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math.DS2024
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…
math.DS2024
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…
math.DS2024
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…