Deep Learning Enhanced Dynamic Mode Decomposition
- URL: http://arxiv.org/abs/2108.04433v1
- Date: Tue, 10 Aug 2021 03:54:23 GMT
- Title: Deep Learning Enhanced Dynamic Mode Decomposition
- Authors: Christopher W. Curtis, Daniel Jay Alford-Lago, Opal Issan
- Abstract summary: We use convolutional autoencoder networks to simultaneously find optimal families of observables.
We also generate both accurate embeddings of the flow into a space of observables and immersions of the observables back into flow coordinates.
This network results in a global transformation of the flow and affords future state prediction via EDMD and the decoder network.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Koopman operator theory shows how nonlinear dynamical systems can be
represented as an infinite-dimensional, linear operator acting on a Hilbert
space of observables of the system. However, determining the relevant modes and
eigenvalues of this infinite-dimensional operator can be difficult. The
extended dynamic mode decomposition (EDMD) is one such method for generating
approximations to Koopman spectra and modes, but the EDMD method faces its own
set of challenges due to the need of user defined observables. To address this
issue, we explore the use of convolutional autoencoder networks to
simultaneously find optimal families of observables which also generate both
accurate embeddings of the flow into a space of observables and immersions of
the observables back into flow coordinates. This network results in a global
transformation of the flow and affords future state prediction via EDMD and the
decoder network. We call this method deep learning dynamic mode decomposition
(DLDMD). The method is tested on canonical nonlinear data sets and is shown to
produce results that outperform a standard DMD approach.
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