32 citations · 59 across the 5 of their papers we have counts for
8 papers
Data-Driven Linearization of Dynamical Systems
George Haller, Bálint Kaszás
Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD…
Modeling Nonlinear Dynamics from Videos
Antony Yang, Joar Axås, Fanni Kádár +2
We introduce a method for constructing reduced-order models directly from videos of dynamical systems. The method uses a non-intrusive tracking to isolate the motion of a user-sele…
Nonlinear Model Reduction to Temporally Aperiodic Spectral Submanifolds
George Haller, Roshan S. Kaundinya
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in…
Vorticity Alignment with Lyapunov Vectors and Rate-of-Strain Eigenvectors
Alex Encinas-Bartos, George Haller
We derive asymptotic estimates for the projection of the vorticity onto principal directions of material stretching in 3D flows. In flows with pointwise bounded vorticity, these es…
Data-Driven Modeling and Forecasting of Chaotic Dynamics on Inertial Manifolds Constructed as Spectral Submanifolds
Aihui Liu, Joar Axås, George Haller
We present a data-driven and interpretable approach for reducing the dimensionality of chaotic systems using spectral submanifolds (SSMs). Emanating from fixed points or periodic o…
Relative Fluid Stretching and Rotation for Sparse Trajectory Observations
Nikolas O. Aksamit, Alex P. Encinas-Bartos, George Haller +1
As most mathematically justifiable Lagrangian coherent structure detection methods rely on spatial derivatives, their applicability to sparse trajectory data has been limited. For…
Quasi-Objective Coherent Structure Diagnostics from Single Trajectories
George Haller, Nikolas Aksamit, Alex P. Encinas Bartos
We derive measures of local material stretching and rotation that are computable from individual trajectories without reliance on other trajectories or on an underlying velocity fi…
Connecting the time evolution of the turbulence interface to coherent structures
M. M. Neamtu-Halic, D. Krug, J. P. Mollicone +3
The surface area of turbulent/non-turbulent interfaces (TNTIs) is continuously produced and destroyed via stretching and curvature/propagation effects. Here, the mechanisms respons…