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1. A comparison of mixed-variables Bayesian optimization approaches

Author

Jhouben Cuesta Ramirez, Rodolphe Le Riche, Olivier Roustant, Guillaume Perrin, Cédric Durantin, and Alain Glière

Subjects
Mechanics of engineering. Applied mechanics, TA349-359, Systems engineering, TA168
Abstract

Abstract Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation. General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem.

Published
2022
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2. DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization

Author

Olivier Roustant, David Ginsbourger, and Yves Deville

Subjects
computer experiments, Gaussian processes, global optimization, Statistics, HA1-4737
Abstract

We present two recently released R packages, DiceKriging and DiceOptim, for the approximation and the optimization of expensive-to-evaluate deterministic functions. Following a self-contained mini tutorial on Kriging-based approximation and optimization, the functionalities of both packages are detailed and demonstrated in two distinct sections. In particular, the versatility of DiceKriging with respect to trend and noise specifications, covariance parameter estimation, as well as conditional and unconditional simulations are illustrated on the basis of several reproducible numerical experiments. We then put to the fore the implementation of sequential and parallel optimization strategies relying on the expected improvement criterion on the occasion of DiceOptim’s presentation. An appendix is dedicated to complementary mathematical and computational details.

Published
2012

35. Revealing the interlevel dependence structure of categorical inputs in numerical environmental simulations with kernel model selection

Author

Jeremy Rohmer, Olivier Roustant, Sophie Lecacheux, Jean-Charles Manceau, Bureau de Recherches Géologiques et Minières (BRGM) (BRGM), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Kriging, Environmental Engineering, Ecological Modeling, Metamodel, [SDU.STU]Sciences of the Universe [physics]/Earth Sciences, Computationally intensive simulator, Model selection, Software, Categorical variables
Abstract

International audience; Model uncertainties are generally integrated in environmental long-running numerical simulators via a categorical variable. By focusing on Gaussian process (GP) models, we show how different categorical kernel models (exchangeable, ordinal, group, etc.) can bring valuable insights into the correlation of the simulator output values computed for different levels of the categorical variable, i.e., the interlevel dependence structure. Supported by two real case applications (cyclone-induced waves and reservoir modeling), we have proposed a cross-validation approach to select the most appropriate kernel by finding a trade-off between predictability, explainability, and stability of the covariance coefficients. This approach can be used effectively to support some physical assumptions regarding the categorical variable. Through comparison to tree-based techniques, we show that GP models can be considered a satisfactory compromise when only a few model runs (∼100) are available by presenting a high predictability and a concise and graphical way to map the interlevel dependence structure.

Published
2022
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36. A comparison of mixed-variables Bayesian optimization approaches

Author

Jhouben Cuesta Ramirez, Rodolphe Le Riche, Olivier Roustant, Guillaume Perrin, Cédric Durantin, Alain Glière, Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information (CEA-LETI), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA), Département Composants et Systèmes (COSYS), Université Gustave Eiffel, Centre d'Études de Limeil-Valenton (CEA-DAM), Direction des Applications Militaires (DAM), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, and Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, Applied Mathematics, Machine Learning (stat.ML), Statistics - Applications, Statistics - Computation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Science Applications, Machine Learning (cs.LG), Machine Learning, Optimization and Control (math.OC), Statistics - Machine Learning, Modeling and Simulation, Applications, Computation, FOS: Mathematics, Applications (stat.AP), Engineering (miscellaneous), Mathematics - Optimization and Control, Computation (stat.CO)
Abstract

Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation.General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem., Accepted for publication in Advanced Modeling and Simulation in Engineering Sciences, march 2022

Published
2021
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37. Linking the Hoeffding--Sobol and Möbius formulas through a decomposition of Kuo, Sloan, Wasilkowski, and Wozniakowski

Author

Cécile Mercadier, Olivier Roustant, Christian Genest, Probabilités, statistique, physique mathématique (PSPM), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA), Department of Mathematics and Statistics McGill University, Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), and McGill University = Université McGill [Montréal, Canada]

Subjects
Statistics and Probability, Möbius decomposition, Hoeffding--Sobol decomposition, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Functional representation, Statistics, Probability and Uncertainty
Abstract

International audience; Extensions of a result of Kuo et al. (Math. Comp., 79 (2010), 953–966) are presented which unify the derivation of the Hoeffding--Sobol and Möbius decompositions of a multivariate function as a sum of terms of increasing complexity.

Published
2021
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38. Functional principal component analysis for global sensitivity analysis of model with spatial output

Author

T. V. E. Perrin, Rodrigo Pedreros, D. Moncoulon, P. Tinard, Jean-Philippe Naulin, Jeremy Rohmer, Olivier Alata, Olivier Roustant, Déborah Idier, Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Bureau de Recherches Géologiques et Minières (BRGM) (BRGM), Laboratoire Hubert Curien (LHC), Institut d'Optique Graduate School (IOGS)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), CCR PARIS FRA, Partenaires IRSTEA, Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), BRGM, Orléans, France, Laboratoire Hubert Curien [Saint Etienne] (LHC), and Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-Institut d'Optique Graduate School (IOGS)

Subjects
FOS: Computer and information sciences, Functional principal component analysis, 021110 strategic, defence & security studies, 021103 operations research, Basis (linear algebra), Computer science, [SDE.IE]Environmental Sciences/Environmental Engineering, 0211 other engineering and technologies, Basis function, 02 engineering and technology, Industrial and Manufacturing Engineering, Methodology (stat.ME), Dimension (vector space), Metric (mathematics), Principal component analysis, Sensitivity (control systems), Safety, Risk, Reliability and Quality, Algorithm, Orthonormality, [STAT.ME]Statistics [stat]/Methodology [stat.ME], Statistics - Methodology, ComputingMilieux_MISCELLANEOUS
Abstract

Motivated by risk assessment of coastal flooding, we consider time-consuming simulators with a spatial output. The aim is to perform sensitivity analysis (SA), quantifying the influence of input parameters on the output. There are three main issues. First, due to computational time, standard SA techniques cannot be directly applied on the simulator. Second, the output is infinite dimensional, or at least high dimensional if the output is discretized. Third, the spatial output is non-stationary and exhibits strong local variations. We show that all these issues can be addressed all together by using functional PCA (FPCA). We first specify a functional basis, such as wavelets or B-splines, designed to handle local variations. Secondly, we select the most influential basis terms, either with an energy criterion after basis orthonormalization, or directly on the original basis with a penalized regression approach. Then FPCA further reduces dimension by doing PCA on the most influential basis coefficients, with an ad-hoc metric. Finally, fast-to-evaluate metamodels are built on the few selected principal components. They provide a proxy on which SA can be done. As a by-product, we obtain analytical formulas for variance-based sensitivity indices, generalizing known formula assuming orthonormality of basis functions., Comment: 26 pages, 12 figures, 1 algoritm

Published
2021
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40. On the choice of the low-dimensional domain for global optimization via random embeddings

Author

David Ginsbourger, Mickaël Binois, Olivier Roustant, Technocentre Renault [Guyancourt], RENAULT, Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, Institute of Mathematical Statistics and Actuarial Science [Bern] (IMSV), University of Bern, Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol

Subjects
FOS: Computer and information sciences, Mathematical optimization, Control and Optimization, Optimization problem, 0211 other engineering and technologies, Machine Learning (stat.ML), 02 engineering and technology, Management Science and Operations Research, REMBO, Domain (software engineering), Methodology (stat.ME), Random search, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Robustness (computer science), FOS: Mathematics, low effective dimensionality, Mathematics - Optimization and Control, Global optimization, Statistics - Methodology, Mathematics, Bayesian optimization, 021103 operations research, Applied Mathematics, Expensive black-box optimization, Computer Science Applications, Optimization and Control (math.OC), zonotope, Embedding, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [STAT.ME]Statistics [stat]/Methodology [stat.ME], Curse of dimensionality
Abstract

International audience; The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional space into the original one, resulting in a more manageable optimization problem. Specifically, in the case of time consuming black-box functions and when the budget of evaluations is severely limited, global optimization with random embeddings appears as a sound alternative to random search. Yet, in the case of box constraints on the native variables, defining suitable bounds on a low dimensional domain appears to be complex. Indeed, a small search domain does not guarantee to find a solution even under restrictive hypotheses about the function, while a larger one may slow down convergence dramatically. Here we tackle the issue of low-dimensional domain selection based on a detailed study of the properties of the random embedding, giving insight on the aforementioned difficulties. In particular, we describe a minimal low-dimensional set in correspondence with the embedded search space. We additionally show that an alternative equivalent embedding procedure yields simultaneously a simpler definition of the low-dimensional minimal set and better properties in practice. Finally, the performance and robustness gains of the proposed enhancements for Bayesian optimization are illustrated on numerical examples.

Published
2020
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41. Parseval inequalities and lower bounds for variance-based sensitivity indices

Author

Fabrice Gamboa, Bertrand Iooss, and Olivier Roustant

Subjects
derivative-based global sensitivity measures, Statistics and Probability, Polynomial chaos, Chaos expansion, Poincaré inequality, Sobol sequence, Sobol-Hoeffding decomposition, Function (mathematics), Differential operator, Parseval's theorem, symbols.namesake, 65C60, Hilbert basis, 62P30, symbols, Applied mathematics, Truncation (statistics), Statistics, Probability and Uncertainty, Sobol indices, 26D10, Mathematics
Abstract

The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol’ sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor Hilbert basis. In this frame, we revisit the computation of the Sobol’ indices with Parseval equalities and give general lower bounds for these indices obtained by truncation. The case of the eigenfunctions system associated with a Poincaré differential operator leads to lower bounds involving the derivatives of the analyzed function and provides an efficient tool for variable screening. These lower bounds are put in action both on toy and real life models demonstrating their accuracy.

Published
2020
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42. Approximating Gaussian Process Emulators with Linear Inequality Constraints and Noisy Observations via MC and MCMC

Author

Déborah Idier, Olivier Roustant, Nicolas Durrande, François Bachoc, Jeremy Rohmer, Andrés F. López-Lopera, Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), PROWLER.io, 72 Hills Road, Cambridge, Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, Computer science, Monte Carlo method, 0211 other engineering and technologies, Machine Learning (stat.ML), 02 engineering and technology, 01 natural sciences, Convexity, Machine Learning (cs.LG), 010104 statistics & probability, symbols.namesake, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Applied mathematics, 0101 mathematics, Gaussian process, 021110 strategic, defence & security studies, Markov chain, Relaxation (iterative method), Markov chain Monte Carlo, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Linear inequality, symbols, [INFO.EIAH]Computer Science [cs]/Technology for Human Learning, Interpolation
Abstract

Adding inequality constraints (e.g. boundedness, monotonicity, convexity) into Gaussian processes (GPs) can lead to more realistic stochastic emulators. Due to the truncated Gaussianity of the posterior, its distribution has to be approximated. In this work, we consider Monte Carlo (MC) and Markov Chain Monte Carlo (MCMC) methods. However, strictly interpolating the observations may entail expensive computations due to highly restrictive sample spaces. Furthermore, having (constrained) GP emulators when data are actually noisy is also of interest for real-world implementations. Hence, we introduce a noise term for the relaxation of the interpolation conditions, and we develop the corresponding approximation of GP emulators under linear inequality constraints. We show with various toy examples that the performance of MC and MCMC samplers improves when considering noisy observations. Finally, on 2D and 5D coastal flooding applications, we show that more flexible and realistic GP implementations can be obtained by considering noise effects and by enforcing the (linear) inequality constraints.

Published
2020
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43. Group kernels for Gaussian process metamodels with categorical inputs

Author

Henry P. Wynn, Jean Giorla, Guillaume Perrin, Espéran Padonou, Yves Deville, Aloïs Clément, Olivier Roustant, Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, Université Clermont Auvergne [2017-2020] (UCA [2017-2020]), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Alpestat, CEA (CEA/DAM), DAM Île-de-France (DAM/DIF), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Department of Statistics - London School of Economics (LSE), London School of Economics and Political Science (LSE), Chaire en mathématiques appliquées OQUAIDO, Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, and Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Computer and information sciences, Statistics and Probability, Computer experiments, 0211 other engineering and technologies, Gaussian processes, Mathematics - Statistics Theory, Statistics Theory (math.ST), 02 engineering and technology, 01 natural sciences, Methodology (stat.ME), 010104 statistics & probability, Matrix (mathematics), symbols.namesake, Block (programming), Kriging, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Discrete Mathematics and Combinatorics, 0101 mathematics, Categorical variable, Gaussian process, Categorical data, Statistics - Methodology, Mathematics, Discrete mathematics, 021103 operations research, Applied Mathematics, Covariance, Positive definiteness, Modeling and Simulation, symbols, Statistics, Probability and Uncertainty, Parametric family
Abstract

Gaussian processes (GP) are widely used as a metamodel for emulating time-consuming computer codes. We focus on problems involving categorical inputs, with a potentially large number L of levels (typically several tens), partitioned in G << L groups of various sizes. Parsimonious covariance functions, or kernels, can then be defined by block covariance matrices T with constant covariances between pairs of blocks and within blocks. However, little is said about the positive definiteness of such matrices, which may limit their practical usage. In this paper, we exploit the hierarchy group/level and provide a parameterization of valid block matrices T, based on a nested Bayesian linear model. The same model can be used when the assumption within blocks is relaxed, giving a flexible parametric family of valid covariance matrices with constant covariances between pairs of blocks. As a by-product, we show that the positive definiteness of T is equivalent to the positive definiteness of a small matrix of size G, obtained by averaging each block. We illustrate with an application in nuclear engineering, where one of the categorical inputs is the atomic number in Mendeleev's periodic table and has more than 90 levels.

Published
2019

44. On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

Author

David Ginsbourger, Olivier Roustant, Nicolas Durrande, Institute of Mathematical Statistics and Actuarial Science [Bern] (IMSV), University of Bern, Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol

Subjects
Statistics and Probability, Field (physics), Gaussian, Harmonic (mathematics), 010103 numerical & computational mathematics, 01 natural sciences, 010104 statistics & probability, symbols.namesake, 510 Mathematics, Statistical physics, 0101 mathematics, Covariance kernels, Gaussian process, Structural priors, Mathematics, Discrete mathematics, Random field, Applied Mathematics, Linear operators, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, RKHS, symbols, Heat equation, Statistics, Probability and Uncertainty, Degeneracy (mathematics), Reproducing kernel Hilbert space
Abstract

International audience; We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.

Published
2016
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45. The tail dependograph

Author

Cécile Mercadier, Olivier Roustant, Probabilités, statistique, physique mathématique (PSPM), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, and Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, Multivariate statistics, Rank (linear algebra), Multivariate extreme value analysis, Hoeffding--Sobol decomposition, Multivariate random variable, Tail dependency graph, 05 social sciences, Economics, Econometrics and Finance (miscellaneous), Tail dependence, Subset and superset, 01 natural sciences, Measure (mathematics), 010104 statistics & probability, Global sensitivity analysis, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 0502 economics and business, Pairwise indices, Pairwise comparison, Statistical physics, 0101 mathematics, Extreme value theory, Engineering (miscellaneous), 050205 econometrics, Mathematics
Abstract

To appear in June (2019); International audience; All characterizations of non-degenerate multivariate tail dependence structures are both functional and infinite-dimensional. Taking advantage of the Hoeffding--Sobol decomposition, we derive new indices to measure and summarize the strength of dependence in a multivariate extreme value analysis. The tail superset importance coefficients provide a pairwise ordering of the asymptotic dependence structure. We then define the tail dependograph, which visually ranks the extremal dependence between the components of the random vector of interest. For the purpose of inference, a rank-based statistic is derived and its asymptotic behavior is stated. These new concepts are illustrated with both theoretical models and real data, showing that our methodology performs well in practice.

Published
2019
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46. Support indices: Measuring the effect of input variables over their supports

Author

Jana Fruth, Olivier Roustant, Sonja Kuhnt, Technische Universität Dortmund [Dortmund] (TU), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Département Décision en Entreprise : Modélisation, Optimisation (DEMO-ENSMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Henri Fayol, Dortmund University of Applied Sciences and Arts, Institut Mines-Télécom [Paris] (IMT), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, Fachhochschule Dortmund - University of Applied Sciences and Arts (FH Dortmund), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol

Subjects
0211 other engineering and technologies, 02 engineering and technology, Variation (game tree), Space (mathematics), Sobol' indices, Industrial and Manufacturing Engineering, Domain (mathematical analysis), Statistics, DGSM, Support Analysis, Applied mathematics, Sensitivity (control systems), Safety, Risk, Reliability and Quality, Sobol indices, Mathematics, 021110 strategic, defence & security studies, [STAT.AP]Statistics [stat]/Applications [stat.AP], 021103 operations research, Sobol sequence, Extension (predicate logic), [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Connection (mathematics), DGSM * Corresponding author, Probability distribution, Sensitivity analysis, Sobol’ indices, [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

International audience; Two new sensitivity indices are presented which give an original solution to the question in sensitivity analysis of how to determine regions within the input space for which the model variation is high. The indices, as functions over the input domain, give insight into the local influence of input variables over the whole domain when the other variables lie in the global domain. They can serve as an informative extension to a standard analysis and in addition are especially helpful in the specification of the input domain, a critical, but often vaguely handled issue in sensitivity analysis. In the usual framework of independent continuous input variables, we present theoretical results that show an asymptotic connection between the presented indices and Sobol’ indices, valid for general probability distribution functions. Finally, we show how the indices can be successfully applied on analytical examples and on a real application.

Published
2018
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47. Total interaction index: A variance-based sensitivity index for second-order interaction screening

Author

Jana Fruth, Sonja Kuhnt, and Olivier Roustant

Subjects
Statistics and Probability, Set (abstract data type), Dimension (vector space), Applied Mathematics, Statistics, Statistical inference, Estimator, Subset and superset, Function (mathematics), Sensitivity (control systems), Variance (accounting), Statistics, Probability and Uncertainty, Mathematics
Abstract

Sensitivity analysis aims at highlighting the input variables that have significant impact on a given model response of interest. By analogy with the total sensitivity index, used to detect the most influential variables, a screening of interactions can be done efficiently with the so-called total interaction index (TII), defined as the superset importance of a pair of variables. Our aim is to investigate the TII, with a focus on statistical inference. At the theoretical level, we derive its connection to total and closed sensitivity indices. We present several estimation methods and prove the asymptotical efficiency of the Liu and Owen estimator. We also address the question of estimating the full set of TIIs, with a given budget of function evaluations. We observe that with the pick-and-freeze method the full set of TIIs can be estimated at a linear cost with respect to the problem dimension. The different estimators are then compared empirically. Finally, an application is given aiming at discovering a block-additive structure of a function, where no prior knowledge is available, neither about the interaction structure nor about the blocks.

Published
2014
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48. Poincaré inequalities on intervals – application to sensitivity analysis

Author

Franck Barthe, Olivier Roustant, Bertrand Iooss, Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Management des Risques Industriels (EDF R&D MRI), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Département Génie mathématique et industriel ( FAYOL-ENSMSE ), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques ( GdR MASCOT-NUM ), Centre National de la Recherche Scientifique ( CNRS ), Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), and EDF ( EDF )

Subjects
Statistics and Probability, derivative-based global sensitivity measures, [ INFO.INFO-MO ] Computer Science [cs]/Modeling and Simulation, Truncated normal distribution, Poincaré inequality, Mathematics - Statistics Theory, Interval (mathematics), Sobol-Hoeffding decomposition, 01 natural sciences, 010104 statistics & probability, symbols.namesake, Kummer's functions, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, spectral gap, Applied mathematics, Sensitivity (control systems), truncated distribution, 0101 mathematics, Sobol indices, Mathematics, Kummer’s functions, 010102 general mathematics, Mathematical analysis, Truncated distribution, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Range (mathematics), Distribution (mathematics), symbols, Probability distribution, finite elements, Statistics, Probability and Uncertainty, Mathematics - Probability
Abstract

International audience; The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincaré inequalities. Typically two kind of sensitivity indices are linked by a Poincaré type inequality , which provide upper bounds of the most interpretable index by using the other one, cheaper to compute. This allows performing a low-cost screening of unessential variables. The efficiency of this screening then highly depends on the accuracy of the upper bounds in Poincaré inequalities. The novelty in the questions concern the wide range of probability distributions involved, which are often truncated on intervals. After providing an overview of the existing knowledge and techniques, we add some theory about Poincaré constants on intervals, with improvements for symmetric intervals. Then we exploit the spectral interpretation for computing exact value of Poincaré constants of any admissible distribution on a given interval. We give semi-analytical results for some frequent distributions (truncated exponential, triangular, truncated normal), and present a numerical method in the general case. Finally, an application is made to a hydrological problem, showing the benefits of the new results in Poincaré inequalities to sensitivity analysis.

Published
2017
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49. Polar Gaussian Processes and Experimental Designs in Circular Domains

Author

Olivier Roustant, Espéran Padonou, Département Décision en Entreprise : Modélisation, Optimisation (DEMO-ENSMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Henri Fayol, Institut Mines-Télécom [Paris] (IMT), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes (LIMOS), SIGMA Clermont (SIGMA Clermont)-Université d'Auvergne - Clermont-Ferrand I (UdA)-Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Blaise Pascal - Clermont-Ferrand 2 (UBP), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Université d'Auvergne - Clermont-Ferrand I (UdA)-SIGMA Clermont (SIGMA Clermont)-Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020]), and Roustant, Olivier

Subjects
Statistics and Probability, Geodesic, Design of Experiments, 0211 other engineering and technologies, Geometry, 02 engineering and technology, 01 natural sciences, Circular domain, 010104 statistics & probability, symbols.namesake, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Discrete Mathematics and Combinatorics, 0101 mathematics, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Gaussian process, Mathematics, 021103 operations research, Applied Mathematics, Log-polar coordinates, Mathematical analysis, Covariance, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Polar coordinates, Latin hypercube sampling, Modeling and Simulation, Kernel (statistics), symbols, Statistics, Probability and Uncertainty, Polar coordinate system, Rotation (mathematics), Gaussian process regression
Abstract

International audience; Predicting on circular domains is a central issue that can be addressed by Gaussian process (GP) regression. However, usual GP models do not take into account the geometry of the disk in their covariance structure (or kernel), which may be a drawback at least for industrial processes involving a rotation or a diffusion from the center of the disk. We introduce so-called polar GPs defined on the space of polar coordinates. Their kernels are obtained as a combination of a kernel for the radius and a kernel for the angle, based on either chordal or geodesic distances on the circle. Their efficiency is illustrated on two industrial applications. We further consider the problem of designing experiments on the disk. Two new Latin hypercube designs are obtained, by defining a valid maximin criterion for polar coordinates. Finally, an extension of the whole methodology to higher dimensions is investigated.Read More: http://epubs.siam.org/doi/abs/10.1137/15M1032740

Published
2016
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50. Composition chimique des dépôts atmosphériques à l’horizon 2020-2040

Author

Manuel Nicolas, Christian Pagé, Aude Pascaud, Anne Probst, Patrice Coddeville, Stéphane Sauvage, Luc Croisé, Olivier Roustant, Abdelkrim Mezdour, École des Mines de Douai (Mines Douai EMD), Institut Mines-Télécom [Paris] (IMT), Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), Département Décision en Entreprise : Modélisation, Optimisation (DEMO-ENSMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Henri Fayol, Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Laboratoire Ecologie Fonctionnelle et Environnement (LEFE), Institut Ecologie et Environnement (INEE), Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Observatoire Midi-Pyrénées (OMP), Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT), Office national des forêts (ONF), Météo-France Direction Interrégionale Sud-Est (DIRSE), Météo-France, CERFACS, Institut de Mathématiques de Toulouse UMR5219 (IMT), Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Laboratoire Ecologie Fonctionnelle et Environnement (ECOLAB), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Observatoire Midi-Pyrénées (OMP), Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Géoazur (GEOAZUR 7329), Université Côte d'Azur (UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])-Centre National de la Recherche Scientifique (CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA), Unité d'écophysiologie forestière, Institut National de la Recherche Agronomique (INRA), Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020]), Office National des Forêts (ONF), Météo France, Centre National de la Recherche Scientifique - CNRS (FRANCE), Ecole Nationale Supérieure des Mines de Saint-Etienne - ENSMSE (FRANCE), Ecole des Mines de Douai (FRANCE), Institut National Polytechnique de Toulouse - INPT (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Blaise Pascal - UBP (FRANCE), Institut français de mécanique avancée - IFMA (FRANCE), Météo France (FRANCE), Office National des Forêts - ONF (FRANCE), Université d'Auvergne - UDA (FRANCE), Centre Européen de Recherche et Formation Avancées en Calcul Scientifique - CERFACS (Toulouse, France), and Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)

Subjects
Nitrates, 010504 meteorology & atmospheric sciences, Prédiction 2020-2040, Sulfates, Géochimie, 010501 environmental sciences, 01 natural sciences, Dépôts atmosphériques, Modélisation, [SDU.STU.CL]Sciences of the Universe [physics]/Earth Sciences/Climatology, [SDU.STU.GC]Sciences of the Universe [physics]/Earth Sciences/Geochemistry, [CHIM]Chemical Sciences, Climatologie, Scénarios, ComputingMilieux_MISCELLANEOUS, Ammonium, Réseaux RENECOFOR-BAPMON-MERA, 0105 earth and related environmental sciences
Abstract

National audience; Les dépôts atmosphériques peuvent causer des dommages importants aux milieux naturels. Des mesures à long terme issues de la surveillance des dépôts atmosphériques en France ont été exploitées pour construire un modèle statistique prévisionnel afin d'estimer les changements de la composition chimique des dépôts atmosphériques à l'horizon 2020-2040. À partir de simulations d'évolutions possibles du climat et des émissions de polluants atmosphériques, les dépôts de sulfate non marin et les dépôts d'ammonium sont susceptibles de diminuer, mais ceux de nitrate pourraient augmenter de façons diverses selon les régions. Le changement des variations saisonnières de pluviométrie pourrait augmenter les flux de dépôts.

Published
2016
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