Perfect. thank you for your video. Do you not mind if you make a video, how do you get your .m data? Thank you in advance

The training data is in a regular grid, but what if your data is not in a grid like this and you actually including the particle in your data? Will I need some kind of boundary condition then?

Hi! Very cool video! Could you please share a link to the source of the data? Was it a book or some kind of dataset? I would like to repeat this result for myself and would be very grateful if you could share a link to the dataset

Thank you for the video, can you please show us the PINN for compressible N-S equation with viscosity and diffusion (continuity equation with diffusion coupled with a momentum type equation with viscosity) in a 2D square ? Thank you in advance

Hello, thanks very much for putting together these great tutorials. Please could I ask for some help with the SnappyHexMesh setup - after I run "snappyHexMesh -overwrite", my boundaryfile is set up with "innerCylinderSmall" and "innerCylinderSmall_slave" boundary definitions - rather than the expected "AM1" and "AMI2" boundary definitions. Please could you help me correct this :)

Could humanity one day utilize this knowledge to enhance the rheological properties of a bolus, thereby simulating an accurate, "real" human swallowing process? I'm a Speech-Language Pathologist working with patients who have Dysphagia.

Hello Sir make video on solving coupled Ode's using deepxde library

Hello Adam, I think your explanations are clear and good, and they serve me as a basis for a simulation of centrifugal compressor. I can't make it and therefore I need support. How can we talk to each other directly?

How about to create a C-Mesh if the AoA is different than zero?

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?

2:53 Can anyone please explain how is the cost function (boundary conditions) obtained using supervised learning?

Thank you for this video. I have two questions in the part def loss(t): 1) why did you write u.sum() at line 3 when you want to compute the gradients? 2) why did you write [0] in the end of line 3?

hi,i replaced the obj file with my obj file but when i run the "mpirun..." , the sum of forces , moment is alway 0 all the time, can you help me

Hello, your code doesn't work. Can you help me?

amazing work!!!!! :)

With what changes would it be possible to create a model that takes as an input an unknown geometry and then predicts the velocity and pressure fields?

How did you initialize your parameters in the network?

how to deal with the derivative with respect to time?

Couldbyou make this available to download?

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!

Hi, from where I can get the stl file you have used?

Do you know how we can add period boundary condition to both sides ?

Does this video mean that the trained model can be generally applied to other fluid situations? Or is this only showing that such nonlinear network can approximate to the given result when trained for certain cases?

Hi there, fantastic work. However, could you provide us a little bit about normalization process of data? Tnx

Neural networks do not give analytical or exact solutions nor do they prove the existence of solutions. There is a huge difference between exact solutions and numerical solutions.

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

It helped a lot. Thank you

What if we don't have training data? No experiments no cfd. Just equations and boundary conditions

great topic, horrible audio 😨

Genuinely fascinated by the use of PINNs to accelerate computation of such important problems like this! Is it in any way possible to train something like this (even if only in 1D) on a strong pc? If so, what specs would you use? (I am planning to conduct further research into this specific use of PINNs 😅)

how can we solve this if we don't know the exact solution. explain how the loss function changes

How can I get the same predicted graph of the paper with your code. 4:48 The graph your code is giving is from 0 to 50 in y-axis and 0 to 100 in x-axis. I tried changing the axis values but I was not getting the same graph as the paper.

Very nice. Thank for teaching us. When I run mine, i got the error [0] --> FOAM FATAL IO ERROR: (openfoam-2112 patch=220610) [0] Cannot find patchField entry for propellerTip [0] [0] file: processor0/0/p.boundaryField at line 11 to 42.

can you tell how did you get cylinder_wake.mat file or how to use a particular data set for the same?

Hi! Thanks for the video, this is great. I have a question, you have an input of size (100,1); then, you use nn.Linear(1,10) to perform a transformation of the data considering the weights. However, this gives a matrix of size (100,10), which will have the same size after the Sigmoid activation. How do the neurons of the hidden layers appear in this output? I cannot get the result in terms of the typical y=sum(w_ij*x_j + b_i) where i is the ith hidden unit (neuron). Are there 100*10 units in this configuration? How many weights are set for training at this point, 100 or 100*10? Thanks for your attention to this matter

Great video. Can this still be applied when p(x) is not zero?

Solving ode!

Large language models and chat box my dad made those two connections.

Thank you very much, this is so nice! 😃 My "Problem" is, that im using PyTorch and OpenFOAM a bit, but not used to C++ to let them "talk" to each other 😞

Thanks for sharing. Notice you model the flow around cylinder that is in the wake of another cylinder. Where the two cylinders of the same diameter? When you model step cylinders , you can get interesting results such as karman vortex shedding and other phenomena. It would defnitely be of interest if you were to apply PINNs to the CFD of other geometric shapes.

عندما كنت لا أزال في المدرسة الابتدائية ، كان هناك Pawe كنت أركب دراجة التقيت به ثم ذهبت إلى الخنفساء للحصول على الآيس كريم ، وفي طريقي إلى المنزل عدت إلى المنزل

Excellent work! I've been delving into a similar area, albeit focused on the individual particle level. I've successfully trained a neural network to calculate particle dynamics in a single step, effectively replacing the need for 25 traditional computational substeps of Verlet integration. Interestingly, the network yields significantly more stable results compared to numeric integration when subjected to high-energy collisions. Unlike Verlet integration, the network simulation does not "explode". Have you experimented with your simulation at energy levels exceeding those used during training?

Parabéns, lindo

Nice start. Thank you for sharing!

Hi, your video inspired me a lot, but I would like to ask you what software did you use to generate your geometry files? When I imported my generated geometry files into openfoam, snappyHexMesh will always prompt "Unknown region name ascii for surface A". I am looking forward to your reply.

Which version of OPENFOAM did you use

Great video! How would you expand this code to encompass other situations like systems of ODE or PDE?

Dear, please let me know which software you are using in these problems?

Well done! Thanks.

You should include a link to the documentation website