Sparse Nonlinear Dynamics Models with SINDy, Part 2: Training Data & Disambiguating Models

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This video discusses data requirements for the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm. Specifically, we discuss the required sampling rate and duration for clean data and how to compute SINDy for noisy data. The integral SINDy extension is described, which enables the discovery of a hierarchy of fluid and plasma models that are more or less complex than the standard Navier-Stokes and MHD models. Finally, we discuss the condition number of the SINDy regression and how this may be improved to better disambiguate between multiple consistent models.

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This video was produced at the University of Washington

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0:00 Introduction & Recap
3:27 Data Sampling Rate and Duration
5:34 Total Variation Regularized Derivative
7:08 Integral SINDy and Applications
12:05 Condition Number and Disambiguating Multiple Consistent Models

Steve Brunton

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And we got all of this education for free, What a time to be alive.

pradiptahafid

It is one of the best videos I have seen. Awesome job, I hope our profs had such skills in describing difficult concepts in such understandable

keb

Nice Lecture Steve. Regarding my personal experience with SINDy, data normalization may also be critical. I suggest you comment this point in a future lecture.

americocunhajr

great job! wish i did my PhD w you 20 years ago :) and with current capacities.

samirelzein

I liked that explanation of why the integral is there at 8:30 or so

alegian

thnx very mach for ur clearly Explanation

nourhamsho

Hi, i'm a physics student, your videos are really awesome, hope to see the next

maximilianobernal

The integral trick seems kind of reminiscent of the approach in finite element analysis. It's been a minute, but I think the upshot was that it lets you relax the assumption of differentiability, so you could have, for instance, a rod whose stiffness or conductivity or whatnot changes discontinuously. I'm wondering if you could do something similar here by having, say, a step function in your library of candidate functions, even though it doesn't really have a derivative in the normal sense.

Virsconte

Thank you. Please do you think I can use Sindy for modelling a building for a temperature and humidity control with MPC?

swk

Great work.. do collecting more initial condition mean that it is nonlocal?

mamadoupathely

And how to solve slow frequency measurements? There are works in this front?

vitorbortolin

So if this sparse identification works on a temporal domain, will there be other sparse identification algorithms work on e.g. geometry domain like shape morphing, or design parameters domain e.g. with different boundary conditions?

iheavense

If we want to design a control algorithm for a complex dynamic system which is not easy to give it's pde，we can use SINDy to learn it directly from data，then everything will be simple，just use tool we learned in Automatic Control System to design the control system。it is so cool！I really want to go back school again and do research for it if I have chance！ Science is so cool and business is so boring。

AyunAyun-my

When the data is noisy, sampling for longer may give a good prediction of the model

herb.

Hi Prof! I have a doubt what if we only have x measurement data, is it possible that SINDy can still identify the correct dynamics in some way?
I have checked through the normal procedure it isn't working also I have read about the HAVOK method. Can we apply this method in PySINDy?

prajjwal

Is the integral SINDy supported in PySINDy?

nathanaelgray

Has anyone used SINDy to construct SGS models? There is limited number of independent tensors when constructing SGS models, and there have been lots of debates which ones to choose. SINDy might just make a closure on that debate.

have_a_nice_day

how do you write like that? I want to learn how to make videos like that.

domasberulis

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