Analyse de dynamiques spatio-temporelles complexes par réduction de modèle et analyses de sensibilité – COSTA-BRAVA

Numerical modelling is increasingly developed in a wide range of domains: engineering, life sciences, economics... Models are tools to support conception, design, decision, prediction... Progress in modelling and increase in computing power lead to computing codes that often: -Are quite complex. Many times these computing codes have been built by an huge number of people. In general, none of these developers knows all the parts of the code. -Contain multiple output variables and voluminous results (so that there are many things to look at, and perception of dependencies between variables can vary depending on the point of view). -Can be very demanding in terms of computer resources, so that many-query applications are out of hand. For example, a realistic simulation of radioactive waste storage behaviour can take several weeks. In such scenarios, so many uncertainties exist. So that, realizations of a large number of different simulations is required. Examples of such complex systems are innumerable: models of the earth's climate, of biological systems like human cells or organs, of nuclear plants, of economic policies... To improve and have a better hold on these tools it is crucial to be able to analyze them under the scopes of sensitivity analysis and uncertainty propagation. More precisely, for a given output of the system, one wish to identify the most influential parameters, and to evaluate the effect of uncertainty in input parameters on model output. Existing stochastic tools are not well suited for high dimension problems (in particular time-dependent problems). While deterministic tools are fully applicable but only provide limited information. In this framework,the main aim of this project is to develop and design innovative stochastic solutions to study high dimension models and to propose new hybrid approaches combining the stochastic and deterministic methods. Indeed, it has been recently recognized that a successful development of such tools will allow achieving a global capability for performing efficiently and accurately, global sensitivity and uncertainty analyses for large-scale systems. Collaborations proposed in this project will bring together top researchers from both deterministic and stochastic communities. Moreover, the skills combined within this project are as well skills in applied mathematics as skills in scientific computing. The aim of this project is to use these complementarities in competences to develop high level theoretical tools (deterministic, stochastic or even hybrid) and to apply them to some real life test cases (Monsoon in west Africa, Corrosion in nuclear plants, ...). Researchers coming both from academic (University, CNRS, INRIA) and industrial (CEA, IFP) laboratories will work together within this ambitious project.