Uploaded December 2022 | Updated September 2026, 2 weeks ago
In this video, we explore the stability of the Forward Euler and Backward/Implicit Euler integration schemes. In particular, we investigate the eigenvalues of these discrete-time update equations, relating the eigenvalues to the stability of the algorithm. This basic stability analysis technique, based on the eigenvalues of the update equation, applies to much more powerful integrators.
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 and goals of stability analysis
2:56 Stability of continuous dynamics
6:57 Stability of discrete time dynamics
9:17 Eigenvalues in the complex plane
14:34 Stability of Euler integration for scalar dynamics
26:42 Stability of Euler integration for matrix systems
In this video, we explore the stability of the Forward Euler and Backward/Implicit Euler integration schemes. In particular, we investigate the eigenvalues of these discrete-time update equations, relating the eigenvalues to the stability of the algorithm. This basic stability analysis technique, based on the eigenvalues of the update equation, applies to much more powerful integrators.
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 and goals of stability analysis
2:56 Stability of continuous dynamics
6:57 Stability of discrete time dynamics
9:17 Eigenvalues in the complex plane
14:34 Stability of Euler integration for scalar dynamics
26:42 Stability of Euler integration for matrix systems
![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")
