SINDy-PI: A robust algorithm for parallel implicit sparse identification of nonlinear dynamics

In this video, Kadierdan Kaheman describes SINDy-PI: A robust algorithm for parallel implicit sparse identification of nonlinear dynamics. The SINDy-PI overcomes the difficulties of using SINDy to identify the rational system or implicit dynamics and made it possible to directly extract the physical laws from data.
Paper:
royalsocietypublishing.org/do...
By: Kadierdan Kaheman, J. Nathan Kutz, and Steven L. Brunton
Code:
github.com/dynamicslab/SINDy-PI
Packages that implements SINDy-PI:
PySINDy:
github.com/dynamicslab/pysindy
DataDrivenDiffEq.jl:
datadriven.sciml.ai/stable/
This video was produced at the University of Washington

[@guneyisktombak6280]

This channel is one of the greatest I have ever watched on KZbin on Machine Learning. Thanks a lot for your passion and outstanding work.

[@CAME18471]

Amazing, as usual for something produced by this research group, congrats!

[@omegasigma4500]

You should make a video on "how to make such great videos". :-) A "Behind the scenes" video would be awesome. Really curious how to make create such great videos.

[@jasonbramburger]

Go Kadierdan! This is so great!

[@salemon289]

Really excited to see this video! I was the guy in B012 that day, I didn't realize that was your group until I talked with Kadierdan lol

[@jacinthphilemongudetti6491]

Thank you guys so much for the videos! But I am having some trouble with calculating damped sinusoidal functions. There is an exponential compenent (e^-x) within the test function and I was wondering how can I make SINDy look out for such exponential functions? I've been using the fourier method with the stlsq optimizer as seen in the "PySINDy: A Python Library for Model Discovery" video but all I get is a sinusoidal wave "line" that connects the starting coordinates with the last coordinate in the data set. Is there a way to specify more terms in the libary? Seems like the fourier method does not work in this case

[@tonvanbommel2521]

Cool alogirthm! Is it also possible to remove the derivatives overall from the sparse regression problem and only introduce it at the reconstruction step?

[@herrkunde6941]

Suppose i had some time series data from a MIMO system. With this method i would permute both sides with the control variables (u1,u2,...) and it would identify the underlying system while agnostic to the external influences?

[@raphaelteixeira8430]

I am very curious to know how to produce these videos with the dark background and latex presentation in transparency. The result is a wonderful aesthetic to present the content. Can anyone help with any tips?

[@muhammadbilalshahid8010]

Amazing!!

[@Gkvhkbt]

Great channel! Can SINDy algorithm can do sparce classification too?

[@Eigensteve]

It is pretty closely related to a method called "sparse representation" and there is a variant of "sparse representation for classification" that is useful. This SR literature is older than SINDy and really interesting. We talk about it in the book, and I think I have a video on it too.

[@Gkvhkbt]

@@Eigensteve Hi! I tried sparce representation for clasification before and it did not work out very well. I nearly need to had perfect data and perfect images to make it work. Did not workout with regular data taken by my camera. So I have an other idea. 1. Collect a set of images from a class X. Assume you taking 100 pictures of a dog. 2. Use RPCA to remove all the noise. 3. Use linear discriminant analisys(LDA) so make an average image of those 100 dog images. LDA is a much better tool to create an average image, than just sum the images and divide with 100. 4. Use pooling to scale down the average image to 32x32. Average pooling or max/min pooling is a free choice. 5 Use SINDy algorithm b = Ax, where b is the class ID vector {0,1,2,3,4...,N} set by the user and A contains the row data of every image. Assume that the first class is on top and it has the class ID 0. Second row in A is another average image and it has the class ID 1 and so on. The goal is as always, find x from b = Ax. 6. When x is found, then the function-model can be built up Class_ID = function(image). In this case, it will work like a 1-layer Neural network. But thanks to SINDy, we can use different kind of candidate functions so it can act like a really non-linear NN. The goal is to minimize computational time by just creating a model with SINDy, rather than use Sparce Representation for Classification, wich takes to much time for real time computer vision.

[@mauroclaudino6720]

Can SINDy-PI be used to discover nonlinear implicit ODE's of the form x_dot = f(x, t, x_dot) where x=x(t)? The Michaelis-Menten example available in PySINDy has the form x_dot = f(x, x_dot) but, apparently, SINDy-PI does not seem to contemplate cases where a temporal term (t or a function of t) is also present in the second member of the implicit ODE.

[@rosshoyt2030]

Very cool! Volume is very quiet on this one by the way

[@Eigensteve]

Thanks, and we will try to increase volume for future videos.

[@dimitrischreiber9140]

Does PySINDY support SINDY-PI?

[@Eigensteve]

I believe it does

[@SiddharthGuptaams]

@@Eigensteve sir I am trying with PySINDy to reconstruct double pendulum equation but trignometric functions like sin and cos are missing ,I think those functionality is not available in PySINDy library ...pls correct me if I am wrong.

[@user-gl2fg6rb9v]

@@SiddharthGuptaamshi ,i am trying reconstruct double pendulum equation in matlab by sindy,,If you've done it, can we talk about it?