Teaching Neural Network to Solve Navier-Stokes Equations

In this video, I demonstrate the process of building a physics informed neural network to predict the behavior of vortex shedding using the Navier-Stokes equations. Below you can find the link to the github repository:

Resources:

Background information:

Thanks for watching, don't forget to leave a like and subscribe for more video on machine learning and fluid dynamics!

[kiaranr]

I'm fascinated by the prospect of using ML for physics problems. Subscribed and looking forward to following your journey.

[malekalkoja]

I have no idea what is this but I watched the whole vid

[georgekarniadakis]

Thanks for highlighting our paper on Vortex Induced Vibrations (VIV). We are now building a digital and physical twin at MIT for this problem. You can use adaptive activation functions to avoid BAD minima!

[fabioasaro]

Lol, the book you scrolled through after the paper is the book which my advisor wrote. It's called: "The Finite Volume Method in Computational Fluid Dynamics: An advanced introduction with openFOAM and Matlab"

[mfinixone]

Solving physics problems with ML, NOW THAT'S WHAT I AM TALKING ABOUT!!!!
Subscribed

[timgoppelsroeder]

This is an awesome use of SL. Makes me want to try a similiar project with PINNs. Great job dude 😄

[முரளி-ழத]

Great content! Keep the good work. Background music is bit distracting, try light music just a suggestion.

[sitrakaforler]

Never had the courage to do it but YES ! I think that it's nearly certain that with a general IA we will find a generalized solution for Navier Stokes Eq :p

CONGRATS !

[thatyougoon]

Could you also compare for computational speed up versus accuracy? It's a fascinating field of research though!

[PastaSenpai]

Hey Adam, don’t understand anything but I support the channel 😂

- Erik

[tempdeltavalue]

It would be interesting to check mse of validation set, also to try something like VAE to be able to change properties of fluid, speed, pressure areas, etc (but also add time component, rnn, lstm, transformer🤔)

[arupkumarsahoo]

Exactly I am searching for why Adam is not effective. Thank you for sharing.

[mtulow]

Definitely subscribing, you've got great content. Where did you find the dataset used?

[a-cr]

Hello I simply love the way you explained the physics informed neural networks and especially the coding part. Kudos!!

I am new to the topic of PINNs and I just wanted to ask you can we implement a PINNs for 1st order coupled ODE system with just one independent variable? like dP/dt = f(x, y); dS/dt = g(x, P); dT/dt = h(x, y, S, T)?
If yes could you please tell some examples where I can find a way to code the same?

Thank you very much in advance!!

Subscribed your channel as well!

[andres.igmendez]

This is exactly the kind of info i was looking for! Thank you! I wonder if you could possible spend more time in a more detailed explanation on how you compute the loss. I see it involves computing some gradients of the outputs, but I cant figure out how is done. I'm not a torch user, so I'm trying to replicate similar stuff with TF.

[tariqerwa]

Thanks your video motivated to do a project with PINNs

[poshtavern]

Wow! This was fantastic -- how did you go about creating the visualizations?

[munum]

It is fairly easy to adjust the code to run on GPU, this will give you significant training speedups

[Anjum]

Great video! Is your final PINN just a compressed representation of the CFD training data, or does your model generalize to different-sized cylinders, different fluids, velocities, etc?

[b.mwhite]

I was thinking through your problem with LBGFS vs mini-batching like SGD or ADAM. Isn't it the case that you can shuffle your mini batches more effectively and/or involve some gradient accumulation, to prevent the overlooking of key physical constraints in the cylinder wake problem? That way you can achieve the same result without needing this much compute and the possible memory bottleneck that your solution involves?