this is the area I'm interested in! I'm only a freshman in college, so I was looking everywhere for experts who is doing research in this field. RUclips algorithm really works out for me this time
Nice video, showing complex mathematics, in a friendly way. Personally, I think the most important skills to have is an understanding of the dynamical system, building an intuition and then forecasting behaviour. Automating it is an extra bonus in my opinion, which will help reduce the time between understanding the dynamics and forecasting results. But the hard skill here, is building the intuition for dynamical systems. Great work, cheers.
The hodgkin huxley approximation is huge for neuromorphic computing. linear approximations mean closed form solutions are applicable, reducing the number of calculations needed during spiking neural network inference. if you'd like to know more, please get in touch with me.
This is soo cool, I would love to see how this compares to more conventional RL methods on MDPs or POMDPs, or PINN approaches (maybe this can also be thought of as a PINN?), especially it would be interesting to compare the network sizes of various methods. I would be interested to help integrate this within Nvidia Isaac sim for virtual world models. I briefly played with and encountered Koopman analysis when I did a project with wavelet feature representations and I've also thought about this potential.
I thought finite dimension Koopman operators cannot express multistability. I'm surprised that the duffing and magnetic pendulum cases somehow work. Are they truly multistable (asymptotically) and also robust to small perturbations in the state?
Great video! I’ll be checking out your paper in detail later today. I had a quick glance at it and I have a few questions and a suggestion. I’m curious: around 13:09, was the change of coordinates that your method learned for the Hodgkin-Huxley model a time varying change of coordinates? Also, did the change of coordinates depend on the initial condition? Last, to the best of my (weak) understanding, the Hodgkin-Huxley model has inputs. If I’m right, how did you handle those? Also, typically, the condition for “asymptotic” (as opposed to “Lyapunov”) stability is that “\dot{V}(x) < 0” (as opposed to “\dot{V}(x) \leq 0”). If you are getting away with a negative semi-definite Lyapunov rate by using a LaSalle’s invariance principle based argument, you should state that in the video and in your paper. FYI, I’m using definitions as they are given in Khalil’s textbook. If my critiques are coming from a difference of terminology, please disregard. Also, I love the figures! Very compelling!
Thank you! The Hodgkin Huxley model we considered does not have inputs, this is the standard model with four states and is given in the paper. The change of coordinates is simply a function of the states. The resultant system in the new coordinates is a linear time-invariant system. This is a good catch but simply a typo! All of the models learned in the paper have Re(\lambda) < 0 and thus \dot{V}
Thanks for your interests! The code is hosted on our project website: generalroboticslab.com/AutomatedGlobalAnalysis as well as GitHub: github.com/generalroboticslab/AutomatedGlobalAnalysis. We can access both of them. Can you try again?
this is the area I'm interested in! I'm only a freshman in college, so I was looking everywhere for experts who is doing research in this field. RUclips algorithm really works out for me this time
DAMN MAN YOU ARE UNDERATED.
You deserve at least a 100k subs.
You got 1 more from me!
Do remember us when you get big!
I don't have to understand all of it, to understand the beauty of it.
Nice video, showing complex mathematics, in a friendly way. Personally, I think the most important skills to have is an understanding of the dynamical system, building an intuition and then forecasting behaviour. Automating it is an extra bonus in my opinion, which will help reduce the time between understanding the dynamics and forecasting results. But the hard skill here, is building the intuition for dynamical systems.
Great work, cheers.
Great video!
The hodgkin huxley approximation is huge for neuromorphic computing. linear approximations mean closed form solutions are applicable, reducing the number of calculations needed during spiking neural network inference. if you'd like to know more, please get in touch with me.
id like to know more
This is soo cool, I would love to see how this compares to more conventional RL methods on MDPs or POMDPs, or PINN approaches (maybe this can also be thought of as a PINN?), especially it would be interesting to compare the network sizes of various methods. I would be interested to help integrate this within Nvidia Isaac sim for virtual world models. I briefly played with and encountered Koopman analysis when I did a project with wavelet feature representations and I've also thought about this potential.
Man I guess even us mathematicians are not safe from AIs automating our job 😂
I thought finite dimension Koopman operators cannot express multistability. I'm surprised that the duffing and magnetic pendulum cases somehow work. Are they truly multistable (asymptotically) and also robust to small perturbations in the state?
Beautiful presentation, by the way.
When AI discovers this, and uses it to predict human reactions, it will play us perfectly
Great video! I’ll be checking out your paper in detail later today. I had a quick glance at it and I have a few questions and a suggestion.
I’m curious: around 13:09, was the change of coordinates that your method learned for the Hodgkin-Huxley model a time varying change of coordinates? Also, did the change of coordinates depend on the initial condition? Last, to the best of my (weak) understanding, the Hodgkin-Huxley model has inputs. If I’m right, how did you handle those?
Also, typically, the condition for “asymptotic” (as opposed to “Lyapunov”) stability is that “\dot{V}(x) < 0” (as opposed to “\dot{V}(x) \leq 0”). If you are getting away with a negative semi-definite Lyapunov rate by using a LaSalle’s invariance principle based argument, you should state that in the video and in your paper. FYI, I’m using definitions as they are given in Khalil’s textbook. If my critiques are coming from a difference of terminology, please disregard.
Also, I love the figures! Very compelling!
Thank you! The Hodgkin Huxley model we considered does not have inputs, this is the standard model with four states and is given in the paper. The change of coordinates is simply a function of the states. The resultant system in the new coordinates is a linear time-invariant system.
This is a good catch but simply a typo! All of the models learned in the paper have Re(\lambda) < 0 and thus \dot{V}
@ Wonderful! Thank you very much.
Can you please fix the SSL on your website so that we could take a look at the code?
Thanks for your interests! The code is hosted on our project website: generalroboticslab.com/AutomatedGlobalAnalysis as well as GitHub: github.com/generalroboticslab/AutomatedGlobalAnalysis. We can access both of them. Can you try again?
@@boyuan_chen Works now, thank you!
Would this be applicable to the Einstein field equations by any chance?
0:24 fingerprints pattern...
Can't access the project website! Please fix
This works for us with a test just now. Could you try again or with a different browser or device?
@@boyuan_chen can't from my end, browser throws SSL_ERROR_UNRECOGNIZED_NAME_ALERT
@@boyuan_chen something to do with SSL certification
@@boyuan_chen it still doesn't work! "Secure connection failed", maybe try outside of your university network?
dx/dt = f(t) = f(x)