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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…
Nonlinear Model Reduction to Random Spectral Submanifolds in Random Vibrations
Zhenwei Xu, Roshan S. Kaundinya, Shobhit Jain +1
Dynamical systems in engineering and physics are often subject to irregular excitations that are best modeled as random. Monte Carlo simulations are routinely performed on such ran…
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…
Nonautonomous Spectral Submanifolds for Model Reduction of Nonlinear Mechanical Systems under Parametric Resonance
Thomas Thurnher, George Haller, Shobhit Jain
We use the recent theory of Spectral Submanifolds (SSM) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions…
Exact Model Reduction by a Slow-Fast Decomposition of Nonlinear Mechanical Systems
George Haller, Sten Ponsioen
We derive conditions under which a general nonlinear mechanical system can be exactly reduced to a lower-dimensional model that involves only the most flexible degrees of freedom.…