Although open physical systems potentially have an infinite number of degrees of freedom, flows are quite often organized around characteristic coherent structures, which play a key-role in both the dynamics and spectral signature of the flow. One can think to von Karman streets, present from lab's flows to island's wakes.
This organization invites both to a modal decomposition (which can be used to understand the connection between the different scales captured by the coherent structures and their time behavior, or to infer reduced-order models) or a topological/kernel based description (wich leads to a interpretation of lagrangian properties).
More generally, these approachs lead to tractable solutions for tackling the curse of dimensionallity ; I am actively exploring these paths.
Von Karman vortices, Rishiri Island, Japan
I am currently interested in:
- Construction of sparse and pertinent representations of dataset/dynamics.
- Modal decompositions.
- Supervised and unsupervised learning (machine learning).
- Modelling and controlling the dynamics based on these representations.
- Efficient computations of these representations.
- Tangible interfaces, in augmented/virtual reality, mainly for 3D data exploration.
My PhD work was splitted into three main objectives.
- Modal decomposition : Involvement in DMD decomposition and Koopman operator analysis.
- Lagrangian Coherent Structure detection : Involvement in High Performance Computations for the extraction of LCS.
- Computer-Human Interaction : Exploration of complexe dataset (e.g. FTLE fields).