Publications

2020

• A Finite Difference Method for Space Fractional Differential Equations with Variable Diffusivity Coefficient
  
  • Mustapha Kassem
  • Furati Khaled
  • Knio Omar
  • Le Maitre Olivier
  Communications on Applied Mathematics and Computation, Springer, 2020, 2 (4), pp.671-688. Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving variable-coefficient one-dimensional (steady state) fractional DEs, with two-sided fractional derivatives (FDs). The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided FD when the right-sided FD is approximated by two consecutive applications of the first-order backward Euler method. Our scheme reduces to the standard second-order central difference in the absence of FDs. The existence and uniqueness of the numerical solution are proved, and truncation errors of order h are demonstrated (h denotes the maximum space step size). The numerical tests illustrate the global O(h) accuracy, except for nonsmooth cases which, as expected, have deteriorated convergence rates. (10.1007/s42967-020-00066-6)
  DOI : 10.1007/s42967-020-00066-6
• Estimation and imputation in Probabilistic Principal Component Analysis with Missing Not At Random data
  
  • Sportisse Aude
  • Boyer Claire
  • Josse Julie
  , 2020. Missing Not At Random (MNAR) values lead to significant biases in the data, since the probability of missingness depends on the unobserved values. They are "not ignorable" in the sense that they often require defining a model for the missing data mechanism, which makes inference or imputation tasks more complex. Furthermore, this implies a strong \textit{a priori} on the parametric form of the distribution. However, some works have obtained guarantees on the estimation of parameters in the presence of MNAR data, without specifying the distribution of missing data \citep{mohan2018estimation, tang2003analysis}. This is very useful in practice, but is limited to simple cases such as self-masked MNAR values in data generated according to linear regression models. We continue this line of research, but extend it to a more general MNAR mechanism, in a more general model of the probabilistic principal component analysis (PPCA), \textit{i.e.}, a low-rank model with random effects. We prove identifiability of the PPCA parameters. We then propose an estimation of the loading coefficients and a data imputation method. They are based on estimators of means, variances and covariances of missing variables, for which consistency is discussed. These estimators have the great advantage of being calculated using only the observed data, leveraging the underlying low-rank structure of the data. We illustrate the relevance of the method with numerical experiments on synthetic data and also on real data collected from a medical register.
• A duality between scattering poles and transmission eigenvalues in scattering theory
  
  • Cakoni Fioralba
  • Colton David
  • Haddar Houssem
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2020, 476 (2244), pp.20200612. (10.1098/rspa.2020.0612)
  DOI : 10.1098/rspa.2020.0612
• Contextual Semantic Interpretability
  
  • Marcos Diego
  • Fong Ruth
  • Lobry Sylvain
  • Flamary Rémi
  • Courty Nicolas
  • Tuia Devis
  , 2020. Convolutional neural networks (CNN) are known to learn an image representation that captures concepts relevant to the task, but do so in an implicit way that hampers model interpretability. However, one could argue that such a representation is hidden in the neurons and can be made explicit by teaching the model to recognize semantically interpretable attributes that are present in the scene. We call such an intermediate layer a \emph{semantic bottleneck}. Once the attributes are learned, they can be re-combined to reach the final decision and provide both an accurate prediction and an explicit reasoning behind the CNN decision. In this paper, we look into semantic bottlenecks that capture context: we want attributes to be in groups of a few meaningful elements and participate jointly to the final decision. We use a two-layer semantic bottleneck that gathers attributes into interpretable, sparse groups, allowing them contribute differently to the final output depending on the context. We test our contextual semantic interpretable bottleneck (CSIB) on the task of landscape scenicness estimation and train the semantic interpretable bottleneck using an auxiliary database (SUN Attributes). Our model yields in predictions as accurate as a non-interpretable baseline when applied to a real-world test set of Flickr images, all while providing clear and interpretable explanations for each prediction.
• Finding optimal Pulse Repetion Intervals with Many-objective Evolutionary Algorithms
  
  • Dufossé Paul
  • Enderli Cyrille
  , 2020.
• Alternative subgroup joint analysis proposal of nonlinear longitudinal and time-to-event data for modeling pregnancy miscarriage
  
  • de La Cruz Rolando
  • Lavielle Marc
  • Meza Cristian
  • Núñez-Antón Vicente
  , 2020. Pregnancies achieved through in-vitro fertilization (IVF) are associated with adverse first trimester outcomes in comparison to spontaneously achieved pregnancies. Human chorionic gonadotrophin β subunit (β-HCG) is a well-known and accurate biomarker for the diagnosis and monitoring of pregnancy after IVF. Low levels of β-HCG during the first trimester of pregnancy are related to miscarriage, ectopic pregnancy and failure of IVF procedure. Longitudinal profiles of β-HCG can be utilized to distinguish between normal and abnormal pregnancies, and to assist and guide the clinician in better management and monitoring of post-IVF pregnancies. Therefore, being able to assess the association between longitudinally measured β-HCG and time to early miscarriage is of crucial interest to clinicians. A common joint modeling approach proposal to achieve this objective is to use subject-specific random effects in a mixed effects model for longitudinal β-HCG data as predictors in a model for the time-to-event (TTE) data. This work was motivated by an observational study with normal and abnormal pregnancies where serum concentrations of β-HCG were measured in 173 young women during a gestational age of 9-86 days at a private clinic in Santiago, Chile. Some women experienced a miscarriage event but the rest did not. For those women who experienced miscarriage, their exact event times were unknown, in such case we have interval censored data, assuming that the event occurred between the last time of the observed β-HCG measurement and ten days after. For our dataset we consider a nonlinear mixed effects (NLME) model for both normal and abnormal pregnancies, but the joint model is considered only for the subgroup of miscarriage women. All the estimation procedures are based on the Stochastic Approximation of the EM (SAEM) algorithm implemented in the Monolix software.
• CYFIP2 containing WAVE complexes inhibit cell migration
  
  • Polesskaya Anna
  • Boutillon Arthur
  • Wang Yanan
  • Lavielle Marc
  • Vacher Sophie
  • Schnitzler Anne
  • Molinie Nicolas
  • Rocques Nathalie
  • Fokin Artem
  • Bièche Ivan
  • David Nicolas B.
  • Gautreau Alexis
  , 2020. Branched actin networks polymerized by the Arp2/3 complex are critical for cell migration. The WAVE complex is the major Arp2/3 activator at the leading edge of migrating cells. However, multiple distinct WAVE complexes can be assembled in a cell, due to the combinatorial complexity of paralogous subunits. When systematically analyzing the contribution of each WAVE complex subunit to the metastasis-free survival of breast cancer patients, we found that overexpression of the CYFIP2 subunit was surprisingly associated with good prognosis. Gain and loss of function experiments in transformed and untransformed mammary epithelial cells revealed that cell migration was always inversely related to CYFIP2 levels. The role of CYFIP2 was systematically opposite to the role of the paralogous subunit CYFIP1 or of the NCKAP1 subunit. The specific CYFIP2 function in inhibiting cell migration was related to its unique ability to down-regulate classical pro-migratory WAVE complexes. The anti-migratory function of CYFIP2 was also revealed in migration of prechordal plate cells during gastrulation of the zebrafish embryo, indicating that the unique function of CYFIP2 is critically important in both physiological and pathophysiological migrations. (10.1101/2020.07.02.184655)
  DOI : 10.1101/2020.07.02.184655
• Maximum Likelihood Estimation of Regularization Parameters in High-Dimensional Inverse Problems: An Empirical Bayesian Approach Part I: Methodology and Experiments
  
  • Vidal Ana Fernandez
  • de Bortoli Valentin
  • Pereyra Marcelo
  • Durmus Alain
  SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2020, 13 (4), pp.1945-1989. (10.1137/20M1339829)
  DOI : 10.1137/20M1339829
• Maximum Likelihood Estimation of Regularization Parameters in High-Dimensional Inverse Problems: An Empirical Bayesian Approach. Part II: Theoretical Analysis
  
  • de Bortoli Valentin
  • Durmus Alain
  • Pereyra Marcelo
  • Vidal Ana Fernandez
  SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2020, 13 (4), pp.1990-2028. (10.1137/20M1339842)
  DOI : 10.1137/20M1339842
• A Review of some recent advancements in Non-Ideal Compressible Fluid Dynamics
  
  • Gori Giulio
  • Le Maitre Olivier
  • Congedo Pietro M
  , 2020. This paper reviews selected advancements concerning the theoretical, numerical and experimental investigation of Non-Ideal Compressible Fluid Dynamics (NICFD) flows for Renewable Energy applications. First, we review the so-called non-ideal oblique shock waves. After, we briefly discuss the state-of-the-art concerning computational models for NICFD applications, with a particular focus on the predictions accuracy assessment. Eventually, we describe a Bayesian framework for inferring the material-dependent parameters appearing in complex thermodynamics models for NICFD.
• Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area
  
  • Gaubert Stéphane
  • Akian Marianne
  • Allamigeon Xavier
  • Boyet Marin
  • Colin Baptiste
  • Grohens Théotime
  • Massoulié Laurent
  • Parsons David P.
  • Adnet Frederic
  • Chanzy Érick
  • Goix Laurent
  • Lapostolle Frédéric
  • Lecarpentier Éric
  • Leroy Christophe
  • Loeb Thomas
  • Marx Jean-Sébastien
  • Télion Caroline
  • Treluyer Laurent
  • Carli Pierre
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2020, 358 (7), pp.843-875. We portray the evolution of the Covid-19 epidemic during the crisis of March-April 2020 in the Paris area, by analyzing the medical emergency calls received by the EMS of the four central departments of this area (Centre 15 of SAMU 75, 92, 93 and 94). Our study reveals strong dissimilarities between these departments. We show that the logarithm of each epidemic observable can be approximated by a piecewise linear function of time. This allows us to distinguish the different phases of the epidemic, and to identify the delay between sanitary measures and their influence on the load of EMS. This also leads to an algorithm, allowing one to detect epidemic resurgences. We rely on a transport PDE epidemiological model, and we use methods from Perron-Frobenius theory and tropical geometry. (10.5802/crmath.99)
  DOI : 10.5802/crmath.99
• Inference methods for gas/surface interaction models: from deterministic approaches to Bayesian techniques
  
  • del Val Anabel
  • Le Maitre Olivier
  • Chazot Olivier
  • Congedo Pietro Marco
  • Magin Thierry E.
  , 2020. In this work we review selected experiments and inference methods for the determination of atmospheric entry gas/surface interaction models for air catalysis and nitrogen ablation. Accurate prediction of the gas/surface interaction during spacecraft reentry remains a challenging problem for thermal protection system design. Attempts to model the surface chemistry of catalytic and ablative materials must account for experimental and model uncertainties. We review two sets of experiments and models adopted in the relevant literature for the rebuilding of catalytic properties and nitridation reaction efficiencies. The review is enriched with new perspectives to these problems by using dedicated Bayesian methods.
• Compactness and Lower-Semicontinuity in <i>GSBD</i>
  
  • Chambolle Antonin
  • Crismale Vito
  Journal of the European Mathematical Society, European Mathematical Society, 2020, 23 (3), pp.701--719. In this paper, we prove a compactness and semicontinuity result in GSBD for sequences with bounded Griffith energy. This generalises classical results in (G)SBV by Ambrosio [1, 2, 3] and SBD by Bellettini-Coscia-Dal Maso [9]. As a result, the static problem in Francfort-Marigo's variational approach to crack growth [27] admits (weak) solutions. Moreover, we obtain a compactness property for minimisers of suitable Ambrosio-Tortorelli's type energies [6], which have been shown to Γ-converge to Griffith energy in [16]. (10.4171/jems/1021)
  DOI : 10.4171/jems/1021
• Optimal make–take fees for market making regulation
  
  • Euch Omar El
  • Mastrolia Thibaut
  • Rosenbaum Mathieu
  • Touzi Nizar
  Mathematical Finance, Wiley, 2020, 31 (1), pp.109-148. Abstract We address the mechanism design problem of an exchange setting suitable make– take fees to attract liquidity on its platform. Using a principal–agent approach, we provide the optimal compensation scheme of a market maker in quasi‐explicit form. This contract depends essentially on the market maker inventory trajectory and on the volatility of the asset. We also provide the optimal quotes that should be displayed by the market maker. The simplicity of our formulas allows us to analyze in details the effects of optimal contracting with an exchange, compared to a situation without contract. We show in particular that it improves liquidity and reduces trading costs for investors. We extend our study to an oligopoly of symmetric exchanges and we study the impact of such common agency policy on the system. (10.1111/mafi.12295)
  DOI : 10.1111/mafi.12295
• Extension of a SIR model for modelling the propagation of Covid-19 in several countries.
  
  • Lavielle Marc
  • Faron Matthieu
  • Lefevre Jeremie
  • Zeitoun Jean-David
  , 2020. Background Several epidemiologic models have been published to forecast the spread of the COVID-19 pandemic yet there are still uncertainties regarding their accuracy. We report the main features of the development of a novel freely accessible model intended to urgently help researchers and decision makers to predict the evolution of the pandemic in their country. Methods and findings We built a SIR-type compartmental model with additional compartments and features. We made the hypothesis that the number of contagious individuals in the population was negligible as compared to the population size. We introduced a compartment D corresponding to the deceased patients and a compartment L representing the group of individuals who will die but who will not infect anybody (due to social or medical isolation). Our model integrated a time-dependent transmission rate, whose variations can be thought to be related to the public measures taken by each country and a cosine function to incorporate a periodic weekly component linked to the way in which numbers of cases and deaths are counted and reported, which can change from day to day. The model was able to accurately capture the different changes in the dynamics of the pandemic for nine different countries whatever the type of pandemic spread or containment measures. The model provided very accurate forecasts in the relatively short term (10 days). Conclusions In early evaluation of the performance of our model, we found a high level of accuracy between prediction and observed data, regardless of the country. The model should be used by the community to help public health decisions as we will refine it over time and further investigate its performance. (10.1101/2020.05.17.20104885)
  DOI : 10.1101/2020.05.17.20104885
• Meta-model of a large credit risk portfolio in the Gaussian copula model
  
  • Bourgey Florian
  • Gobet Emmanuel
  • Rey Clément
  SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics, 2020, 11 (4), pp.1098-1136. We design a meta-model for the loss distribution of a large credit portfolio in the Gaussian copula model. Using both the Wiener chaos expansion on the systemic economic factor and a Gaussian approximation on the associated truncated loss, we significantly reduce the computational time needed for sampling the loss and therefore estimating risk measures on the loss distribution. The accuracy of our method is confirmed by many numerical examples. (10.1137/19M1292084)
  DOI : 10.1137/19M1292084
• Hydroxychloroquine with or without azithromycin and in-hospital mortality or discharge in patients hospitalized for COVID-19 infection: a cohort study of 4,642 in-patients in France
  
  • Sbidian Emilie
  • Josse Julie
  • Lemaître Guillaume
  • Mayer Imke
  • Bernaux Melodie
  • Gramfort Alexandre
  • Lapidus Nathanaël
  • Paris Nicolas
  • Neuraz Antoine
  • Lerner Ivan
  • Garcelon Nicolas
  • Rance Bastien
  • Grisel Olivier
  • Moreau Thomas
  • Bellamine Ali
  • Wolkenstein Pierre
  • Varoquaux Gaël
  • Caumes Eric
  • Lavielle Marc
  • Mekontso Dessap Armand
  • Audureau Etienne
  , 2020. Objective To assess the clinical effectiveness of oral hydroxychloroquine (HCQ) with or without azithromycin (AZI) in preventing death or leading to hospital discharge. Design Retrospective cohort study. Setting An analysis of data from electronic medical records and administrative claim data from the French Assistance Publique - Hopitaux de Paris (AP-HP) data warehouse, in 39 public hospitals, Ile-de-France, France. Participants All adult inpatients with at least one PCR-documented SARS-CoV-2 RNA from a nasopharyngeal sample between February 1st, 2020 and April 6th, 2020 were eligible for analysis. The study population was restricted to patients who did not receive COVID-19 treatments assessed in ongoing trials, including antivirals and immunosuppressive drugs. End of follow-up was defined as the date of death, discharge home, day 28 after admission, whichever occurred first, or administrative censoring on May 4, 2020. Intervention Patients were further classified into 3 groups: (i) receiving HCQ alone, (ii) receiving HCQ together with AZI, and (iii) receiving neither HCQ nor AZI. Exposure to a HCQ/AZI combination was defined as a simultaneous prescription of the 2 treatments (more or less one day). Main outcome measures The primary outcome was all-cause 28-day mortality as a time-to-event endpoint under a competing risks survival analysis framework. The secondary outcome was 28-day discharge home. Augmented inverse probability of treatment weighted (AIPTW) estimates of the average treatment effect (ATE) were computed to account for confounding. Results A total of 4,642 patients (mean age: 66.1 +/- 18; males: 2,738 (59%)) were included, of whom 623 (13.4%) received HCQ alone, 227 (5.9%) received HCQ plus AZI, and 3,792 (81.7%) neither drug. Patients receiving "HCQ alone" or "HCQ plus AZI" were more likely younger, males, current smokers and overall presented with slightly more co-morbidities (obesity, diabetes, any chronic pulmonary diseases, liver diseases), while no major difference was apparent in biological parameters. After accounting for confounding, no statistically significant difference was observed between the "HCQ" and "Neither drug" groups for 28-day mortality: AIPTW absolute difference in ATE was +1.24% (-5.63 to 8.12), ratio in ATE 1.05 (0.77 to 1.33). 28-day discharge rates were statistically significantly higher in the "HCQ" group: AIPTW absolute difference in ATE (+11.1% [3.30 to 18.9]), ratio in ATE (1.25 [1.07 to 1.42]). As for the "HCQ+AZI" vs neither drug, trends for significant differences and ratios in AIPTW ATE were found suggesting higher mortality rates in the former group (difference in ATE +9.83% [-0.51 to 20.17], ratio in ATE 1.40 [0.98 to 1.81];p=0.062). Conclusions Using a large non-selected population of inpatients hospitalized for COVID-19 infection in 39 hospitals in France and robust methodological approaches, we found no evidence for efficacy of HCQ or HCQ combined with AZI on 28-day mortality. Our results suggested a possible excess risk of mortality associated with HCQ combined with AZI, but not with HCQ alone. Significantly higher rates of discharge home were observed in patients treated by HCQ, a novel finding warranting further confirmation in replicative studies. Altogether, our findings further support the need to complete currently undergoing randomized clinical trials. (10.1101/2020.06.16.20132597)
  DOI : 10.1101/2020.06.16.20132597
• Signatures of degradation mechanisms from photovoltaic plants
  
  • Hrelja Nikola
  , 2020. The degradation of the PV (Photovoltaic) performance over its lifetime is usually determined with the variation of power at maximum power point (Pmpp). However, the same amount of Pmpp losses can have different causes, which have, different expectations of evolution with time.Existing Performance loss rate (PLR) methods are not suitable to identify these root causes and mechanisms from the field data. EDF’s physical model is a sophisticated version of a 2-diode model. This model contains parameters that can reflect degradation over time. When the current-voltage curve (IV curve) measurements are available from the field the parameters of the physical model can be straightforwardly estimated. However, the IV curve measurements are rarely available from the PV production sites the parameter, estimation is challenging since only limited data about the observed system is available. Estimating the model parameters using only Pmpp and weather data is the challenge here allowing a more precise evaluation of the health state of the system, rather than estimating only the performance loss metric.Sensitivity analysis was performed on various photovoltaic physical models namely the single diode model and the EDF code. A sensitivity analysis was performed on different photovoltaic physical models, namely the single-diode model and the EDF code. The three most influential parameters identified by our methodology are the series resistance (Rs), the shunt resistance (Rsh) and the short-circuit current (Isc). These identified parameters were used in the calibration of the PV performance model. The constraints of the sensitivity analysis were defined based on expert knowledge and available literature. Finally, three parameters were identified as the influential ones (on degradation) namely the series resistance (Rs), shunt resistance (Rsh) and the short circuit current (Isc). These identified parameters will be used in the calibration of the PV performance model.The Approximate Bayesian Computation (ABC) was used for the calibration of our computational code. The proposed algorithm aims to identify the posterior distribution of parameters by calibrating the computational code to the observed data. The ABC method expresses the probability of the observed data under a prior statistical model with certain parameter values. Because the code is computationally intensive, Polynomial Chaos Expansion (PCE) was used as a surrogate model to replace the original code and speed up the calibration process.The algorithm has been validated on simulated synthetic data (Digital Power Plant) with added Gaussian noise, some systematic discrepancy, and a known parameter degradation evolution. The results on the synthetic data show that the evolution of parameters can be estimated in noisy measurement conditions.The proposed method has then been applied to the real outdoor data collected during the operation of the photovoltaic plant in Bolzano (Italy, during the period of 2011-2019). The method only gives robust results in the summer and autumn because of stable weather conditions. In these months, the results show that the power decline of the fielded modules can be attributed to the decline in the Isc while the parameters Rs and Rsh do not show any significant change over 8 years. Additional analysis is needed to define the precise degradation mechanism associated with the evolution of extracted parameters and their correlation with outdoor operating conditions.As a perspective, we suggest using our new method to look into a big amount of data sets with known and unknown mechanisms to learn about the robustness of the method and the evolution of the parameters that could reveal more interesting characteristics and suggest physical arguments for studying breaking points and changes in failure mechanisms over the lifetime of PV power plants.
• Algorithmic market making for options
  
  • Baldacci Bastien
  • Bergault Philippe
  • Guéant Olivier
  , 2020. In this article, we tackle the problem of a market maker in charge of a book of options on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic optimal control problem of an option market maker is in fact tractable. More precisely, when volatility is modeled using a classical stochastic volatility model -- e.g. the Heston model -- the problem faced by an option market maker is characterized by a low-dimensional functional equation that can be solved numerically using a Euler scheme along with interpolation techniques, even for large portfolios. In order to illustrate our findings, numerical examples are provided.
• Mathematic modelization of spring magnets
  
  • Nicolas Léa
  , 2020. This thesis is dedicated to the study of nanocomposite materials, which are the most promising and active approach to making the best permanent magnets today. This type of magnet is called a spring magnet.Mathematically speaking, the study of these materials is difficult.because the usual models are non-linear and the material dependence ofthe parameters vary on a very small scale. Thus, solving the magnetic models for these magnets directly is impractical, as the small dimensions of the materials would increase the number of cells in the mesh prohibitively. A more practical way is to derive a macroscopic model using homogenization techniques, which refers to a set of averaging methods in partial differential equations. In other words, homogenization searchs for effective parameters (also called homogenized, or macroscopic) to describe disordered or highly heterogeneous media.The thesis consists of four chapters, the first of which introduces the framework of our study, and the next three are largely independent. In the second chapter, we study the stochastic homogenization of the Landau-Lifschitz-Gilbert equation, which describes the temporal evolution of magnetization in a ferromagnetic continuum, in order to obtain a homogeneous model for spring magnets, from a heterogeneous model. Once this homogeneous model has been identified, we study in the third chapter the behaviour of a homogeneous, but not uniform permanent magnet, by solving an eigenvalue problem. Finally, the fourth chapter deals with the numerical calculation of homogenized coefficients, which requires the resolution of a partial differential equation. We explore in this chapter a method using finite elements, as well as multi-grid methods.
• Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module
  
  • Fang Chengran
  • Nguyen Van-Dang
  • Wassermann Demian
  • Li Jing-Rebecca
  NeuroImage, Elsevier, 2020, 222, pp.117198. (10.1016/j.neuroimage.2020.117198)
  DOI : 10.1016/j.neuroimage.2020.117198
• Early indicators of intensive care unit bed requirement during the COVID-19 epidemic: A retrospective study in Ile-de-France region, France
  
  • Covid-19 Aphp-Universities-Inria-Inserm Group Collective Name
  PLoS ONE, Public Library of Science, 2020.
• Low-frequency source imaging in an acoustic waveguide
  
  • Garnier Josselin
  Inverse Problems, IOP Publishing, 2020, 36 (11), pp.115004. (10.1088/1361-6420/abae10)
  DOI : 10.1088/1361-6420/abae10
• Extension of AK-MCS for the efficient computation of very small failure probabilities
  
  • Razaaly Nassim
  • Congedo Pietro Marco
  Reliability Engineering and System Safety, Elsevier, 2020, 203, pp.107084. We consider the problem of estimating a probability of failure p f , defined as the volume of the excursion set of a complex (e.g. output of an expensiveto-run finite element model) scalar performance function J below a given threshold, under a probability measure that can be recast as a multivariate standard gaussian law using an isoprobabilistic transformation. We propose a method able to deal with cases characterized by multiple failure regions, possibly very small failure probability p f (say ∼ 10 −6 − 10 −9), and when the number of evaluations of J is limited. The present work is an extension of the popular Kriging-based active learning algorithm known as AK-MCS, as presented in [1], permitting to deal with very low failure probabilities. The key idea merely consists in replacing the Monte-Carlo sampling, used in the original formulation to propose candidates and evaluate the failure probability, by a centered isotropic Gaussian sampling in the standard space, whose standard deviation is iteratively tuned. This extreme AK-MCS (eAK-MCS) inherits its former multi-point enrichment algorithm allowing to add several points at each iteration step, and provide an estimated failure probability based on the Gaussian nature of the Kriging surrogate. Both the efficiency and the accuracy of the proposed method are showcased through its application to two to eight dimensional analytic examples, characterized by very low failure probabilities: p f ∼ 10 −6 − 10 −9. Numerical experiments conducted with unfavorable initial Design of Experiment suggests the ability of the proposed method to detect failure domains. (10.1016/j.ress.2020.107084)
  DOI : 10.1016/j.ress.2020.107084
• Sampling scheme for intractable copula function, application to the computation of tail events in factor copula model
  
  • Bénézet Cyril
  • Gobet Emmanuel
  • Targino Rodrigo
  , 2020.