Sensitivity analysis and dimension reduction
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.
11:00 a.m. to 12:00 p.m., LJLL, University Paris 6 (UPMC), Jussieu campus, seminar room 15-16-309. Coffee from 10:45 a.m.
