Dynamical Systems by Steve L. Brunton

source: Steve Brunton        2016年4月23日

1 26:44 Sparse Identification of Nonlinear Dynamics (SINDy)--
This video illustrates a new algorithm for the sparse identification of nonlinear dynamics (SINDy).  In this work, we combine machine learning, sparse regression, and dynamical systems to identify nonlinear differential equations purely from measurement data.
From the Paper:
Discovering governing equations from data by sparse identification of nonlinear dynamical systems.
PNAS 113(15):3932—3937, 2016.
Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz  
Code available at: http://faculty.washington.edu/sbrunto...
For more details, see our papers: https://scholar.google.com/citations?...
http://www.pnas.org/content/113/15/3932
http://arxiv.org/abs/1509.03580
2 31:31 Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control
3 4:38 Koopman Observable Subspaces & Nonlinearization
4 10:18 Koopman Operator Optimal Control
5 30:35 Compressed Sensing and Dynamic Mode Decomposition
6 47:07 Hankel Alternative View of Koopman (HAVOK) Analysis [FULL]
7 22:41 Hankel Alternative View of Koopman (HAVOK) Analysis [SHORT]
8 9:39 Magnetic field reversal and Measles outbreaks: HAVOK models of chaos
9 5:27 Linear model for chaotic Lorenz system [HAVOK]