Workshops
Professor Tony Patera, MIT, USA - An overview on reduced basis/error estimation and applications to uncertainty quantification;
Professor Kai-Tai Fang, Beijing Normal University - China Design and Modeling for experiments with model uncertainty;
Emmanuel Vazquez, Supelec, France - On kriging and sequential search algorithms;
Round table with R.Gentleman from R and D.Bateman from Octave;
Professor Robert B. Gramacy, Statistical Laboratory, Department of Mathematics, University of Cambridge, UK. - Bayesian treed Gaussian process models;
Professor Laurent Carraro, Département 3MI, Ecole des mines de Saint-Etienne, France - Scientific contributions in the DICE consortium;
Professor Francis Bach, Département d'Informatique, Ecole Normale Supérieure, France - Multiple kernel learning;
Round table : software integration of contributions in a single free platform;
Olivier Lemaitre (LIMSI) -
Fabio Nobile, Politecnico di Milano - Sparse Grid Stochastic Collocation methods for Uncertainty Quantifi cation
Géraud Blatman and Thierry Crestaux - thesis work
Michael Baudin (Scilab) and Jean-Marc Martinez (CEA) - Scilab toolbox NISP.
Marc Berveiller (EDF) and Régis Lebrun (EADS) - developments on functional chaos in OpenTURNS.
Alberto Pasanisi (EDF-R&D) - Introduction
Josselin Garnier (Université Paris 7) - Interacting particle systems for the analysis of rare events
Philippe Naveau (Lab. Sciences du Climat et l'Environnement, CNRS) - Applications of multivariate extreme value theory to environmental data analysis
Pierre Del Moral (INRIA, Université Bordeaux 1) - Sur les interprétations particulaires d'événements rares (On rare events particular interpretation)
Régis Lebrun (EADS IW) Algorithmes de simulation en espace standard (Simulation algorithms in standard space)
Bruno Sudret (Phiméca) - Méta-modèles pour le calcul de probabilités d'événements rares (Metamodels for rare event probability calculation)
Fabien Mangeant (EADS IW) Calcul de quantiles faibles pour une application de guidage (Small quantile calculation for a guiding application)
Miguel Munoz Zuniga (EDF-R&D, Université Paris 7) Estimation de faibles probabilités de défaillance par une méthode originale de Monte Carlo accélérée (Extreme failure probability estimation by an original accelerated Monte-Carlo method)
Alberto Pasanisi : Conclusion
C. Perez (INRIA) Tendances dans le calcul haute performance
C. Prieur (UJF), L. Viry (UJF), B. Depardon (Sysfera) Analyse de sensibilité pour la mousson en Afrique de l'ouest: de la méthodologie au calcul distribué
D. Busby (IFP Energies Nouvelles) Cougar
F. Gaudier (CEA) Uranie
R. Barate (EDF), I. Dutka-Malen (EDF), P. Benjamin (EADS) OpenTURNS
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Workshop 1 - (2008-10-08)
The first OPUS workshop took place at EDF/Clamart(near Paris) on October 8 2008. This workshop was organized by Guennadi Andrianov from EDF and Anestis Antoniadis and Christophe Prud'homme both from UJF/LJK.
Three talks were organized in the morning :
Professor Tony Patera, MIT, USA - An overview on reduced basis/error estimation and applications to uncertainty quantification
We discuss reduced basis approximation and associated a posteriori error estimation for reliable real-time solution of parametrized partial differential equations.
The crucial ingredients are rapidly convergent Galerkin approximations over a space spanned by "snapshots" on the parametrically induced solution manifold; rigorous and sharp a posteriori error estimators for the outputs/quantities of interest; effective constructions for stability-constant lower bounds; efficient Greedy (in parameter) or POD (in time)/Greedy (in parameter) selection of quasi-optimal samples; and Offine-Online computational procedures for rapid calculation in the many-query and real-time contexts.
We consider linear and nonlinear elliptic problems, linear and nonlinear parabolic equations, and linear hyperbolic equations. Examples are drawn from heat transfer (steady and unsteady conduction and convection), acoustics (in the frequency and time domains), solid mechanics (e.g., crack stress intensity factors), and fluid dynamics (the incompressible Navier-Stokes equations). Finally, we discuss the application of our reduced basis approximations and error bounds to uncertainty analysis. We consider two contexts, both of which exploit the many-query efficiency and reliability of the reduced basis formulation. In the first - forward - context, we explore output variation in the presence of stochastic parameter dependence. In the second - inverse - context, we address parameter estimation in the presence of numerical and experimental output error. In both cases we realize computational savings of several orders of magnitude relative to classical approaches.
Presentation slides.
More information (papers, talks, software,...) at : http://augustine.mit.edu
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Professor Kai-Tai Fang, Beijing Normal University, China - Design and Modeling for experiments with model uncertainty
Presentation slides.
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Emmanuel Vazquez, Supelec, France - On kriging and sequential search algorithms
The optimization of functions whose evaluation involves time-consuming computer programs has often to be achieved with a small budget of evaluations. In this context, the Expected Improvement (EI) algorithm - a kriging based approach to optimization - has become popular for it can lead to significant savings in the number of function evaluations over traditional optmization methods. The EI algorithm is known as a sequential Bayesian global optimization technique. During the optimization, the expensive-to-evaluate function is replaced by a cheap approximation, and the probabilistic framework of kriging is used to account for the uncertainty on the function approximation. This talk will start with a presentation of the technique and will discuss several variations, including the recently proposed Informational Approach to Global Optimization (IAGO) strategy, which takes a step forward in this domain and has successfully been applied in the context of industrial problems. Finally, we will show that the ideas supporting Bayesian optimization can be generalized to derive other types of sequential search algorithms, e.g. algorithms to estimate quantiles or probabilities of failure.
Presentation slides.
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Round table with R.Gentleman from R and D.Bateman from Octave.
People from Scilab, Debian/GNU/Linux and other open-source/free software were present at the round table
The "process" sub-session addressed the collaborative development process issues, for example the natural willingness of each partner to stick to its habits i.e. use specific dependencies and development environments (R, Matlab, Scilab, Octave, C++, ...). We shall discuss of good processes to establish and pitfalls to avoid.
The "service and long term prospects" sub-session will start right after the coffee-break. It will address the issues of commercial service around open source/free software and the project life after the initial funding dries out.
In both sub-sessions the question of intellectual property, copyright and licensing is important and thus shall be discussed although from different point of views.
Presentation slides.
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Workshop 2 (2009-04-29)
The second OPUS workshop, dealing with machine learning and model selection, with an emphasis on DICE consortium's work, took place on the 29th of April, 2009, at the CEA in Saclay. Continuing the formula of two half-days from the first workshop, the morning was spent on three theoretical presentations (R. Gramacy, F. Bach, L. Carraro), while the afternoon was spent as a round table dealing with software integration of contributions in a single free platform.
The first returns are positive. However, improvement is possible. In the next workshop, it seems mandatory to introduce the Opus project, as well as its aims and ways to contribute. Indeed, these elements will facilitate comprehension of the context as wall as constitute a basis for the talks of the afternoon.
Workshop program.
Professor Robert B. Gramacy, Statistical Laboratory, Department of Mathematics, University of Cambridge, UK - Bayesian treed Gaussian process models;
Computer experiments often require dense sweeps over input parameters to obtain a qualitative understanding of their response. However, such sweeps are unnecessary in regions where the response is easily predicted; well-chosen designs could allow a mapping of the response with far fewer simulation runs. I explore a modern approach that couples two standard regression models: Gaussian processes and treed partitioning. A Bayesian perspective yields an explicit measure of (nonstationary) predictive uncertainty that can be used to guide sampling. The methods will be illustrated through several examples, including a motivating example which involves the computational fluid dynamics of a NASA re-entry vehicle.
Related documents :
Slides
Figures
Adaptive Design and Analysis of Supercomputer Experiments (2009) with Herbert K.H. Lee. Technometrics, 51(2), pp. 130-145; preprint on arXiv:0805.4359;
Bayesian treed Gaussian process models with an application to computer modeling (2008) with Herbert K.H. Lee. Journal of the American Statistical Association, 103(483), pp. 1119-1130; preprint on arXiv:0710.4536;
tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models (2007). Journal of Statistical Software, 19(9); snapshot of the R vignette for the tgp package as of June 2007;
Categorical inputs, sensitivity analysis, optimization and importance tempering with tgp version 2, an R package for treed Gaussian process models (2009) with Matt Taddy. To appear in the Journal of Statistical Software; snapshot of one of two R vignettes in the tgp package as of January 2010
The tgp package on cran (http://www.cran.r-project.org/web/packages/tgp/index.html)
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Professor Laurent Carraro, Département 3MI, Ecole des mines de Saint-Etienne, France - Scientific contributions in the DICE consortium;
Presentation slides.
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Professor Francis Bach, Département d'Informatique, Ecole Normale Supérieure, France - Multiple kernel learning;
Multiple kernel learning refers to a theoretical and algorithmic framework aimed at learning the kernel directly from data for supervised learning techniques such as the support vector machine (SVM). The framework is based on a convex parameterization of the set of kernels and a convex formulation which can be cast as a block L1-norm regularization. In this talk, I will explore some applications and large-scale optimization algorithms, as well as some recent links with sparsity-inducing norm theory.
Presentation slides.
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Round table : dealing with software integration of contributions in a single free platform.
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Workshop 3 (2009-10-25) - "Spectral methods and polynomial chaos"
On the 25th of November, within the Opus project, a workshop titled "Spectral methods and polynomial chaos" took place at EADS in Suresnes. Both theoretical aspects and software implementation were discussed, on the morning and afternoon respectively.
General Opus presentation.
Olivier Lemaitre, LIMSI
Spectral methods for uncertainty propagation; numerical fluid mechanics application.
Slides.
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Fabio Nobile, MOX, Department of Mathematics, Politecnico di Milano, Italy
Sparse Grid Stochastic Collocation methods for Uncertainty Quantifi cation
This talk focuses on the numerical approximation of di fferential problems whose coefficients, forcing terms, boundary conditions, etc. (hereafter called parameters) are uncertain and modeled as random vectors. In particular, we present sparse grid stochastic collocation methods, where the deterministic problem is successively solved on a sequence of cleverly chosen points in the parameter space, typically Gauss points with respect to the underlying probability measure.
We present a general sparse grid construction that allows us to achieve approximation in a given multivariate polynomial space. This includes the "classical" Smolyak construction that provides approximation in a hypebolic-cross type polynomial space, as well as a construction for approximations in total degree polynomial spaces. The general algorithm allows us to work also in anisotropic polynomial spaces, where the maximum polynomial degree used for each random variable depends on the relative importance that such random variable has on the output quantity.
In context of the numerical approximation of elliptic Partial Di fferential Equations with random coefficients, we present a strategy to select a proper anisotropic space.
Numerical examples show that the stochastic polynomial sparse grid approximation can be very e ffective for problems that feature a high regularity with respect to the random parameters, and greatly reduces the curse of dimensionality with respect to a full tensor product approximation. Also, a properly
chosen anisotropy allows us to obtain far superior results whenever the random variables have highly diff erent infuence on the output quantity.
In all cases examined, the stochastic sparse grid approach is superior to simple Monte Carlo Sampling.
References
[1] J. Bäck, F. Nobile, L. Tamellini, and R. Tempone, "Stochastic Galerkin and collocation methods for PDEs with random coefficients: a numerical comparison," ICES Report 09-33, ICES, The University of Texas at Austin, 2009. Submitted to special volume of "Lecture Notes in computational Science and Engineering", Springer. Proceedings of the ICOSAHOM '09 Conference.
[2] F. Nobile and R. Tempone, "Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients",
Int. J. Num. Methods Engrg., vol. 80, no. 6-7, pp. 979-1006, 2009. Special Issue: Uncertainty Quanti cation in Computational and Prediction Science.
[3] F. Nobile, R. Tempone, and C. Webster, "An anisotropic sparse grid stochastic collocation method for partial di fferential equations with random input data," SIAM J. Numer. Anal., vol. 46, no. 5, pp. 2411-2442, 2008.
[4] F. Nobile, R. Tempone, and C. Webster, "A sparse grid stochastic collocation method for partial di fferential equations with random input data," SIAM J. Numer. Anal., vol. 46, no. 5, pp. 2309-2345, 2008.
[5] I. Babuska, F. Nobile, and R. Tempone, "A stochastic collocation method for elliptic partial di fferential equations with random input data," SIAM J. Numer. Anal., vol. 45, no. 3, pp. 1005-1034, 2007.
Abstract.
Slides.
Website.
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Géraud Blatman and Thierry Crestaux
Thesis work: sparse adaptative polynomial chaos based on LAR procedure.
Slides.
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Michael Baudin (Scilab) and Jean-Marc Martinez (CEA) - Scilab toolbox NISP.
Presentation slides.
Further slides.
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Marc Berveiller (EDF) and Régis Lebrun (EADS) - developments on functional chaos in OpenTURNS.
Slides.
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Workshop 4 - (2010-06-29) "Uncertainty propagation, rare quantile and extreme failure proability estimation"
Alberto Pasanisi (EDF-R&D) - Introduction
Slides.
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Josselin Garnier (Université Paris 7) - Interacting particle systems for the analysis of rare events
Slides.
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Philippe Naveau (Lab. Sciences du Climat et l'Environnement, CNRS) - Applications of multivariate extreme value theory to environmental data analysis
Slides.
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Pierre Del Moral (INRIA, Université Bordeaux 1) - Sur les interprétations particulaires d'événements rares (On rare events particular interpretation)
Slides.
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Régis Lebrun (EADS IW) Algorithmes de simulation en espace standard (Simulation algorithms in standard space)
Slides.
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Bruno Sudret (Phiméca) - Méta-modèles pour le calcul de probabilités d'événements rares (Metamodels for rare event probability calculation)
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Fabien Mangeant (EADS IW) Calcul de quantiles faibles pour une application de guidage (Small quantile calculation for a guiding application)
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Miguel Munoz Zuniga (EDF-R&D, Université Paris 7) Estimation de faibles probabilités de défaillance par une méthode originale de Monte Carlo accélérée (Extreme failure probability estimation by an original accelerated Monte-Carlo method)
Slides.
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Alberto Pasanisi : Conclusion
Slides.
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Workshop 5 - (2011-03-22) "Calcul haute performance, environnements de calcul et logiciels, applications à la quantification d'incertitudes"
C. Perez (INRIA) Tendances dans le calcul haute performance
Slides
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C. Prieur (UJF), L. Viry (UJF), B. Depardon (Sysfera) Analyse de sensibilité pour la mousson en Afrique de l'ouest: de la méthodologie au calcul distribué
Slides
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D. Busby (IFP Energies Nouvelles) Cougar
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F. Gaudier (CEA) Uranie
Slides
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R. Barate (EDF), I. Dutka-Malen (EDF), P. Benjamin (EADS) OpenTURNS
Slides
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Around Opus
Tuesday, 27 September 2011 21:10 | 
Author: Administrator | 
