Friday, 13th of February14h (Shannon amphitheatre, 660 building) (see location)
Jean-Christophe Loiseau(DynFluid lab, ENSAM)
Dimensionality reduction and system identification of physical systems : chaotic convection, a case studyOver the past few years, data-driven methods and machine learning have been having a transformative impact in numerous fields such as cognitive neuroscience, computer vision, recommendation systems or engineering. Fluid dynamics, be it experimental or computational, is no exception to this trend. In this seminar, we will illustrate how dimensionality reduction and system identification techniques, grounded in the field of statistical learning, can be used to obtain accurate and physically interpretable low-order models describing the large-scale dynamics of complex flow systems. For that purpose, the flow within an annular thermosyphon will be considered as a case study. Such flow configurations, characterized by an unstable temperature stratification, are of utmost importance in numerous applications, ranging from industrial heat exchangers to geophysical, atmospheric or oceanic convection cells, as they can exhibit Lorenz-like chaotic dynamics. From a mathematical point of view, special emphasis will be given to dynamic mode decomposition (DMD), a dimensionality reduction technique that has originated from fluid dynamics in 2010 and is related to the Koopman operator. In particular, we will present a tractable closed-form solution to the DMD problem and discuss some of its statistical properties. Regarding the system identification, a variant of the sparse identification of nonlinear dynamics (SINDy) approach (a recent framework for system identification) will be presented wherein some physical constraints can be enforced in the identification step. A side-by-side comparison of the statistics of the high-dimensional and the identified low-order one will then be provided before concluding with some guidelines and open questions pertaining to the application of machine learning techniques for physical systems.
All TAU seminars: here