Merveille Cyndie TALLA MAKOUGNE - Dynamic models of turbulent flows using physically constrained diffusion models

This thesis project lies at the frontier of several fields. The aim is to adapt a statistical learning model of the diffusion type, recently proposed in the literature, to the specific framework of the reconstruction of turbulent flows. To this end, our innovative diffusion models will be implemented, in particular by coupling them to a reduced stochastic model of the flow dynamics. A Koopman-type representation of stochastic differential equations will thus be undertaken. This exploratory work will combine issues of statistical learning, definition of reduced dynamic models guided by data, stochastic flow representation, and reconstruction of the state of a flow from data. By proposing new diffusion models for the rapid reconstruction of the dynamics of turbulent flows, this thesis will ultimately enable better control of the risks associated with airborne contamination of indoor air.