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Modeling and Optimization of Complex Systems

Natural or artificial, complex systems are everywhere. Although there is still no unanimously accepted formal definition of their nature, they are characterized by the interaction of components of various sizes and a heterogeneous, uncertain nature whose overall evolution is dominated by couplings and retro-actions.

>A field where modeling faces conceptual challenges in describing the different components and their interactions correctly and defining the original condition and expected use
>A field where simulation requires suitable languages and scalable, configurable software architecture
>A field where applied mathematics, computer science, biology, physics, mechanics and economics overlap
>A field where collective properties sometimes reveal surprises.

Some ongoing projects:

"Mathématiques et biodiversité” (Mathematics and Biodiversity) winner of the La Recherche magazine prize
Sylvie Méléard and her team were awarded the Mathematics prize from La Recherche magazine for their work linking mathematics and biodiversity. Their mathematical models allow us to have a better understanding of the impact of ecological parameters on natural selection. This research, supported by the Mathematical Modeling and Biodiversity Chair in partnership with Véolia Environnement and the Muséum National d’Histoire Naturelle (National Natural History Museum), is aimed at developing mathematics in order to anticipate and better understand the evolution of biodiversity behavior over time.

Coupling electrons with light: the future of electronics and optics
The Irradiated Solids Laboratory (LSI) has developed TURBO-EELS, a new algorithm for modeling the collective vibrations of electrons in solids. Using light to stimulate vibrations has many applications: in particular it can decrease the size of electronic and optical circuits to a nanometric scale. This is why it is important to have simulation tools which can calculate nanostructures on a quantum scale. This research work is the result of  collaboration with the École Internationale d’Études Avancées (International School of Advances Studeis - SISSA) and the Centre International de Physique Théorique (ICTP - International Center for Theoretical Physics) in Trieste. Iurii Timrov's thesis received the Certificat de Compétences en Calcul Intensif (Certificate of proficiency in high-performance computing - C3I) label.