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2017

Linearly-Recurrent Autoencoder Networks for Learning Dynamics

Otto, Samuel E., Rowley, Clarence W.

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This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator.

Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical systems.
This paper addresses a fundamental problem associated with EDMD: a trade-off between representational capacity of the dictionary and over-fitting due to insufficient data.
A new neural network architecture combining an autoencoder with linear recurrent dynamics in the encoded state is used to learn a low-dimensional and highly informative Koopman-invariant subspace of observables.

Linearly-Recurrent Autoencoder Networks for Learning Dynamics · Around

Built on

B. O. Koopman
1931
Earlier work this paper cites.
B. Moore
1981
Earlier work this paper cites.
K. Zhou, G. Salomon, and E. Wu
1999
Earlier work this paper cites.
G. E. Dullerud and F. Paganini
2000
Earlier work this paper cites.
P. J. Schmid and D. S. Henningson
2001
Earlier work this paper cites.
M. Espinoza, A. K. Suykens, and B. D. Moor
2005
Earlier work this paper cites.
I. Mezić
2005
Earlier work this paper cites.
C. W. Rowley
2005
Earlier work this paper cites.
C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D. S. Henningson
2009
Earlier work this paper cites.
S. Tao, D. Chen, and W. Zhao
2009
Earlier work this paper cites.
Y.-L. Xu and D.-R. Chen
2009
Earlier work this paper cites.
P. J. Schmid
2010
Earlier work this paper cites.
D. M. Luchtenburg and C. W. Rowley
2011
Earlier work this paper cites.

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