Isao Ishikawa (Kyoto University)

In this talk, we will introduce JetEDMD, a new theoretical framework as a finite-dimensional approximation of the push-forward on the spaces of analytic functionals.

JetEDMD provides a reasonable modification of Extended Dynamic Mode Decomposition (EDMD) and elucidates new mathematical machinery by combining the structure of reproducing kernel Hilbert spaces with the jet spaces on the state space of the dynamical system.

As applications, I will present methods for the data-driven estimation of equilibrium points and the reconstruction of vector fields from discrete trajectory data with a rigorous convergence result. Finally, I will discuss some current mathematical challenges and future research directions within this framework.