Uploaded October 2022 | Updated September 2026, 2 weeks ago
This video *derives* the eigenvalues and eigenvectors of a matrix "A" to solve the matrix system of equations dx/dt = A*x.
Playlist: youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Overview
1:26 Problem Setup
2:33 The Simplest System of ODEs: Decoupled (Diagonal) Dynamics
10:25 Finding a Coordinate System Where Dynamics Look Diagonal
15:42 Deriving the Eigenvalue/Eigenvector Equation
19:03 A Picture of the Eigenvalue Equation
22:27 Recap and Summary
This video *derives* the eigenvalues and eigenvectors of a matrix "A" to solve the matrix system of equations dx/dt = A*x.
Playlist: youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Overview
1:26 Problem Setup
2:33 The Simplest System of ODEs: Decoupled (Diagonal) Dynamics
10:25 Finding a Coordinate System Where Dynamics Look Diagonal
15:42 Deriving the Eigenvalue/Eigenvector Equation
19:03 A Picture of the Eigenvalue Equation
22:27 Recap and Summary
![AI/ML+Physics Part 5: Employing an Optimization Algorithm [Physics Informed Machine Learning]](https://i.ytimg.com/vi/T4iJ10TAIMg/mqdefault.jpg "AI/ML+Physics Part 5: Employing an Optimization Algorithm [Physics Informed Machine Learning]
This video discusses the fifth stage of the machine learning process: (5) selecting and implementing an optimization algorithm to train the model. There are opportunities to incorporate physics into this stage of the process, such as using constrained optimization to force a model onto a susbpace or submanifold characterized by a symmetry or other physical constraint.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:45 Case Study: KKT Constrained Least Squares
06:18 Case Study: Physics Informed DMD
14:00 Loss vs Optimization of Subspace Constraints
17:50 Subspace Constraints and Symmetry
19:28 Case Study: Symbolic Regression and Evolutionary Optimization
22:25 Parsimony and Sparse Optimization Algorithms
25:03 Case Study: SINDy and SR3
28:38 Parsimony and Sparsity Hyperparameters
30:55 Outro")
