffusion-encoding magnetic field gradients, was developed to account for the motion and deformation. In that work, the motivation was to cancel the effect of the motion and deformation in the MRI image and the space scale of interest spans multiple voxels. In the present work, we adapt the mathematical equation to study the diffusion MRI signal at the much smaller scale of biological cells.We start with the Bloch-Torrey equation defined on a cell that is moving and deforming and linearize the equation around the magnitude of the diffusion-encoding gradient. The result is a second order signal model in which the linear term gives the imaginary part of the diffusion MRI signal and the quadratic term gives the apparent diffusion coefficient (ADC) attributable to the biological cell. We numerically validate this model for a variety of motions and deformations. (10.1016/j.jmr.2020.106809)
  DOI : 10.1016/j.jmr.2020.106809
• An efficient dimension reduction for the Gaussian process emulation of two nested codes with functional outputs
  
  • Marque-Pucheu Sophie
  • Perrin Guillaume
  • Garnier Josselin
  Computational Statistics, Springer Verlag, 2020, 35 (3), pp.1059-1099. In this paper, we first propose an efficient method for the dimension reduction of the functional input of a code with functional output. It is based on the approximation of the output by a model which is linear with respect to the functional input. This approximation has a sparse structure, whose parameters can be accurately estimated from a small set of observations of the code. The Gaussian predictor based on this projection basis is significantly more accurate than the one based on a projection obtained with Partial Least Squares. Secondly, the surrogate modeling of two nested codes with functional outputs is considered. In such a case, the functional output of the first code is one of the inputs of the second code. The Gaussian process regression of the second code is performed using the proposed dimension reduction. A Gaussian predictor of the nested code is obtained by composing the predictors of the two codes and linearizing this composition. Moreover, two sequential design criteria are proposed. Since we aim at performing a sensitivity analysis, these criteria are based on a minimization of the prediction variance. Moreover, one of the criteria enables to choose, if it is possible, which of the two codes to run. Thus, the computational budget is optimally allocated between the two codes and the prediction error is substantially reduced. (10.1007/s00180-019-00926-7)
  DOI : 10.1007/s00180-019-00926-7
• Linear predictor on linearly-generated data with missing values: non consistency and solutions
  
  • Le Morvan Marine
  • Prost Nicolas
  • Josse Julie
  • Scornet Erwan
  • Varoquaux Gaël
  , 2020, PMLR 108, pp.3165-3174. We consider building predictors when the data have missing values. We study the seemingly-simple case where the target to predict is a linear function of the fully-observed data and we show that, in the presence of missing values, the optimal predictor may not be linear. In the particular Gaussian case, it can be written as a linear function of multiway interactions between the observed data and the various missing-value indicators. Due to its intrinsic complexity, we study a simple approximation and prove generalization bounds with finite samples, highlighting regimes for which each method performs best. We then show that multilayer perceptrons with ReLU activation functions can be consistent, and can explore good trade-offs between the true model and approximations. Our study highlights the interesting family of models that are beneficial to fit with missing values depending on the amount of data available.
• A Privacy-preserving Method to Optimize Distributed Resource Allocation
  
  • Jacquot Paulin
  • Beaude Olivier
  • Benchimol Pascal
  • Gaubert Stephane
  • Oudjane Nadia
  SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2020, 30 (3), pp.2303-2336. We consider a resource allocation problem involving a large number of agents with individual constraints subject to privacy, and a central operator whose objective is to optimize a global, possibly nonconvex, cost while satisfying the agents' constraints, for instance an energy operator in charge of the management of energy consumption flexibilities of many individual consumers. We provide a privacy-preserving algorithm that does compute the optimal allocation of resources, avoiding each agent to reveal her private information (constraints and individual solution profile) neither to the central operator nor to a third party. Our method relies on an aggregation procedure: we compute iteratively a global allocation of resources, and gradually ensure existence of a disaggregation, that is individual profiles satisfying agents' private constraints, by a protocol involving the generation of polyhedral cuts and secure multiparty computations (SMC). To obtain these cuts, we use an alternate projection method, which is implemented locally by each agent, preserving her privacy needs. We adress especially the case in which the local and global constraints define a transportation polytope. Then, we provide theoretical convergence estimates together with numerical results, showing that the algorithm can be effectively used to solve the allocation problem in high dimension, while addressing privacy issues. (10.1137/19M127879X)
  DOI : 10.1137/19M127879X
• PODNet: Pooled Outputs Distillation for Small-Tasks Incremental Learning
  
  • Douillard Arthur
  • Cord Matthieu
  • Ollion Charles
  • Robert Thomas
  • Valle Eduardo
  , 2020, 12365, pp.86-102. Lifelong learning has attracted much attention, but existing works still struggle to fight catastrophic forgetting and accumulate knowledge over long stretches of incremental learning. In this work, we propose PODNet, a model inspired by representation learning. By carefully balancing the compromise between remembering the old classes and learning new ones, PODNet fights catastrophic forgetting, even over very long runs of small incremental tasks --a setting so far unexplored by current works. PODNet innovates on existing art with an efficient spatial-based distillation-loss applied throughout the model and a representation comprising multiple proxy vectors for each class. We validate those innovations thoroughly, comparing PODNet with three state-of-the-art models on three datasets: CIFAR100, ImageNet100, and ImageNet1000. Our results showcase a significant advantage of PODNet over existing art, with accuracy gains of 12.10, 6.51, and 2.85 percentage points, respectively. Code is available at https://github.com/arthurdouillard/incremental_learning.pytorch (10.1007/978-3-030-58565-5_6)
  DOI : 10.1007/978-3-030-58565-5_6
• Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities
  
  • Bellettini Giovanni
  • Chambolle Antonin
  • Kholmatov Shokhrukh
  Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, Royal Society of Edinburgh, 2020, 151 (4), pp.1135--1170. Under suitable assumptions on the family of anisotropies, we prove the existence of a weak global 1/(n+1)-Hölder continuous in time mean curvature flow with mobilities of a bounded anisotropic partition in any dimension using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We improve the Hölder exponent to 1/2 in the case of partitions with the same anisotropy and the same mobility and provide a weak comparison result in this setting for a weak anisotropic mean curvature flow of a partition and an anisotropic mean curvature two-phase flow. (10.1017/prm.2020.53)
  DOI : 10.1017/prm.2020.53
• Differential tomography of micromechanical evolution in elastic materials of unknown micro/macrostructure
  
  • Pourahmadian Fatemeh
  • Haddar Houssem
  SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2020, 13 (3), pp.1302–1330. Differential evolution indicators are introduced for 3D spatiotemporal imaging of micromechanical processes in complex materials where progressive variations due to manufacturing and/or aging are housed in a highly scattering background of a-priori unknown or uncertain structure. In this vein, a three-tier imaging platform is established where: (1) the domain is periodically (or continuously) subject to illumination and sensing in an arbitrary configuration; (2) sequential sets of measured data are deployed to distill segment-wise scattering signatures of the domain's internal structure through carefully constructed, non-iterative solutions to the scattering equation; and (3) the resulting solution sequence is then used to rigorously construct an imaging functional carrying appropriate invariance with respect to the unknown stationary components of the background e.g., pre-existing interstitial boundaries and bubbles. This gives birth to differential indicators that specifically recover the 3D support of micromechanical evolution within a network of unknown scatterers. The direct scattering problem is formulated in the frequency domain where the background is comprised of a random distribution of monolithic fragments. The constituents are connected via highly heterogeneous interfaces of unknown elasticity and dissipation which are subject to spatiotemporal evolution. The support of internal boundaries are sequentially illuminated by a set of incident waves and thusinduced scattered fields are captured over a generic observation surface. The performance of the proposed imaging indicator is illustrated through a set of numerical experiments for spatiotemporal reconstruction of progressive damage zones featuring randomly distributed cracks and bubbles. (10.1137/19M1305707)
  DOI : 10.1137/19M1305707
• Challenging common bolus advisor for self-monitoring type-I diabetes patients using Reinforcement Learning
  
  • Logé Frédéric
  • Le Pennec Erwan
  • Amadou-Boubacar Habiboulaye
  , 2020. Patients with diabetes who are self-monitoring have to decide right before each meal how much insulin they should take. A standard bolus advisor exists, but has never actually been proven to be optimal in any sense. We challenged this rule applying Reinforcement Learning techniques on data simulated with T1DM, an FDA-approved simulator developed by Kovatchev et al. modeling the gluco-insulin interaction. Results show that the optimal bolus rule is fairly different from the standard bolus advisor, and if followed can actually avoid hypoglycemia episodes.
• Minimax optimal rates for Mondrian trees and forests
  
  • Mourtada Jaouad
  • Gaïffas Stéphane
  • Scornet Erwan
  Annals of Statistics, Institute of Mathematical Statistics, 2020, 48 (4), pp.2253-2276. (10.1214/19-AOS1886)
  DOI : 10.1214/19-AOS1886
• Sampling scheme for intractable copula function, application to the computation of tail events in factor copula model
  
  • Bénézet Cyril
  • Gobet Emmanuel
  • Targino Rodrigo
  , 2020.
• Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method
  
  • Agarwal Ankush
  • Claisse Julien
  Stochastic Processes and their Applications, Elsevier, 2020. We study semi-linear elliptic PDEs with polynomial non-linearity and provide a probabilistic representation of their solution using branching diffusion processes. When the non-linearity involves the unknown function but not its derivatives, we extend previous results in the literature by showing that our probabilistic representation provides a solution to the PDE without assuming its existence. In the general case, we derive a new representation of the solution by using marked branching diffusion processes and automatic differentiation formulas to account for the non-linear gradient term. In both cases, we develop new theoretical tools to provide explicit sufficient conditions under which our probabilistic representations hold. As an application, we consider several examples including multi-dimensional semi-linear elliptic PDEs and estimate their solution by using the Monte Carlo method. (10.1016/j.spa.2020.02.009)
  DOI : 10.1016/j.spa.2020.02.009
• Bayesian inference of spatially varying Manning’s n coefficients in an idealized coastal ocean model using a generalized Karhunen-Loève expansion and polynomial chaos
  
  • Siripatana Adil
  • Le Maitre Olivier
  • Knio Omar
  • Dawson Clint
  • Hoteit Ibrahim
  Ocean Dynamics, Springer Verlag, 2020, 70 (8), pp.1103-1127. Bayesian inference with coordinate transformations and polynomial chaos for a Gaussian process with a parametrized prior covariance model was introduced in [61] to enable and infer uncertainties in a parameter-ized prior field. The feasibility of the method was successfully demonstrated on a simple transient diffusion equation. In this work, we adopt a similar approach to infer a spatially varying Manning's n field in a coastal ocean model. The idea is to view the prior on the Manning's n field as a stochastic Gaussian field, expressed through a covariance function with uncertain hyper-parameters. A generalized Karhunen-Loeve (KL) expansion, which incorporates the construction of a reference basis of spatial modes and a coordinate transformation, is then applied to the prior field. To improve the computational efficiency of the method proposed in [61], we propose to use two polynomial chaos expansions to: (i) approximate the coordinate transformation, and (ii) build a cheap surrogate of the large-scale advanced circulation (ADCIRC) numerical model. These two surrogates are used to accelerate the Bayesian inference process using a Markov chain Monte Carlo algorithm. Water elevation data are inverted within an observing system simulation experiment framework, based on a realistic ADCIRC model, to infer the KL coordinates and hyper-parameters of a reference 2D Manning's field. Our results demonstrate the efficiency of the proposed approach and suggest that including the hyper-parameter uncertainties greatly enhances the inferred Manning's n field, compared to using a covariance with fixed hyper-parameters. (10.1007/s10236-020-01382-4)
  DOI : 10.1007/s10236-020-01382-4
• Sampling scheme for intractable copula function, application to the computation of tail events in factor copula model
  
  • Bénézet Cyril
  • Gobet Emmanuel
  • Targino Rodrigo
  , 2020.