Dynamic mode decomposition (DMD) is a factorization and dimensionality reduction
technique for data sequences. In its most common form, it processes high-dimensional …

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

In recent years, we have witnessed a significant shift toward ever-more complex and ever-
larger-scale systems in the majority of the grand societal challenges tackled in applied …

We derive a data-driven method for the approximation of the Koopman generator called
gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic …

In this review paper, we will present different data-driven dimension reduction techniques for
dynamical systems that are based on transfer operator theory as well as methods to …

Information about the behavior of dynamical systems can often be obtained by analyzing the
eigenvalues and corresponding eigenfunctions of linear operators associated with a …

We propose a novel cluster-based reduced-order modelling (CROM) strategy for unsteady
flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt …

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

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 …

Dynamical systems often exhibit the emergence of long-lived coherent sets, which are
regions in state space that keep their geometric integrity to a high extent and thus play an …