This paper aims at reviewing nonlinear methods for model order reduction in structures with
geometric nonlinearity, with a special emphasis on the techniques based on invariant …

The sparse identification of nonlinear dynamics (SINDy) is a recently proposed data-driven
modelling framework that uses sparse regression techniques to identify nonlinear low-order …

Invariant manifolds are important constructs for the quantitative and qualitative
understanding of nonlinear phenomena in dynamical systems. In nonlinear damped …

In fluid dynamics, predicting and characterizing bifurcations, from the onset of unsteadiness
to the transition to turbulence, is of critical importance for both academic and industrial …

In the absence of governing equations, dimensional analysis is a robust technique for
extracting insights and finding symmetries in physical systems. Given measurement …

Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to
understand and describe their behavior. However, there is a scarcity of plasma models of …

This work investigates nonlinear dimensionality reduction as a means of improving the
accuracy and stability of reduced-order models of advection-dominated flows. Nonlinear …

Flow past three identical circular cylinders is numerically investigated using the immersed
boundary method. The cylinders are arranged in an equilateral-triangle configuration with …

We derive low-dimensional, data-driven models for transitions among exact coherent states
in one of the most studied canonical shear flows, the plane Couette flow. These one-or two …

The aim of this paper is to provide a complete description of the bifurcation scenario of a
uniform flow past a rotating circular cylinder up to. Linear stability theory is used to depict the …