Matrix decompositions | Time series
Dynamic mode decomposition (DMD) is a dimensionality reduction algorithm developed by Peter Schmid in 2008.Given a time series of data, DMD computes a set of modes each of which is associated with a fixed oscillation frequency and decay/growth rate. For linear systems in particular, these modes and frequencies are analogous to the normal modes of the system, but more generally, they are approximations of the modes and eigenvalues of the composition operator (also called the Koopman operator). Due to the intrinsic temporal behaviors associated with each mode, DMD differs from dimensionality reduction methods such as principal component analysis, which computes orthogonal modes that lack predetermined temporal behaviors. Because its modes are not orthogonal, DMD-based representations can be less parsimonious than those generated by PCA. However, they can also be more physically meaningful because each mode is associated with a damped (or driven) sinusoidal behavior in time. (Wikipedia).
Dynamic Mode Decomposition (Overview)
In this video, we introduce the dynamic mode decomposition (DMD), a recent technique to extract spatio-temporal coherent structures directly from high-dimensional data. DMD has been widely applied to systems in fluid dynamics, disease modeling, finance, neuroscience, plasma physics, robot
From playlist Data-Driven Dynamical Systems with Machine Learning
Dynamic Mode Decomposition (Examples)
In this video, we continue to explore the dynamic mode decomposition (DMD). In particular, we look at recent methodological extensions and application areas in fluid dynamics, disease modeling, neuroscience, and multiscale physics. http://dmdbook.com/ https://www.eigensteve.com/
From playlist Data-Driven Dynamical Systems with Machine Learning
Dynamic Mode Decomposition (Code)
In this video, we code up the dynamic mode decomposition (DMD) in Matlab and use it to analyze the fluid flow past a circular cylinder at low Reynolds number. Code and data available at: http://dmdbook.com/ https://www.eigensteve.com/
From playlist Data-Driven Dynamical Systems with Machine Learning
System Identification: Dynamic Mode Decomposition with Control
This lecture provides an overview of dynamic mode decomposition with control (DMDc) for full-state system identification. DMDc is a least-squares regression technique based on the singular value decomposition (SVD). Dynamic mode decomposition with control J. L. Proctor, S. L. Brunton, an
From playlist Data-Driven Control with Machine Learning
Compressed Sensing and Dynamic Mode Decomposition
This video illustrates how to leverage compressed sensing to compute the dynamic mode decomposition (DMD) from under-sampled or compressed data. From the Paper: Compressed Sensing and Dynamic Mode Decomposition. JCD 2(2):165—191, 2015. Steven L. Brunton, Joshua L. Proctor, Jonathan H.
From playlist Research Abstracts from Brunton Lab
How to integrate by partial fractions
Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook How to integrate by the method of partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is a fraction such that the numerator
From playlist A second course in university calculus.
The Spectral Proper Orthogonal Decomposition
I made this video in an attempt to popularize the Spectral POD technique. It is an incredibly powerful analysis tool for understanding the data coming from a multitude of sensors. It elevates the Fourier Transform to a whole new level; hence I call it "The Mother of All Fourier Transforms"
From playlist Summer of Math Exposition 2 videos
How to Set Up the Partial Fraction Decomposition
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to Set Up the Partial Fraction Decomposition. Just setting them up. See my other videos for actual solved problems.
From playlist Partial Fraction Decomposition
Singular Value Decomposition (SVD): Mathematical Overview
This video presents a mathematical overview of the singular value decomposition (SVD). These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz Amazon: https://www.amazon.com/Data-Driven-Science-En
From playlist Data-Driven Science and Engineering
Steve Brunton: "Dynamical Systems (Part 2/2)"
Watch part 1/2 here: https://youtu.be/2VBN_dJZLWc Machine Learning for Physics and the Physics of Learning Tutorials 2019 "Dynamical Systems (Part 2/2)" Steve Brunton, University of Washington Institute for Pure and Applied Mathematics, UCLA September 6, 2019 For more information: http
From playlist Machine Learning for Physics and the Physics of Learning 2019
Kernel Learning for Robust Dynamic Mode Decomposition
In this video abstract, I present our new data-driven method for learning high-dimensional, nonlinear dynamical systems via kernel methods. This work is in collaboration with Profs Benjamin Herrmann, Beverley McKeon and Steve Brunton. The paper is available on arXiv: Title: Kernel Learni
From playlist Research Abstracts from Brunton Lab
Dynamic Eigen Decomposition I: Parameter Variation in System Dynamics
Video 1 in a series about dynamic eigen decomposition (DED) theory and applications. Here we cover basic theoretical aspects of the DED as applied to a 2 degree of freedom mechanical oscillator with parameter variation. The surprising fact we uncover is that dynamic eigenvectors are preser
From playlist Summer of Math Exposition Youtube Videos
DDPS | Koopman Operator Theory for Dynamical Systems, Control and Data Analytics by Igor Mezic
Description: There is long history of use of mathematical decompositions to describe complex phenomena using simpler ingredients. One example is the decomposition of string vibrations into its primary, secondary, and higher modes. Recently, a spectral decomposition relying on Koopman opera
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Physics-Informed Dynamic Mode Decomposition (PI-DMD)
In this video, Peter Baddoo from MIT (www.baddoo.co.uk) explains how physical laws can be integrated into the dynamic mode decomposition. Title: Physics-informed dynamic mode decomposition (piDMD) Authors: Peter J. Baddoo, Benjamin Herrmann, Beverley J. McKeon, J. Nathan Kutz, and Steven
From playlist Research Abstracts from Brunton Lab
(New Version Available) Partial Fraction Decomposition - Part 1 of 2
New Version Available: https://youtu.be/c2oLHtPA03U This video explain how to perform partial fraction decomposition with linear factors. http://mathispower4u.yolasite.com/
From playlist Integration Using Partial Fraction Decomposition