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 …

Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …

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 …

The dynamic mode decomposition (DMD)—a popular method for performing data-driven
Koopman spectral analysis—has gained increased popularity for extracting dynamically …

The Koopman operator provides a powerful way of analysing nonlinear flow dynamics using
linear techniques. The operator defines how observables evolve in time along a nonlinear …

Time-resolved particle image velocimetry (TR-PIV) has become widespread in fluid
dynamics. Essentially a velocity field movie, the dynamic content provides temporal as well …

Wind pressures on buildings with different aspect ratios were investigated via higher-order
dynamic mode decomposition (HODMD) in this study. Taken's embedding theorem was …