Modeling of Missing Dynamical Systems: Deriving Parametric Models using a Nonparametric Framework

Understand

In this paper, we consider modeling missing dynamics with a nonparametric non-Markovian model, constructed using the theory of kernel embedding of conditional distributions on appropriate Reproducing Kernel Hilbert Spaces (RKHS), equipped with orthonormal basis functions.

• Depending on the choice of the basis functions, the resulting closure model from this nonparametric modeling formulation is in the form of parametric model.
• This suggests that the success of various parametric modeling approaches that were proposed in various domains of applications can be understood through the RKHS representations.
• When the missing dynamical terms evolve faster than the relevant observable of interest, the proposed approach is consistent with the effective dynamics derived from the classical averaging theory.