Dynamical Systems by Steve L. Brunton

source: Steve Brunton        2016年4月23日

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?...
31:31 Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control
4:38 Koopman Observable Subspaces & Nonlinearization
10:18 Koopman Operator Optimal Control
30:35 Compressed Sensing and Dynamic Mode Decomposition
47:07 Hankel Alternative View of Koopman (HAVOK) Analysis [FULL]
22:41 Hankel Alternative View of Koopman (HAVOK) Analysis [SHORT]
9:39 Magnetic field reversal and Measles outbreaks: HAVOK models of chaos
5:27 Linear model for chaotic Lorenz system [HAVOK]

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