Analyse de sensibilité et réduction de dimension. Application à l'océanographie

Alexandre Janon 1, 2
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Mathematical models seldom represent perfectly the reality of studied systems, due to, for instance, uncertainties on the parameters that define the system. In the context of geophysical fluids modelling, these parameters can be, e.g., the domain geometry, the initial state, the wind stress, the friction or viscosity coefficients. Sensitivity analysis aims at measuring the impact of each input parameter uncertainty on the model solution and, more specifically, to identify the ``sensitive'' parameters (or groups of parameters). Amongst the sensitivity analysis methods, we will focus on the Sobol indices method. The numerical computation of these indices require numerical solutions of the model for a large number of parameters' instances. However, many models (such as typical geophysical fluid models) require a large amount of computational time just to perform one run. In these cases, it is impossible (or at least not practical) to perform the number of runs required to estimate Sobol indices with the required precision. This leads to the replacement of the initial model by a emph{metamodel} (also called emph{response surface} or emph{surrogate model}), which is a model that approximates the original model, while having a significantly smaller time per run, compared to the original model. This thesis focuses on the use of metamodel to compute Sobol indices. More specifically, our main topic is the quantification of the metamodeling impact, in terms of Sobol indices estimation error. We also consider a method of metamodeling which leads to an efficient and rigorous metamodel, which can be used in the geophysical context.
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Alexandre Janon. Analyse de sensibilité et réduction de dimension. Application à l'océanographie. Mathématiques générales [math.GM]. Université de Grenoble, 2012. Français. ⟨NNT : 2012GRENM066⟩. ⟨tel-00757101v2⟩



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