Stochastic elliptic operators defined by non-gaussian random fields with uncertain spectrum

This paper present a construction and the analysis of a class of non-Gaussian positive-definite matrix-valued homogeneous random fields with uncertain spectral measure for stochastic elliptic operators. Then the stochastic elliptic boundary value problem in a bounded domain of the 3D-space is introduced and analyzed for stochastic homogenization

Programming Languages for Scientific Computing

Scientific computation is a discipline that combines numerical analysis, physical understanding, algorithm development, and structured programming. Several yottacycles per year on the world's largest computers are spent simulating problems as diverse as weather prediction, the properties of material composites, the behavior of biomolecules in solution, and the quantum nature of chemical compounds. This article is intended to review specfic languages features and their use in computational science. We will review the strengths and weaknesses of different programming styles, with examples taken from widely used scientific codes.Comment: 21 page

Probabilistic learning on manifold for optimization under uncertainties

Plenary LectureInternational audienceThis paper presents a challenging problem devoted to the probabilistic learning on manifold for the optimization under uncertainties and a novel idea for solving it. The methodology belongs to the class of the statistical learning methods and allows for solving the probabilistic nonconvex constrained optimization with a fixed number of expensive function evaluations. It is assumed that the expensive function evaluator generates samples (defining a given dataset) that randomly fluctuate around a "manifold". The objective is to develop an algorithm that uses a number of expensive function evaluations at a level essentially equal to that of the deterministic problem. The methodology proposed consists in using an algorithm to generate additional samples in the neighborhood of this manifold from the joint probability distribution of the design parameters and of the random quantities that defined the objective and the constraint functions. This is achieved by using the probabilistic learning on manifold from the given dataset generated by the optimizer without performing additional expensive function evaluations. A statistical smoothing technique is developed for estimating the mathematical expectations in the computation of the objective and constraint functions at any point of the admissible set by using only the additional samples. Several numerical illustrations are presented for validating the proposed approach

Stochastic mechanical model of vocal folds for producing jitter and for identifying pathologies through real voices

International audienceJitter, in voice production applications, is a random phenomenon characterized by the deviation of the glottal cycle length with respect to a mean value. Its study can help in identifying pathologies related to the vocal folds according to the values obtained through the different ways to measure it. This paper aims to propose a stochastic model, considering three control parameters, to generate jitter based on a deterministic one-mass model for the dynamics of the vocal folds and to identify parameters from the stochastic model taking into account real voice signals experimentally obtained. To solve the corresponding stochastic inverse problem, the cost function used is based on the distance between probability density functions of the random variables associated with the fundamental frequencies obtained by the experimental voices and the simulated ones, and also on the distance between features extracted from the voice signals , simulated and experimental, to calculate jitter. The results obtained show that the model proposed is valid and some samples of voices are synthesized considering the identified parameters for normal and pathological cases. The strategy adopted is also a novelty and mainly because a solution was obtained. In addition to the use of three parameters to construct the model of jitter, is the discussion of a parameter related to the bandwidth of the power spectral density function of the stochastic process to measure the quality of the signal generated. A study about the influence of all the main parameters is also performed. The identification of the parameters of the model considering pathological cases is maybe of all novelties introduced by the paper the most interesting

Probabilistic Learning on Manifolds (PLoM) with Partition

The probabilistic learning on manifolds (PLoM) introduced in 2016 has solved difficult supervised problems for the ``small data'' limit where the number N of points in the training set is small. Many extensions have since been proposed, making it possible to deal with increasingly complex cases. However, the performance limit has been observed and explained for applications for which $N$ is very small (50 for example) and for which the dimension of the diffusion-map basis is close to $N$. For these cases, we propose a novel extension based on the introduction of a partition in independent random vectors. We take advantage of this novel development to present improvements of the PLoM such as a simplified algorithm for constructing the diffusion-map basis and a new mathematical result for quantifying the concentration of the probability measure in terms of a probability upper bound. The analysis of the efficiency of this novel extension is presented through two applications.Comment: 20 pages, 13 figures, preprin

Uncertainties in structural dynamics for composite sandwich panels

International audienceThis paper concerns uncertainties in structural dynamics for composite sandwich panels constituted of two thin carbon-resin skins and one high stiffness closed-cell foam core. Each skin is constituted of two unidirectional plies [60/-60]. Such light composite sandwich panels, manufactured with a same process, generally present a significant dispersion for their Frequency Response Functions (FRF) in the Low-Frequency (LF) and Medium-Frequency (MF) ranges. The objectives of this paper are (1) to study the dispersion due to the process by using experiments (2) to develop a predictive mean mechanical model based on the use of the laminated composite thin plate theory in dynamics and (3) to use a nonparametric probabilistic approach for data and model uncertainties to improve the predictability of the mean model in the MF dynamics

Vibroacoustics of a cavity coupled with an uncertain composite panel

International audienceThis paper deals with uncertainties in vibroacoustics of a bounded cavity whose wall is constituted of a rigid wall and of a deformable part constituted of a Composite Sandwich Panel (CSP). Such a CSP has two thin carbon-resin skins and one high stiffness closed-cell foam core. The objectives of this paper is (1) to study the robustness of acoustic response with respect to the dispersion of the CSP induced by the manufacturing process, (2) to develop a predictive mean mechanical model of the vibroacoustic system and (3) to use a nonparametric probabilistic approach for data and model uncertainties of the CSP in order to analyze the robustness of the mean vibroacoustics model in the LF and MF bands to predict internal acoustic level

Probabilistic approach for model and data uncertainties and its experimental identification in structural dynamics: Case of composite sandwich panels

International audienceThis paper deals with the experimental identification and the validation of a non-parametric probabilistic approach allowing model uncertainties and data uncertainties to be taken into account in the numerical model developed to predict low- and medium-frequency dynamics of structures. The analysis is performed for a composite sandwich panel representing a complex dynamical system which is sufficiently simple to be completely described and which exhibits, not only data uncertainties, but above all model uncertainties. The dynamical identification is experimentally performed for eight panels. The experimental frequency response functions are used to identify the non-parametric probabilistic approach of model uncertainties. The prediction of the low- and medium-frequency dynamical responses obtained with the stochastic system is compared with the experimental measurements

Identification et validation expérimentale d'un modèle stochastique des incertitudes en vibroacoustique d'un panneau composite.

National audienceWe present a probabilistic model allowing uncertainties induced by modeling errors and system-parameter uncertainties to be taken into account for a multi-layer composite sandwich panel. The sensitivity of the internal noise inside a bounded cavity coupled with the panel is analyzed with respect to uncertainties. Eight composite panels have been constructed by using the same manufacturing process. Experimental measurements of the vibration and acoustic responses have been performed in the low- and medium- frequency ranges. These measurements allow the probabilistic model of uncertainties to be identified.We present the probabilistic numerical model and its comparison with the experiments for validation