Uploaded December 2022 | Updated September 2026, 2 weeks ago
In this video, we explore the error of the Forward Euler integration scheme, using the Taylor series. We show that the error at each time step scales with dt^3, where dt is the time-step of the integrator. This basic error analysis technique, based on the Taylor series, 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 %%%
In this video, we explore the error of the Forward Euler integration scheme, using the Taylor series. We show that the error at each time step scales with dt^3, where dt is the time-step of the integrator. This basic error analysis technique, based on the Taylor series, 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 %%%
![Neural ODEs (NODEs) [Physics Informed Machine Learning]](https://i.ytimg.com/vi/nJphsM4obOk/mqdefault.jpg "Neural ODEs (NODEs) [Physics Informed Machine Learning]
This video describes Neural ODEs, a powerful machine learning approach to learn ODEs from data.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
02:09 Background: ResNet
05:05 From ResNet to ODE
07:59 ODE Essential Insight/ Why ODE outperforms ResNet
// 09:05 ODE Essential Insight Rephrase 1
// 09:54 ODE Essential Insight Rephrase 2
11:11 ODE Performance vs ResNet Performance
12:52 ODE extension: HNNs
14:03 ODE extension: LNNs
14:45 ODE algorithm overview/ ODEs and Adjoint Calculation
22:24 Outro")
