Steven Brunton
@eigensteve
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Teaches math to engineers: Professor @UW researching #MachineLearning for #Dynamics and #Control , especially for #FluidDynamics .
Joined April 2016
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FREE PDF for 2ND EDITION OF OUR BOOK!!!
We are committed to open science and open education:
Free book:
Free code ()
Free lectures ()
2nd ed of "Data Driven Science and Engineering" out this summer!!!!
New to 2nd ed:
* Python+Matlab Code
* New Chapters on Reinforcement Learning & Physics Informed Machine Learning
* New Sections Throughout
* Extensive Homework
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Just finished filming an entire 8 week series on Differential Equations and Dynamical Systems!!
This is one of my favorite topics in all of math. And this finishes up all the videos for a two-quarter, 60 hour set of lectures on Engineering Mathematics!
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Excited to drop a new 2-week video series:
Crash Course in Complex Analysis!!!
This is a super useful topic that comes up everywhere in mathematical physics, differential equations, and modern scientific computing. Check it out!
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My favorite topic in dynamical systems: Chaos!!!
This is what got me interested in applied math as an undergrad. The three body problem in planetary dynamics, the double pendulum, turbulence, and more!
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New video! Partial Differential Equation (PDE) Overview
Super excited to be deriving and solving PDEs in this series!!! Next up: heat equation in 1D, 2D, ND; separation of variables; wave equation; Navier-Stokes equations, and more!!!
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Vector calculus & PDEs!
Powerful & beautiful intersection of math and physics. How to encode physical conservation laws as partial differential equations.
And still relevant for modern machine learning!
(~20 vid series... how I wish I'd learned it)
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Big news today: Nathan Kutz and I have finished all of the video lectures for our book "Data Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control"!
All videos for every section are free on youtube and at our book website
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Its nice to see the recent excitement around Q-learning!
Here's a clip from a video all about Deep Reinforcement Learning, including Deep Q Learning
#machinelearning
#ai
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First new video after being back from Sabbatical!!
PDE 101: Separation of Variables... or how I learned to stop worrying and solve Laplace's equation
One of the most important concepts in all of partial differential equations
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Numerical Integration to Simulate Nonlinear Dynamics! The final phase of our series on Differential Equations
Topics
#Chaos
Forward/backward Euler
Stability & accuracy
Runge-Kutta
Symplectic & variational integrators
Uncertainty propagation
Code examples
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New on arXiv!!! 🚨🚨🔥🔥🤯🤯
A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning
by Sam Otto, with N. Zolman, N. Kutz, & myself
A tour de force in machine learning & differential geometry
(w/ beautiful drawings by Sam)
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I'm excited to announce the first video in a new series on sparsity and compression. This is one of my favorite topics in applied math and statistics.
Check out the video on YouTube:
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New video series: Physics Informed Machine Learning!
Physics may be embedded into AI/ML in 5 stages:
1 choose what to Model
2 curate training Data
3 design an Architecture
4 craft a Loss Function, and
5 implement Optimization Algorithm to train the model
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Finished the 2nd Edition of "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" with Nathan Kutz today for Cambridge.
Now w Python + MATLAB, extensive HW, and YouTube videos for all sections! (Code in Julia and R soon)
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2nd ed of "Data Driven Science and Engineering" out this summer!!!!
New to 2nd ed:
* Python+Matlab Code
* New Chapters on Reinforcement Learning & Physics Informed Machine Learning
* New Sections Throughout
* Extensive Homework
Big news today: Nathan Kutz and I have finished all of the video lectures for our book "Data Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control"!
All videos for every section are free on youtube and at our book website
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New Video!! 🌊🌊🌊
Lagrangian Coherent Structures (LCS) in unsteady fluids with Finite Time Lyapunov Exponents (FTLE)
YouTube link:
This topic is near and dear to my heart. My first research project in grad school focused on FTLE.
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Model Based Reinforcement Learning: Policy Iteration, Value Iteration, and Dynamic Programming
(Second video in the series!)
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New video!
Reinforcement Learning: Machine Learning Meets Control Theory
Reinforcement learning is a powerful technique at the intersection of machine learning and control theory, inspired by how animals learn to interact with their environment.
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Engineering Math, Halloween Edition:
No One Can Hear You Scream in Phase Space!!!
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Reinforcement Learning Series: Overview of Methods
Video:
This video introduces the variety of methods for model-based and model-free reinforcement learning.
New video out each Friday over next 4 weeks!
Book Chapter:
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I've been looking forward to Gauss's Divergence Theorem for a long time!
Gauss's theorem is one of the most powerful tools in all of mathematical physics. It's how we derive conservation laws from physics and translate them into PDEs.
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New video! Robust Principal Component Analysis (RPCA)
PCA is a backbone of statistics & machine learning but is fragile to outliers & missing data.
RPCA addresses this issue & is used in many fields including the Netflix prize, image science, & fluids.
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4th Video in Reinforcement Learning Sequence!
Overview of Deep Reinforcement Learning Methods
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Major step in series on ODEs: Solving matrix systems of equations with eigenvalues and eigenvectors!
Eigenvectors make the most sense to me as the transformation to diagonalize a matrix system xdot=A*x.
Just finished filming an entire 8 week series on Differential Equations and Dynamical Systems!!
This is one of my favorite topics in all of math. And this finishes up all the videos for a two-quarter, 60 hour set of lectures on Engineering Mathematics!
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Very excited about an upcoming series of videos on Turbulent Fluid Dynamics and Turbulence Modeling (with machine learning).
Thought I'd share some upcoming YouTube thumbnails:
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Div Grad & Curl: Building blocks of vector calculus
When I learned there was no motivation for why.
Just math on a board.
You are learning so you can translate physics, the language of the universe, into math, the language of differential equations.
Vector calculus & PDEs!
Powerful & beautiful intersection of math and physics. How to encode physical conservation laws as partial differential equations.
And still relevant for modern machine learning!
(~20 vid series... how I wish I'd learned it)
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New video on Machine Learning for Fluid Mechanics!
This is one of my favorite topics and the APS fluid dynamics meeting is coming up. So I will be posting new fluids videos + tweets for the next two weeks!
Living Van Gogh Starry Night by Petros Vrellis
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Deep Reinforcement Learning!!!
Video link on youtube:
#MachineLearning
#ReinforcementLearning
#DeepLearning
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New video: The Anatomy of a Dynamical System
This was a fun one to make, and timing with new NSF AI Institute in Dynamic Systems is a pure coincidence!
Full Video:
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By popular demand, a new video:
Deep Learning of Coordinates and Dynamics
(with beautiful visualization by Malin Christersson)
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I can’t tell you how excited I am that
@bingbrunton
is making Neuroscience videos!
If you like my YouTube channel, you will love hers!!
Subscribe to her channel for new videos!
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New video on the Sparse Identification of Nonlinear Dynamics (SINDy), 5 years later
Machine learning is enabling the discovery of dynamical systems models and governing equations purely from measurement data.
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3rd Video in Reinforcement Learning Sequence!
Q-Learning: Model Free Reinforcement Learning and Temporal Difference Learning
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The Gradient Operator!
I filmed this at 7pm the day before I moved across the country to California for sabbatical... that's how much I love gradients & I love teaching you about gradients.
Div Grad & Curl: Building blocks of vector calculus
When I learned there was no motivation for why.
Just math on a board.
You are learning so you can translate physics, the language of the universe, into math, the language of differential equations.
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This video shows how to use the singular value decomposition (SVD) to perform least-squares regression for non-square systems of equations.
Video:
Full SVD Playlist:
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Brand new lecture on The Wave Equation... One of the most important equations in all of physics!
Walked my guitar a few miles to campus (up hill, both ways) to save you from the indignity of my air guitar...
#Mathematics
#Physics
#YouTube
#music
#guitar
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5th Video in Reinforcement Learning Sequence!
Optimal Nonlinear Control with Hamilton Jacobi Bellman (HJB) and Dynamic Programming
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Very excited to share a new video diving into the mathematics of compressed sensing.
I'm always surprised that it's possible to reconstruct full images from a random subsampling of pixels.
More videos on this topic each Friday.
YouTube video:
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Control volumes with fission and fusion and lasers, oh my!
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New video!!
Part 1 of deriving the Reynolds Averaged Navier Stokes (RANS) equations for fluid turbulence...
(I had a little extra coffee in this edited version)
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This is one of my favorite videos in the sparsity series: Sparse Regression with the LASSO
We use LASSO all the time to discover interpretable models that prevent overfitting (like SINDy)
Check out the YouTube video!
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New in 2nd Ed:
Chapters: Reinforcement Learning & Physics Informed Machine Learning
Sections: Autoencoders; RNNs; GANs; MPC; ML for ROMs; Laplace; SVD error bounds
Code in Python and Matlab in text
HW throughout
Videos for all sections
Finished the 2nd Edition of "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" with Nathan Kutz today for Cambridge.
Now w Python + MATLAB, extensive HW, and YouTube videos for all sections! (Code in Julia and R soon)
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Ever notice a striking similarity between the Laplace and Fourier transforms?
In this video, I show how the Laplace transform is really just a weighted, one-sided Fourier transform (I call it a political transform) for badly behaved functions.
1/2
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It has been about 5 years since the sparse identification of nonlinear dynamics (SINDy) paper was published, so I decided to make a short video on SINDy 5 years later.
Turned into (at least) 6 videos covering over 2 hours :)
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Announcing Collimator 2.0!!!
New features:
* Powered by JAX
* Generative AI
* AutoDifferentiation
* PID AutoTune
* SINDy blocks
* Model Predictive Control
* Real-Time Collaboration
* Hardware in the Loop
Kudos to the amazing team
@CollimatorAI
Try it @
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New video!!! What is Turbulence?
We live in turbulent times... and turbulent fluids.
Here, we discuss fundamental characteristics of turbulence with examples from nature and engineering.
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I'm really looking forward to releasing new videos over the next few weeks:
Robust principal component analysis (RPCA)
Sparse sensor placement optimization
The anatomy of a dynamical system
Moore's law
Reinforcement learning
Deep reinforcement learning
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Second video on sparsity and compression. We ask the question of why natural signals are so compressible.
Audio signals, images, streaming videos. All these signals are massively massively compressible.
This one is a mind bender!
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Still surprised that this works!
...Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders...
Check out the video:
and paper:
by Joseph Bakarji et al.
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This video is like eating your kale or going to the gym 🥬🥬🥬🏋️🏋️🏋️... it is going to make you stronger!
One of the most complicated math derivations yet, and this is only the first x-component of the RANS (Reynolds Averaged Navier Stokes) equations!
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Someone posed a really interesting question to me recently:
"Can you tell the number of matches in a box by the sound it makes when you shake it?"
Reminds me of "Can One Hear the Shape of a Drum?" by Mark Kac
Curious to hear your thoughts and comments...
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New video on the Shannon-Nyquist sampling theorem!
This is a cornerstone of signal processing theory, with important connections to signal compression and sparse sampling.
YouTube:
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Excited to partner with
@cassyniapp
to generate citable DOIs for my videos!!!
Example: if you want to cite my video on Reinforcement Learning
DOI
Youtube
Check out the complete collection
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Very excited to announce a new review paper on "Modern Koopman Theory for Dynamical Systems"
which was a great collaboration with Marko Budišić (
@dynamicalmarko
), Eurika Kaiser, and Nathan Kutz.
Check it out here:
1/n
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Sparse Nonlinear Models for Fluid Dynamics w Machine Learning & Optimization
This summarizes some of my favorite collaborative work with some amazing researchers, including
@loiseau_jc
and
@georgios_rigas
(papers below)
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Is this youtube cover for this Friday's video clickbaity or not if I actually do talk about death stars and mushroom clouds?
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Just got copies of the 2nd Edition of "Data Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" from
@CambridgeUP
!!!
I love that "new book" smell :)
Officially available on Amazon now:
2nd ed of "Data Driven Science and Engineering" out this summer!!!!
New to 2nd ed:
* Python+Matlab Code
* New Chapters on Reinforcement Learning & Physics Informed Machine Learning
* New Sections Throughout
* Extensive Homework
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Excited about this upcoming seminar "Machine Learning for Scientific Discovery, with Examples in Fluid Mechanics" at Fluid Mechanics Webinar Series on 04 Nov
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Check out these excellent tutorial videos by Alan Kaptanoglu describing how to use the newest PySINDy software library! Eight videos to become an expert in data-driven model discovery with SINDy!!
Video:
PySINDy library:
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Everybody needs to check this out!! One of the most thoughtful and comprehensive tools to apply machine learning for scientific discovery. Really a tour de force
Three years ago, I started working on an easy-to-use tool for interpretable machine learning in science. I wanted it to do for symbolic regression what Theano did for deep learning.
Today, I am beyond excited to share with you the paper describing it!
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We were so fortunate to have
@MilesCranmer
at UW for a collaborative visit this past week!
He also filmed up his awesome work on "Interpretable Deep Learning for New Physics Discovery"
Really blown away by this great video!
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Draft of new "Reinforcement Learning" chapter for 2nd Ed of our Data-Driven Science and Engineering Book
Please comment/DM/email with any typos, comments, or suggestions. We have a few weeks to polish.
Thanks in advance!!!
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30 minute overview video on turbulence closure modeling, including Reynolds averaged Navier-Stokes (RANS) and large eddy simulation (LES).
This is all building up to how we use machine learning and deep learning to model turbulent fluids (next video!)
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I've been thinking a lot about how managing COVID-19 is really a control problem. So I made a short video series about control theory and COVID-19. Spread it around (the video, not the virus!):
#COVID19
#controltheory
#dynamics
#modeling
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New lecture on: Robust Regression with the L1 Norm
Check it out on YouTube:
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@PhTaheri
I love teaching and research.
Teaching improves my research and research enriches my teaching. They also provide useful counterbalances to each other.
Not a formula for everyone, and very glad we have excellent teaching profs and research profs, but I don’t want to choose one.
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This was a super fun video to make. I walk through my favorite turbulence simulations and experiments. (also motivates use of machine learning) Hope you enjoy!!
YouTube:
Stunning turbulence simulation in video from
@ricardovinuesa
@pschlatt1
@SimEx_KTH
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Faculty position in Physics-Based Machine Learning/Artificial Intelligence (
@ME_at_UW
)
This is a very broad search and is part of a larger cluster hire in
@uwengineering
. Lots of great colleagues and resources in this exciting area!
Come join us
@UW
!!!
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Eigenfoxes!
Wildlife photographer Roeselien Raimond photographed 64 foxes from the same angle to allow for easy comparisons, and the result reveals the wildly diverse characteristics of such animals [source, read more: ]
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I'm a big fan of
@AnnualReviews
. They provide an overview and context for important research topics.
There is no AR in Machine Learning & AI
This could really benefit ML researchers and outside users, since progress is so rapid and could use codification.
What do y'all think?
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The art of "what is possible" in AI and Machine Learning is changing so fast!!! ⚡️⚡️⚡️
I made this video in April, and it is already dated... need to make monthly updates! 🤣
Next video up: A Machine Learning Primer
Stay tuned!
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Occasionally I get some pretty strange youtube comments.
Once someone told me that instead of a forehead, I have a fivehead.
Didn't bother me or anything, but I think about it *every* time I put on 25% more sunscreen...
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Excited to be on my way to the
#ACC
in San Diego!! Honored to be giving one of the kickoff semi-plenary lectures tomorrow AM: “Machine Learning for Sparse Nonlinear Modeling and Control”
Also excited that
@CollimatorAI
will have a booth where I’ll be hanging out. Come say hi!!!
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Super excited about this paper!
So much of the history of mathematical physics involves discovering effective coordinate transformation to simplify dynamics. Now with deep learning, we are able to learn these transformations from data!
Our new paper uses deep learning to find coordinates to globally transform a nonlinear PDE to a linear PDE! Read about choosing a good architecture & diverse training data. Cautionary tale about extrapolation. W/ Craig Gin,
@eigensteve
, and Nathan Kutz.
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I challenged myself to build an extremum seeking controller (ESC) in
@CollimatorAI
in 2 minutes!
What will you build?
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If you like my youtube channel, you will love Nathan Kutz's channel and videos!! Subscribe now!
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Huge thanks to Andy Freeberg (
@Freebeazy
)
@ME_at_UW
and Dennis Wise for the great story and photos about my math YouTube channel!
With over four million views and 90,000 subscribers,
@eigensteve
's YouTube channel simplifies the mathematical fundamentals behind data-driven engineering concepts. We talked to Professor Brunton to learn the backstory:
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Come be our colleague
@ME_at_UW
in
@uwengineering
on the beautiful
@UW
Seattle campus!!!
Several open faculty positions including
Assistant Professor physics-based Machine Learning/Artificial Intelligence
Apply now!
(Apps reviewed starting early Jan'24)
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Here is a free PDF of our Annual Review of Fluid Mechanics article on Machine Learning for Fluid Mechanics:
New video on Machine Learning for Fluid Mechanics!
This is one of my favorite topics and the APS fluid dynamics meeting is coming up. So I will be posting new fluids videos + tweets for the next two weeks!
Living Van Gogh Starry Night by Petros Vrellis
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So excited to be on sabbatical this year
@Caltech
with
@bingbrunton
!
Huge thanks to everyone at Caltech and the Moore Distinguished Scholar Program!
PS: We are living two doors down from a house we lived in half a lifetime ago. It is so nice to be back 😎🤓
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Haha I didn’t know I was a hand model now!! 🤓😜👋
(Important to note that I don’t agree w the fear mongering here, just here for the dope hand gestures)
Top AI researchers and CEOs warn against ‘risk of extinction’ in 22-word statement
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I don't think this has ever happened to me before... arXiv submission worked on the first try!
96 pages, 27 figures, >350 references... this is definitely a LaTeX high water mark
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🤯🤯🤯Blown away by how fast
@CollimatorAI
has integrated generative AI using GPT-4 into their modeling framework.
Now possible to design and analyze control systems symbolically from text prompts!
Check out Collimator and control smarter! 🧠🧠🧠
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Heading to the filming studio today to start a new lecture series… need to get into the zone on my walk to work…
Bringing out the big guns…
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The Koopman and Perron Frobenius operators in dynamical systems form an important example of such an adjoint pair.
Pullback of functions and pushforward of measures are dual one with each other.
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Full GPT integration in
@CollimatorAI
2.0!!!
Use GPT as a co-pilot to design controllers, create and analyze block diagrams, derive equations of motion, and much more!
Try it out at
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This project is a good example of making everything open source: code, data, videos, CAD files, even latex… eventually the experiment will be remotely accessible on the cloud.
Sharing is caring
Here's the first of what will be a suite of papers on the double pendulum from Kaheman,
@eigensteve
, Kutz, and I. First up, how to build your own!
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Excited to have
@laurezanna
kick off our Physics Informed Machine Learning seminar for the winter quarter!!!
New Time: 12pm PST
Friday, February 4, 2022
Data-driven turbulence closures for ocean and climate models: advances and challenges
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Check out this excellent video by Ariana Mendible!!
We all love the SVD/PCA/POD for dimension reduction, but it fails for traveling waves where separation of variables doesn't hold.
Ariana shows how to fix this for systems with traveling waves.
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This is a good one!
Let’s celebrate Gauss’ bday by showing that the squared Gaussian integral is equal to π.
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Neat time lapse lecture from the lightboard photoshoot!
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Excited to share this great paper by JL Callaham
Learning dominant physical processes with data-driven balance models
Idea: cluster data in "equation space" to find regions with simplified physics
Open Access
@NatComm
:
w/ JV Koch,
@bingbrunton
& JN Kutz
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I love the FFT. So I made a video series on Fourier Analysis. Check it out.
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Fear and loathing in Hamburg
A hotel in Germany uses 3D carpets to prevent guests from running in the Passage.
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Excited that Rose Yu
@yukirose
will be our 1st seminar speaker of the quarter!!!
Title: Incorporating Symmetry for Learning Spatiotemporal Dynamics
Friday Nov 5: 9-10am PT
UW Data-Driven Methods for Science & Engineering Seminar
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Super excited about this upcoming podcast!
⚡ Q&A with Steven Brunton ⚡ –
@eigensteve
I will interview him in around one month on
#MachineLearning
&
#FluidMechanics
. Send us your questions! :)
Steve:
Myself:
#engineeredmind
#turbulence
#cfd
#computervision
#fluidflow
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