The aim of numerical methods is to contribute to the efficient propagation of uncertainties and the resolution of inverse problems.
These methods need to take account of model and measurement uncertainties, integrating the sometimes long-term temporal component (climate change) with a view to updating the model or evaluating a stochastic performance indicator.
They concern :
- construction of metamodels based on edp, Levi processes or observations: exploitation of combinations of information, taking into account the confidence placed in them and their influence on the variable of interest, sensitivity analysis,
- propagation of uncertainties through the measurement chain: direct problem (from measurement to sensor) and inverse problem (from sensor to measurement),
- relating measurement/model/calculation errors to optimize model updating,
- regularization ill-posed problems in the context of inverse problems to optimize robustness,
- modeling of spatial variability in the case of non-stationary 3D fields to optimize measurements for RBU (Risk Based Inspection) methods,
- Reliability based optimization (RBO) for time-dependent problems.