KoopduMonde

The so-called "ensemble-based" prevision methods in oceanography and meteorology use an ensemble of numerical simulations to estimate the state of the system corresponding at best to the observations. These methods are limited by the requirement of running again the simulations in order to reach good performances. Could we avoid this expensive step and exploit at maximum the information contained in the ensemble of non-linear trajectories? The objective of this project is to incorporate tools from statistical learning and dynamical systems theory to ensemble data assimilation methods for large scale dynamical systems. More precisely, the seminal idea is to learn the eigenfunctions of the Koopman operator restricted to a reproducing kernel Hilbert space (RKHS) transported by the dynamical system.