Hello I have question, I hope that you can help, is the NN trained this way only capable of predicting on the collocations points for which it was trained using the physics based loss function?
azad amitoz No. you incorporate the interior point and bc loss while training with collocation points. Then you use the model to predict the interior points. So it should work for any PDE
This video is really useful. All explanations are so clear. Thank you. BTW, would you mind giving a short video about the inverse problems using this method? Thank you.
Thinking about it before the solution is told. The way u solve this is by calculating an aproximation for the derivatives pluging that to the pde the absolute value of what should be zero is the error
Dear Sir, Can you help me understand how to use this algorithm for second-order ODEs? I understood the theoretical content in this video very well but I am at a loss on understanding how to specify the cost function in the program. If the second-order ODE 𝑑2 𝑥𝑚 (𝑡)/𝑑𝑡2 = −2*𝑘𝑚*𝑏𝑚*𝑑𝑥𝑚 (𝑡)/𝑑𝑡 − 𝑘𝑚2𝑥𝑚 (𝑡)+ 𝐺𝑚*𝑘𝑚 (𝑝𝑚 +C*𝑆 (𝑥𝑛 (𝑡))) is in this way and how can we specify this in a cost function? Can you kindly provide an example code to understand better? I am learning how to solve ODEs through neural networks. Thank you very much for providing us wonderful content.
there are few problem in taking cost function 1. boundary conditions are not eniterly meet unlike FEM. 2. if we take some multiplier to increase satisfaction of boundary condition we compromise on differential equation
you cant do it for different inputs. once training is done i.e. loss has sufficiently reduced, you can predict the "u" with the same "X" which u gave during training.. that predicted u will be satisfying the equation for given X alone
Yes, it would allow us to solve these problems much more efficiently as we iteratively get to know the nature of the output due to more and more experimental data.The challenge is that u should have prior legitimate belief of your input and output.Your belief should not be arbitrary. Apart from this,as we already know that neural nets are universal approximaters ,they can learn anything arbitrarily close in theory as long as we have sufficient computational resources.So,yes u may see them in your software packages in future.
@@BVSrinivasan i did a research project on this and i found that, when using pre trained pinn models to solve pdes it is actually quicker than numerical solvers, and it becomes noticeably quicker when you want to solve over more and more domain points - is this in line with your results?
I have a doubt. How can backpropagating twice results into second order derivative? I have been trying to derive myself from scratch but feeling like i am missing something in between.
Very great video. Thank you very much Sir. Could you direct me to the list with the full videos of this course. Tried to look for it under NPTEL-NOC IITM channel, but just way too many courses and videos, do not know where the other videos are located.
Hey, quite frankly extremely interesting video, except you don't put the papers you cite in the description. Neither do you let us see the code you're talking about. I'd be very interested to take a look at these.
Great professor...well explained.. Dear Sir, I have a question..can we solve any Nonlinear Partial Differential using this technique?? Also please let me which software is better for NN MATLAB or Python??
i have a question, when i run the code in github, it always have some errors, i want to ask which tensorflow version is foe the code in github,How to configure a virtual environment？Thank you！
@@sumanthnethi6834 Hello, i have a question when i ran the code, i can obtained the loss, but i cannot obtain the figure from the code, do you know why? thankyou!
each equation will be a contribution in loss function. So keep adding the contributions in loss functions. So will have residual for each equation in loss function
Jungang Chen you get a lot higher speed that’s what motivated this topic. The tasks that used to take 1-2 hours can now be done in 1-2 secs that’s why a lot of research is going into this to make it more accirate
![Neural ODEs (NODEs) [Physics Informed Machine Learning]](http://i.ytimg.com/vi/nJphsM4obOk/mqdefault.jpg)
Great video. Amazing content available for free by NPTEL by one of the finest teachers.
Really great video explaining the concept behind PINNs!
Finally found the best explanation for PINN. Thank you for making it simple which helped me to understand the concept.
I rarely comment on youtube videos but, I gotta say, this is really good and very well explained content!
Warning: High quality content!
😂😂👌
I've been working in CFD for quite some time and I must tell you that this is a game changer !! amazing stuff
Hello I have question, I hope that you can help, is the NN trained this way only capable of predicting on the collocations points for which it was trained using the physics based loss function?
azad amitoz No. you incorporate the interior point and bc loss while training with collocation points. Then you use the model to predict the interior points. So it should work for any PDE
@@morzariadeep Ok so it works for all the interior point after training ! Thankx for clarifying
Absolutely amazing, I'm watching it so smoothly as if I'm watchin a movie
Highly conceptual...... Dont move around, this is Master of others.
Excellent video. Did a good job of explaining the essence of the paper and topic in general
Thank you!
This explanation was extremely clear and useful! Thank you sir!
Thank you!
What a great professor.
Thank you Sir for explaining such a difficult topic deligently
This video is really useful. All explanations are so clear. Thank you. BTW, would you mind giving a short video about the inverse problems using this method? Thank you.
Thanks.We will prepare a video for it and upload it.
At least! A great video.
Great video Thank You for this
Thank you for such a great video!
I love this lecture
Amazing content! thanks.
very well explained but unfortunately the big missing here is the access to a concrete example code and allow to the audience to play with it
Nice explanation. Thanks.
Clear & concise!
Where could I find the other lectures?
Great explanation
Thinking about it before the solution is told.
The way u solve this is by calculating an aproximation for the derivatives pluging that to the pde the absolute value of what should be zero is the error
nice mmm very good video
Dear Sir, Can you help me understand how to use this algorithm for second-order ODEs? I understood the theoretical content in this video very well but I am at a loss on understanding how to specify the cost function in the program. If the second-order ODE 𝑑2
𝑥𝑚 (𝑡)/𝑑𝑡2 = −2*𝑘𝑚*𝑏𝑚*𝑑𝑥𝑚 (𝑡)/𝑑𝑡 − 𝑘𝑚2𝑥𝑚 (𝑡)+ 𝐺𝑚*𝑘𝑚 (𝑝𝑚 +C*𝑆 (𝑥𝑛 (𝑡))) is in this way and how can we specify this in a cost function? Can you kindly provide an example code to understand better? I am learning how to solve ODEs through neural networks. Thank you very much for providing us wonderful content.
The cost function is just the ODE or Residual in the code.
there are few problem in taking cost function 1. boundary conditions are not eniterly meet unlike FEM. 2. if we take some multiplier to increase satisfaction of boundary condition we compromise on differential equation
What exactly is in the 'data' folder (in Github code)? Does it have just the collation points along with initial and boundary conditions?
glad I chanced on this video...
I must say, it's great video..... I have a question, after training it, how can we predict the results for different inputs??
you cant do it for different inputs. once training is done i.e. loss has sufficiently reduced, you can predict the "u" with the same "X" which u gave during training.. that predicted u will be satisfying the equation for given X alone
@@ramkumars2329 Are you sure of this? Can you point this fact from the paper? as per my understanding it should work on the other x values.
@@rteja764 It will work for every x value. This is basically NN as a regression fit so it works like any regression fit.
Amazing video! I have one question, the results from the NN, what is compare to in the loss function in order to calculate the difference?
Thanks for the fantastically clear explanation. I have a question, does this novel idea allow for more efficient solving than current solvers??
Yes, it would allow us to solve these problems much more efficiently as we iteratively get to know the nature of the output due to more and more experimental data.The challenge is that u should have prior legitimate belief of your input and output.Your belief should not be arbitrary. Apart from this,as we already know that neural nets are universal approximaters ,they can learn anything arbitrarily close in theory as long as we have sufficient computational resources.So,yes u may see them in your software packages in future.
It depends on the problem but, typically, no. We are attempting to do that in our lab. As are other groups around the world :-)
@@BVSrinivasan i did a research project on this and i found that, when using pre trained pinn models to solve pdes it is actually quicker than numerical solvers, and it becomes noticeably quicker when you want to solve over more and more domain points - is this in line with your results?
@@joshuamills7633 Yes. Also, the accuracy will level off as you add more domain points in PINNs unlike conventional methods.
great video. thanks.
I have a doubt. How can backpropagating twice results into second order derivative? I have been trying to derive myself from scratch but feeling like i am missing something in between.
Very great video. Thank you very much Sir. Could you direct me to the list with the full videos of this course. Tried to look for it under NPTEL-NOC IITM channel, but just way too many courses and videos, do not know where the other videos are located.
Actually I just found the full playlist of this course here ruclips.net/video/_M-nDb0MIa4/видео.html
@@mingx009 tHANKS
Sir, would you like to think about making a redio which to show how to write and run the code?
Here's the code: ruclips.net/video/0gyv5wTKU04/видео.html
Hey, quite frankly extremely interesting video, except you don't put the papers you cite in the description. Neither do you let us see the code you're talking about. I'd be very interested to take a look at these.
Thank you for your great lecture. Can you please provide the complete playlist of the course?
ruclips.net/p/PLyqSpQzTE6M-SISTunGRBRiZk7opYBf_K
Just be vary of the week 5 lectures.. which aren't in correct order..
Just look out for the lecture number!
@@ACC861 thank you
can you garuantee that the neural network will not be breaking conservation equations(which would be trivial for analytical methods).
HI, Thanks you for your presentatio. It was excelent. I have a question, Have you changed your code at new Ternsorflow version?? Thanks again
Could you tell me in which version of Tensorflow does this code actually run?
@@krishnachaitanyavaddepally2539 it uses tensorflow 1.x
@@shelzz1 I have a version in PyTorch: ruclips.net/video/0gyv5wTKU04/видео.html
What is the name of this course ?
hi sir, the surname Laganis does not exist. I think you mean Gabriele Lagani. Could you confirm? Are there any lecture notes?
can this be applied to solve system of ode? by summing each residue of the ode system?
Can you help me about solving Integral equation with use Neural network???
Great professor...well explained..
Dear Sir, I have a question..can we solve any Nonlinear Partial Differential using this technique??
Also please let me which software is better for NN MATLAB or Python??
python is best, it will be easy for you to link your problem easily with the existing codes.
Not only nonlinear as well as linear of any type.
Thank u sir
For nonlinear problem u need more deep network
@@dbelor3764 Thank you Belor..
This lecture is part of some playlist or course ?
Yes
Grea!
Sir, can you please give a full step by step solution via this method
We will put in some demo videos with a step by step solution later. In the meantime, please see the reference papers for this.
Hi, anyone knows or has a code for python in a simple example using this? .
i have a question, when i run the code in github, it always have some errors, i want to ask which tensorflow version is foe the code in github,How to configure a virtual environment？Thank you！
The code worked for me using tensorflow version 1.14
@@sumanthnethi6834 Hello, i have a question when i ran the code, i can obtained the loss, but i cannot obtain the figure from the code, do you know why? thankyou!
How can we apply the same concept with a system of ODEs?
each equation will be a contribution in loss function. So keep adding the contributions in loss functions. So will have residual for each equation in loss function
what is the name of course
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Any Pros of using NN to solve PDEs?
High Dimensional PDEs are computationally expensive to solve using FEM/FDMs using NNs can speed up the process.
@@amanpreetsingh3009 However NNs are not robust as FEM/FDMs
Jungang Chen you get a lot higher speed that’s what motivated this topic. The tasks that used to take 1-2 hours can now be done in 1-2 secs that’s why a lot of research is going into this to make it more accirate
@@amanpreetsingh3009 for 1d it's working but I am not able to do for 2d or 3d
Can anyone explain to me how the "data" is obtained to model this NN?
I solved this one using PyTorch. In case anyone is interested, here is the link: ruclips.net/video/0gyv5wTKU04/видео.html