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

Advances in experimental techniques and the ever-increasing fidelity of numerical
simulations have led to an abundance of data describing fluid flows. This review discusses a …

We consider the frequency domain form of proper orthogonal decomposition (POD), called
spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space …

The integration of data and scientific computation is driving a paradigm shift across the
engineering, natural, and physical sciences. Indeed, there exists an unprecedented …

The Koopman operator is a linear but infinite-dimensional operator that governs the
evolution of scalar observables defined on the state space of an autonomous dynamical …

We develop a new method which extends dynamic mode decomposition (DMD) to
incorporate the effect of control to extract low-order models from high-dimensional, complex …

Used to analyze the time-evolution of fluid flows, dynamic mode decomposition (DMD) has
quickly gained traction in the fluids community. However, the existing DMD literature focuses …

This paper deals with an extension of dynamic mode decomposition (DMD), which is
appropriate to treat general periodic and quasi-periodic dynamics, and transients decaying …

A survey is given of the major developments in three-dimensional velocity field
measurements using the tomographic particle image velocimetry (PIV) technique. The …

A data driven, kernel-based method for approximating the leading Koopman eigenvalues,
eigenfunctions, and modes in problems with high dimensional state spaces is presented …