Section: New Results

Complex systems design

Participant : Erick Herbin.

In collaboration with Dassault Aviation, EADS, EDF.

The preliminary design of complex systems can be described as an exploration process of a so-called design space, generated by the global parameters. An interactive exploration, with a decisional visualization goal, needs reduced-order models of the involved physical phenomena. We are convinced that the local regularity of phenomena is a relevant quantity to drive these approximated models. Roughly speaking, in order to be representative, a model needs more informations where the fluctuations are the more important (and consequently, where irregularity is the more important).

In collaboration with Dassault Aviation, EDF and EADS, we study how the local regularity can provide a good quantification of the concept of granularity of a model, in order to select the good level of fidelity adapted to a required precision.

Our works in that field can be expressed into:

• The definition and the study of stochastic partial differential equations driven by processes with prescribed regularity (that do not enter into the classical theory of stochastic integration).

• The study of the evolution of the local regularity inside stochastic partial differential equations (SPDE). Stochastic 2-microlocal analysis should provide informations about the local regularity of the solutions, in function of the coefficients of the equations. The knowledge of the fine behaviour of the solution of the SPDE will provide important informations in the view of numerical simulations.