Uploaded October 2022 | Updated September 2026, 2 weeks ago
This video describes how to write a high-order linear differential equation as a matrix system of first-order differential equations. This is a major step towards solving general ODEs using eigenvalues and eigenvectors, leveraging the full power of linear algebra.
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
1:54 Introduce New Variables
7:11 Writing as Matrix System of Equations
12:12 Summary and Takeaways
14:51 Eigenvalues of Matrix System are Roots of the Characteristic Polynomial
17:40 Example 3x3 Matrix System of ODEs
This video describes how to write a high-order linear differential equation as a matrix system of first-order differential equations. This is a major step towards solving general ODEs using eigenvalues and eigenvectors, leveraging the full power of linear algebra.
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
1:54 Introduce New Variables
7:11 Writing as Matrix System of Equations
12:12 Summary and Takeaways
14:51 Eigenvalues of Matrix System are Roots of the Characteristic Polynomial
17:40 Example 3x3 Matrix System of ODEs
![[6/8] Control for Societal-Scale Challenges: Road Map 2030 [Education]](https://i.ytimg.com/vi/VuAFZPwygyE/mqdefault.jpg "[6/8] Control for Societal-Scale Challenges: Road Map 2030 [Education]
This video explores the importance of education in realizing the ambitious goals of this road map document. This follows Chapter 6 of the Control for Societal-Scale Challenges: Road Map 2030 document.
https://www.ieeecss.org/control-societal-scale-challenges-road-map-2030
The production of this video was supported by the IFAC.
Roadmap Abstract: The world faces some of its greatest challenges of modern time and how we address them will have a dramatic impact on the life for generations to come. Simultaneously, control systems, consisting of information enriched by various degrees of analytics followed by decision-making, are pervading a variety of sectors, not only in engineering but beyond, into financial services, socio-economic analysis, entertainment and sports, and political and social sciences. Increased levels of automation are sought after in various sectors and being introduced into new domains. All of these advances and transformations urge a shift in the conversation toward how control systems can meet grand societal- scale challenges. The document seeks to chart a roadmap for the evolution of control systems, identifying several areas where our discipline can have an impact over the next decade.
Edited by: Anuradha M. Annaswamy, Karl H. Johansson, and George J. Pappas
Authors: Andrew Alleyne, Frank Allgöwer, Aaron D. Ames, Saurabh Amin, James Anderson, Anuradha M. Annaswamy, Panos J. Antsaklis, Neda Bagheri, Hamsa Balakrishnan, Bassam Bamieh, John Baras, Margret Bauer, Alexandre Bayen, Paul Bogdan, Steven L. Brunton, Francesco Bullo, Etienne Burdet, Joel Burdick, Laurent Burlion, Carlos Canudas de Wit, Ming Cao, Christos G. Cassandras, Aranya Chakrabortty, Giacomo Como, Marie Csete, Fabrizio Dabbene, Munther Dahleh, Amritam Das, Eyal Dassau, Claudio De Persis, Mario di Bernardo, Stefano Di Cairano, Dimos V. Dimarogonas, Florian Dörfler, John C. Doyle, Francis J. Doyle III, Anca Dragan, Magnus Egerstedt, Johan Eker, Sarah Fay, Dimitar Filev, Angela Fontan, Elisa Franco, Masayuki Fujita, Mario Garcia-Sanz, Dennice Gayme, Wilhelmus P.M.H. Heemels, João P. Hespanha, Sandra Hirche, Anette Hosoi, Jonathan P. How, Gabriela Hug, Marija Ilić, Hideaki Ishii, Ali Jadbabaie, Matin Jafarian, Samuel Qing-Shan Jia, Tor Arne Johansen, Karl H. Johansson, Dalton Jones, Mustafa Khammash, Pramod Khargonekar, Mykel J. Kochenderfer, Andreas Krause, Anthony Kuh, Dana Kulić, Françoise Lamnabhi-Lagarrigue, Naomi E. Leonard, Frederick Leve, Na Li, Steven Low, John Lygeros, Iven Mareels, Sonia Martinez, Nikolai Matni, Tommaso Menara, Katja Mombaur, Kevin Moore, Richard Murray, Toru Namerikawa, Angelia Nedich, Sandeep Neema, Mariana Netto, Timothy O’Leary, Marcia K. O’Malley, Lucy Y. Pao, Antonis Papachristodoulou, George J. Pappas, Philip E. Paré, Thomas Parisini, Fabio Pasqualetti, Marco Pavone, Akshay Rajhans, Gireeja Ranade, Anders Rantzer, Lillian Ratliff, J. Anthony Rossiter, Dorsa Sadigh, Tariq Samad, Henrik Sandberg, Sri Sarma, Luca Schenato, Jacquelien Scherpen, Angela Schoellig, Rodolphe Sepulchre, Jeff Shamma, Robert Shorten, Bruno Sinopoli, Koushil Sreenath, Jakob Stoustrup, Jing Sun, Paulo Tabuada, Emma Tegling, Dawn Tilbury, Claire J. Tomlin, Jana Tumova, Kevin Wise, Dan Work, Junaid Zafar, Melanie Zeilinger
This video was produced at the University of Washington")
![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")
