Modeling, Simulation and Optimization of Complex Dynamic Systems

To reliably produce and simulate phenomena: this is the challenge for modeling. There is a plethora of complex dynamic systems that provide better knowledge and comprehension: meteorological, biology, engineering, internet, etc. Multidisciplinary by excellence, modeling associates mathematics, informatics, automation and the disciplines of the involved field. One of the objectives of the research will focus on implementing new interactions between these disciplines.

These complex systems require heterogeneous mathematical systems that are both multi-model, and multi-scale in time and space, and that are associated with resolution and data assimilation methods (varying greatly in nature and quality, and often unreliable), as well as high-performance calculation tools. Stochastical, or stochastical/deterministic-mixed approaches need to be developed. New computational reasoning models (neural nets, automatons, multi-agent and hybrid systems) are often necessary when the simplifications introduced run the risk of masking significant effects, or when traditional models are not appropriate.

«  Multidisciplinary by excellence, modeling associates mathematics, informatics, automation and the disciplines of the involved field. »

Modeling for automation is very specific according to the need to control a system. It consists of simplifying and extracting the main mechanisms of interaction that affect the evolution of a process, in order to facilitate designing effective action strategies. This need to reduce models to their most important components poses a genuine scientific challenge when the systems involved are dimensionally or structurally complex.

Faced with the increasing complexity of multi-scale models and dynamic systems, simulation requires new developments relating to digital algorithms. Their effectiveness is measured in terms of precision and calculation time, but the key to their performance also lies within its capacity to program and efficiently operate extremely heterogeneous calculation platforms (multi-processor systems, large clusters and large-scale distributed information systems). In addition, the simulations produce significant data flow that can be used offline or online through virtual reality technology, or through immersion in interactive real-time simulations. Finally, the simulation must also help prevent risks and manage uncertainties, concerns to be taken into account from the time the data is assimilated, and in the models themselves.

Optimization of these very large-scale systems must be improved in terms of robustness of the results in relation to the uncertainties or minor variations. The automatic methods for calculating the successive derivations must be extended to include very large systems, while guaranteeing good performance in terms of time and accuracy. Optimization of the entities resulting from the various disciplines, from phenomena that are simultaneously continuous and discrete, and from dynamic systems are technologies that must render the algorithms more efficient.