Uploaded November 2022 | Updated September 2026, 2 weeks ago
We have seen that the error of numerical differentiation typically scales with the time step dt. So why can't we just reduce the time step arbitrarily small to control the error? This video describes how numbers are stored in a computer and how small roundoff errors are amplified by very small dt's, giving a lower limit to how small we can make our time steps.
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 Numerical roundoff error: How numbers are stored in a computer
8:40 Two sources of error: Roundoff and Taylor series
We have seen that the error of numerical differentiation typically scales with the time step dt. So why can't we just reduce the time step arbitrarily small to control the error? This video describes how numbers are stored in a computer and how small roundoff errors are amplified by very small dt's, giving a lower limit to how small we can make our time steps.
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 Numerical roundoff error: How numbers are stored in a computer
8:40 Two sources of error: Roundoff and Taylor series
![Fourier Neural Operator (FNO) [Physics Informed Machine Learning]](https://i.ytimg.com/vi/W8PybqAk6Ik/mqdefault.jpg "Fourier Neural Operator (FNO) [Physics Informed Machine Learning]
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:54 Operators as Images, Fourier as Convolution
04:43 Zero-Shot Super Resolution
07:33 Generalizing Neural Operators
09:47 Conditions and Operator Kernels
10:53 Mesh Invariance
12:31 Why Neural Operators // Or Neural operators vs other methods
13:47 Result: Greens Function
15:14 Laplace Neural Operators
17:14 Outro")
