This is wonderful. It does not matter yet that the solution is a perfect match ; what matters is that we're opening the black box of chaotic behaviour and starting to understand its main "gears"
If chaos can be cast as an intermittently forced linear system, does this method have a chance to transform computationally generated chaos (turing) into linear representation?
Great video. I'm not so familiar with chaos theory, but what can be the advantage of discovering the f function, apart from solving equations? For example, can you be able to describe the behaviour of signal y with a differential function that can highlight ascending, decreasing, stationary trend of the input signal? Or maybe z(t) can answer the question?
Great work, truly inspiring results as well. I'm curious if learning the latent variable distributions will result in better performance, as in some kind of Variational Auto Encoder. Of course it would require a change of the loss functions, and make everything difficult again. But with a dynamic system like the Lorenz system there are regions where a point is more likely to end up. And regions where the direction are highly uncertain. It makes sense to me to want to allow explicit modeling of these attributes. The output of this model gives the scaling parameters to 3 functions of the form (z1 + z2 + z3)^2, so i would expect that you can find the distributions they belong to as if they are random variables. Or even add a single parameter to add linear noise/uncertainty to each variable to approximate a similar effect.
Thanks for sharing your wonderful work! But I don't understand why that neuron network is diffeomorphic since the dimensionalities of delay coordinates and full state coordinates are different. If I am not mistaken, a diffeomorphism must be established between two spaces of the same dimension. (referring to 8:10)
Good question! The diffeomorphism is between the attractor (or curve) in the delay coordinates and the attractor in the original (high dimensional) coordinates. The map between the attractors can be one-to-one even if the dimensions of their corresponding coordinate systems are different.
Hi, I really enjoy these videos, especially the embedding theory and time-delay coordinates. Correct me if I'm wrong, but is the necessary condition for discovering the "true state dynamics" that the system has to be fully observable from the data I measure? If it is not then I can only discover the dynamics which are observable, right?
Very interesting work! It’s exciting to see these ideas used to get such precise results. People in my area work with very large systems and use ideas like Takens’ and autoencoders to get low dimensional representations of these systems. It’s nice to see how powerful they are when the equations of motion are low dimensional enough to be practically discoverable.
@@Eigensteve Thank you, Dr. Brunton, you and your colleagues' work are truly inspiring, and have made a great contribution to the 'AI for Science' community :)
I feel a bit concerned by the idea that EEG's are a Data Source for the AI. How long before my thoughts and IDEAS are no longer "private" and personal ?
Great video! Why do these works always study chaotic things? Could you try to capture or give examples of learning simple dynamics like a pendulum or more interesting, the behavior of school of fish or bird flock? Could this improve upon the social force work to describe human behavior in a crowd?
It is because the most research questions revolve around "newer" and more complicated topics. Chaotic system dynamics is the crossroads for many approaches and opinions on the proper way to model physics. The problem lies in the absurdity of a deterministic equation that is continuous differentiable and bounded with arbitrary outputs to the smallest of deviations on the input. It brought many to question a lot about how we model the world, and trying to find a better method is why so many fields spend so much time on it. That said, i agree that other systems that are less "classic theoretical" can be more interesting.
can we somehow turn this into code where we can execute with python libraries numpy + panda and perhaps with some variable to play around to get intuition
yes, there are some conditions to considere but the theoretical (maths) behindf neural networks allows to determine that having some boundaries of depht and width. Hornik, Kurt (1991). "Approximation capabilities of multilayer feedforward networks". Neural Networks. 4 (2): 251-257. doi:10.1016/0893-6080(91)90009-T
This. Mathematicians, even the best communicators among them (which is evident this group is among the best), still fail to bring their research back to Earth because they spend too much effort making it as general as possible. I'm an experimental fluid dynamicist and I still can't grasp most of what is being said here. It's really a pity how the incentive structure works. Even this very video, if you think about it, is a contribution out of their goodwill. They don't need to do this, nor they are rewarded to do it. They just do it in an effort to communicate, but it is still not quite enough. I mean, whatever this presentation was - I'm sure it's interesting research. But the effort required to communicate it effectively is just not worth their time. Truly a pity.
@@thecolorblindphotographer2511 thanks for the comment, i often want to test stuff that i see cool like this because knowing that each research actually contains answers to problems that we have faced or going to face .
@@azizutkuozdemir There are a lot in the research field, and many students studying dynamical systems that would enjoy this brief overview. His channel seems to have overviews of more advanced topics, which is very fascinating.
This is wonderful. It does not matter yet that the solution is a perfect match ; what matters is that we're opening the black box of chaotic behaviour and starting to understand its main "gears"
I don't know much dynamics or chaos theory, but as a rookie theoretical ML guy, I found this presentation extremely clear and interesting !
Awesome !!!
Merci beaucoup pour la mise en ligne gratuite !
Fantastic job! Well done
Awesome work Joseph-and beautiful video!
What if the measurement is reliable up to a gaussian (i.e. is a probability disturubution)?
If chaos can be cast as an intermittently forced linear system, does this method have a chance to transform computationally generated chaos (turing) into linear representation?
You don't have to just do svd using HAVOK
Beautiful work!!
Beautiful! Love it.
بسيار زيبا
Nice job 👍
.
Great video. I'm not so familiar with chaos theory, but what can be the advantage of discovering the f function, apart from solving equations? For example, can you be able to describe the behaviour of signal y with a differential function that can highlight ascending, decreasing, stationary trend of the input signal? Or maybe z(t) can answer the question?
Great work, truly inspiring results as well. I'm curious if learning the latent variable distributions will result in better performance, as in some kind of Variational Auto Encoder. Of course it would require a change of the loss functions, and make everything difficult again. But with a dynamic system like the Lorenz system there are regions where a point is more likely to end up. And regions where the direction are highly uncertain.
It makes sense to me to want to allow explicit modeling of these attributes. The output of this model gives the scaling parameters to 3 functions of the form (z1 + z2 + z3)^2, so i would expect that you can find the distributions they belong to as if they are random variables. Or even add a single parameter to add linear noise/uncertainty to each variable to approximate a similar effect.
Yes can use in Social Robotic and analysis with equilibria analysis
Amazing class!
Thanks for sharing your wonderful work! But I don't understand why that neuron network is diffeomorphic since the dimensionalities of delay coordinates and full state coordinates are different. If I am not mistaken, a diffeomorphism must be established between two spaces of the same dimension. (referring to 8:10)
Good question! The diffeomorphism is between the attractor (or curve) in the delay coordinates and the attractor in the original (high dimensional) coordinates. The map between the attractors can be one-to-one even if the dimensions of their corresponding coordinate systems are different.
Just beautiful
Hi, I really enjoy these videos, especially the embedding theory and time-delay coordinates. Correct me if I'm wrong, but is the necessary condition for discovering the "true state dynamics" that the system has to be fully observable from the data I measure? If it is not then I can only discover the dynamics which are observable, right?
Very interesting work! It’s exciting to see these ideas used to get such precise results. People in my area work with very large systems and use ideas like Takens’ and autoencoders to get low dimensional representations of these systems. It’s nice to see how powerful they are when the equations of motion are low dimensional enough to be practically discoverable.
Is your code available?
All code should be available on github, link in the arxiv paper in the description.
@@Eigensteve Hi again, Dr Brunton. Thank you!
@@Eigensteve I'm afraid I cannot find such link in the arxiv paper
@@Aikman94 Shoot, I think you are right. Here is the link: github.com/josephbakarji/deep-delay-autoencoder
@@Eigensteve Thank you, Dr. Brunton, you and your colleagues' work are truly inspiring, and have made a great contribution to the 'AI for Science' community :)
soo good
referring to 7:44 , have you decided using diffeomorphic transformation based from someelse thesis ?
I feel a bit concerned by the idea that EEG's are a Data Source for the AI. How long before my thoughts and IDEAS are no longer "private" and personal ?
Great video! Why do these works always study chaotic things? Could you try to capture or give examples of learning simple dynamics like a pendulum or more interesting, the behavior of school of fish or bird flock? Could this improve upon the social force work to describe human behavior in a crowd?
It is because the most research questions revolve around "newer" and more complicated topics. Chaotic system dynamics is the crossroads for many approaches and opinions on the proper way to model physics. The problem lies in the absurdity of a deterministic equation that is continuous differentiable and bounded with arbitrary outputs to the smallest of deviations on the input. It brought many to question a lot about how we model the world, and trying to find a better method is why so many fields spend so much time on it.
That said, i agree that other systems that are less "classic theoretical" can be more interesting.
nice!
I'll just take your word for it ; but really , chaos is such a misnomer ! "Read the paper" Sounds like the old "left as an exercise for the student"
I don't understand the details, but the end results and implications are amazing! Good luck discovering law's of physics
is there example piece of code that similates time delay embedding ?
banger
AI helps us understand chaos helps us understand AI helps us understand chaos helps us...
….have to be happy with what you have to be happy with what you have….
Pretty cool stuff ... But don't understand the mathematics 😅 😢
can we somehow turn this into code where we can execute with python libraries numpy + panda and perhaps with some variable to play around to get intuition
Yes! That's a brilliant idea
The code will be available on github soon :)
@@JosephBakarji fantasticc
@@JosephBakarji eagerly waiting for that doc : )
nice example at the end , but quite puzzling :D
Have neural networks used to estimate the result of any equations ?
yes, there are some conditions to considere but the theoretical (maths) behindf neural networks allows to determine that having some boundaries of depht and width.
Hornik, Kurt (1991). "Approximation capabilities of multilayer feedforward networks". Neural Networks. 4 (2): 251-257. doi:10.1016/0893-6080(91)90009-T
Do it to the bible 💫
so can we decode the brain now ?
from sec 1 : he reminds me steve jobs :D
can you give example what does turning into dictionary mean ?
why did you apply diffeomorphism ?
please give human understandable example on
measurements
time-delay
before moving further .... do you want to show off or make public learn ?
This. Mathematicians, even the best communicators among them (which is evident this group is among the best), still fail to bring their research back to Earth because they spend too much effort making it as general as possible. I'm an experimental fluid dynamicist and I still can't grasp most of what is being said here. It's really a pity how the incentive structure works. Even this very video, if you think about it, is a contribution out of their goodwill. They don't need to do this, nor they are rewarded to do it. They just do it in an effort to communicate, but it is still not quite enough.
I mean, whatever this presentation was - I'm sure it's interesting research. But the effort required to communicate it effectively is just not worth their time. Truly a pity.
@@thecolorblindphotographer2511 thanks for the comment, i often want to test stuff that i see cool like this because knowing that each research actually contains answers to problems that we have faced or going to face .
It is human understandable. The video is targeted at an adept dynamical systems audience.
@@evileyes155 how many people are that target audience ?
@@azizutkuozdemir There are a lot in the research field, and many students studying dynamical systems that would enjoy this brief overview. His channel seems to have overviews of more advanced topics, which is very fascinating.
dont try to explain somthing that u dont understant. tnx