The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

A common way to represent a system's dynamics is to specify how the state evolves in time.
An alternative viewpoint is to specify how functions of the state evolve in time. This evolution …

Dynamic mode decomposition (DMD) describes complex dynamic processes through a
hierarchy of simpler coherent features. DMD is regularly used to understand the …

Koopman operators globally linearize nonlinear dynamical systems and their spectral
information is a powerful tool for the analysis and decomposition of nonlinear dynamical …

Koopman operators are infinite‐dimensional operators that globally linearize nonlinear
dynamical systems, making their spectral information valuable for understanding dynamics …

Koopman operators linearize nonlinear dynamical systems, making their spectral
information of crucial interest. Numerous algorithms have been developed to approximate …

We consider the data-driven approximation of the Koopman operator for stochastic
differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the …

Kernel analog forecasting (KAF), alternatively known as kernel principal component
regression, is a kernel method used for nonparametric statistical forecasting of dynamically …

Dynamical systems provide a comprehensive way to study complex and changing behaviors
across various sciences. Many modern systems are too complicated to analyze directly or …

The Earth's climate system is a classical example of a multiscale, multiphysics dynamical
system with an extremely large number of active degrees of freedom, exhibiting variability on …