Complex spatio-temporal dynamics analysis by model reduction and sensitivity analysis

Scientific context of the project

Complex computer models

Mathematical modelisations and numerical simulations get more and more developed in a large range of scientific fields: engineering, life sciences, economy… Advances in modelisations and increase in computational power lead to computations that:

• are complex: the numerical codes of interest have been written by large groups of people, and no individual is familiar with every part of the code;
• involve many input variables and large output data;
• can be very computationally expensive. For instance, a single realistic simulation of the behavior of stored nuclear waste can take several weeks of computation time.

To name a few, modern simulators of biological systems such as human cells or organs, Earth climate, nuclear power plants or economic policies share those features.

Uncertainty quantification and sensitivity analysis

In order to make the best use of our models of complex systems, it is crucial to analyze them using uncertainty propagation and sensitivity analysis. More specifically, we want, for a given model, to quantify the impact of the uncertain inputs on the model outputs, and to identify the inputs which have the most important influence on the outputs. Existing stochastic tools are not convincing for high-dimensional, time-dependent problems. Deterministic tools are usable in these cases, but they provide limited information.

Goals of the Costa Brava project

The main goal of the Costa Brava project is to design new hybrid approaches that originally combine stochastic and deterministic approaches. It has been recognized that such tools will help attaining a global uncertainty analysis for large-scale models. Another challenge in this project is to implement modern software tools to analyze computer experiments featuring a complex spatio-temporal evolution.

Collaborations enabled by this project involve stochastic and deterministic tools, as well as skills in applied mathematics and scientific computing. We aim at using those complementaries to develop high-level theoretical deterministic, stochastic, and hybrid tools, and to apply these tools to specific test cases. Researchers involved in this ambitious project come from both academic (universities, CNRS, INRIA) and industrial (CEA, IFP Energies nouvelles) laboratories.