Uploaded October 2022 | Updated September 2026, 2 weeks ago
This video investigates a 2-dimensional linear system of ordinary differential equations with a positive and a negative real eigenvalue. These solutions are known as unstable saddle points. Saddle points are extremely useful for energy-efficient transport, including for bipedal walking and locomotion, for fight jets, and also for interplanetary transport. We investigate the solutions using eigenvalues and eigenvectors, as well as with phase portrait pictures.
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 of saddle points
4:52 Drawing a saddle in phase space
10:52 Saddle example: Human walking
14:42 Saddle example: Particle in a potential well
17:24 Saddle example: Planetary transport in the solar system
This video investigates a 2-dimensional linear system of ordinary differential equations with a positive and a negative real eigenvalue. These solutions are known as unstable saddle points. Saddle points are extremely useful for energy-efficient transport, including for bipedal walking and locomotion, for fight jets, and also for interplanetary transport. We investigate the solutions using eigenvalues and eigenvectors, as well as with phase portrait pictures.
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 of saddle points
4:52 Drawing a saddle in phase space
10:52 Saddle example: Human walking
14:42 Saddle example: Particle in a potential well
17:24 Saddle example: Planetary transport in the solar system
![AI/ML+Physics Part 3: Designing an Architecture [Physics Informed Machine Learning]](https://i.ytimg.com/vi/fiX8c-4K0-Q/mqdefault.jpg "AI/ML+Physics Part 3: Designing an Architecture [Physics Informed Machine Learning]
This video discusses the third stage of the machine learning process: (3) choosing an architecture with which to represent the model. This is one of the most exciting stages, including all of the new architectures, such as UNets, ResNets, SINDy, PINNs, Operator networks, and many more. There are opportunities to incorporate physics into this stage of the process, such as incorporating known symmetries through custom equivariant layers.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:03 The Architecture Zoo/Architectures Overview
06:29 What is Physics?
12:38 Case Study: Pendulum
17:10 Defining a Function Space
20:51 Case Studies: Physics Informed Architectures
23:36 ResNets
24:26 UNets
25:15 Physics Informed Neural Networks
26:50 Lagrangian Neural Networks
27:24 Deep Operator Networks
27:49 Fourier Neural Operators
28:23 Graph Neural Networks
30:02 Invariance and Equivariance
35:59 Outro")
![AI/ML+Physics Part 2: Curating Training Data [Physics Informed Machine Learning]](https://i.ytimg.com/vi/g-S0m2zcKUg/mqdefault.jpg "AI/ML+Physics Part 2: Curating Training Data [Physics Informed Machine Learning]
This video discusses the second stage of the machine learning process: (2) collecting and curating training data to inform the model. There are opportunities to incorporate physics into this stage of the process, such as data augmentation to incorporate known symmetries.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
03:02 Augmenting Data with Physics
04:16 Coordinates Matter!
06:38 Simulated vs Experimental Data
10:42 Big Data vs Diverse Data
12:48 Generalizing Models with Physics
16:31 Data is Expensive
17:42 Data is Biased
18:58 Rare Events
21:24 Small Signals
24:13 Galileo Dropped the Ball
27:10 Hidden Variables
29:22 Preview: Discovering Governing Equations
30:42 The Digital Twin
35:09 Outro")
