Résumé : Mathematical models seldom represent perfectly the reality of studied systems, due to, for instance, uncertainties on the parameters that
define the system. For instance, in 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 metamodel (also called response surface or surrogate model), which is a model that approximates the original model, while having a significantly smaller time per run, compared to the original model.
We will focus 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.
Lieu : bâtiment Fermat, salle 2102
Résumé : Dubrovin’s conjecture (ICM 1998) predicts an intriguing relation between the quantum cohomology ring of a smooth projective variety X and its derived category of coherent sheaves. I will explain some aspects of this story taking symplectic isotropic Grassmannians IG(m,2n) as the main example and stress the importance of the big quantum cohomology in the formulation of the conjecture. If time permits I will exhibit a relation between the quantum cohomology of IG(m,2n) and unfoldings of isolated hypersurface singularities, and its counterpart for the derived category of coherent sheaves on IG(m,2n). The talk is based on joint works, some finished and some still in progress, with A. J. Cruz Morales, S. Galkin, A. Mellit, N.Perrin, and A. Kuznetsov.
Lieu : Fermat 2205
Lieu : Fermat 2205