➤ Uncertainty quantification has now become a mandatory step in numerical sciences and modeling in a context where computational sciences are constantly increasing.
➤ The main idea is to quantify the uncertainty in the model outputs (called quantities of interest) that are due to uncertainties of various types in the model (aleatory and epistemic errors). These errors relate for instance to model parameters, initial conditions, boundary conditions or model equations.
➤ The classical methods for uncertainty quantification are based on the Monte-Carlo approach that allows to estimate the probability density function (pdf) of quantity of interest with respect to the pdf of the input variables that are considered as aleatory variables. These methods are computationally expensive as they imply a considerable number of model integrations. Numerous alternative methods (intrusive or non-intrusive) aim at building a surrogate model using a limited number of model integrations, which statistics and surface response can be estimated at a limited cost.
➤ This activity is transversal to the following transversal axis at CERFACS Assimilation de données and research axis Environnement , Climat, Aérodynamique and Combustion. The applications at CERFACS relate to flood forecasting, wildland fire propagation, climate variability or combustion chamber ignition.
➤ Uncertainty quantification methods can be associated to ensemble based data assimilation algorithms. The identification of uncertainty sources and the quantification of this uncertainty on the quantities of interest formulated in the observation space allow to specify the control vector for the data assimilation algorithm. Additionnaly, these algorithms rely on a stochastic estimate of the errors statistics, that can be estimated at a limited computational cost using a surrogate model. The link between uncertainty quantification and data assimilation is established for the following applications: hydraulique and feux de forêt. A surrogate model based on a Polynomial Chaos expansion is used in place of the forward model, in order to limit the cost of the ensemble generation within the data assimilation algorithm.
➤ A platform dedicated to uncertainty quantification is under development in the framework of the dynamical coupling software OpenPALM using the OpenTURNS (EDF/EADS/Phimeca) library. This preliminary tool offers classical non-intrusive approachs for small to medium dimension problems involving a limited number of model integrations. It is designed for straigthforward use for applicative simple cases that are of interest for CERFACS and its shareholders.
➤ The development of advanced methods adapted to large dimension problems remain an open research field and a challenge for geosciences, combustion and aerodynamics that CERFACS is willing to tackle with.
- TOSCA CNES – PhD N. El Mocayd (co-funding EDF)
- Contract SCHAPI
- PhD CERFACS (Oct. 2016-2019)