Hi Ben my Question is if I'm having an issue with audio and data strings bombardment maliciously engaging my synapse. Do you think fitting pinn's or over fitting pinn's to stabilise the nuclei would be the Answer. I've tried neural Clips and they come out/ tried Apache CNN and Hadoop to stabilise the nucleus. its been 4 years now and its very aggravating/infuriating and frustrating any help would be greatly appreciated

Hello, I am a 3DCG designer. I am currently creating content about this software, but I am still unsure how to effectively leverage its strengths in branding as advertisements. After watching this video, you can feel that you have a lot of insights. If you have any requests for showing simulations realistically in 3DCG, could you please tell me what kind of examples would be preferred by engineers? Additionally, within our company, there are negative opinions about overly photorealistic appearances since the software is primarily used for analysis. I would also like to hear your opinion on this matter. Thank you.

How can I create a residual of shear stress or von misses stress for a fluid flow

Use your chosen grid and develop two additional grids, with y+ equal to 5 and 50. Show how you calculated the first cell height and discuss convergence and the results of these two grids. What is the effect of y+? how to solve this ques..my case is periodic hill imcompressible steady state

Perfect description of Y plus.

i'm just curious. does the neural network need to be trained with its exact solution?

Where can we download the python script file

I think every have their own scripting work for this done. As part of their methods team. But having a software which can create FEM deck based on the analysis inputs ( taking BC , materials , loads ) will be genAi usecase.

Your content is like a virtual hug. Much-needed in today's world. Thank you!

Hey guys, First off I would like to thank Jousef for creating such nice content. Following are the best books related to CFD I can undoubtedly recommend: 1) J. H. Ferziger , M. Perić , R. L. Street, Computational Methods for Fluid Dynamics 4th ed., 2020. 2) H. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method 2nd ed., 2007. 3) F. Moukalled , L. Mangani , M. Darwish, The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab, 2016. Some of them were also mentioned by Tobias in the video. Hope it helps!

One of the rare instances, EM being truthful.

Thank you! How to proove the discretisation error at the 21:14?

Amazing explanation of y+...

If i learn fea for Electromagnetism for design , would this help me learning cfd for fluid mechanics

at 14:30, it seems like external force will not operate on Unn. External force will be a constant term in the physics loss function.

I love all of the questions!! 🤓 Ben is a great teacher!

y+ is really a fancy Reynolds number in turbulent.

Fantastic work and top explanation… thank you , from Victoria, Australia 🇦🇺

Excellent overview!

A possibly useful method would be to have the neural network identify the invariants or a Lie group for a differential equation. Another approach, compute all scalar quantities and have neural network find the right combination of scalar quantities to find a Lagrangian for a physical system.

code link where can I get?

Great work!

that blend to the beat at 29:59.. thank you

Hello Joszef, I would like to know what boundary conditions you would recommend to test external aerodynamics with k-omega SST IDDES. I am trying to figure out what should I use for k, nut and omega. I got 5 patches : object, side walls (not real walls, with top right and left wall), the floor, the inlet and the outlet. Thank you very much for your answer!

Very nice lesson! I'm stuck on the Task 3 though, I can't get the network to converge for w0=80. Here's the code if anyone can spot what I'm missing here: torch.manual_seed(123) # define a neural network to train pinn = FCN(1,1,32,3) # define additional a,b learnable parameters in the ansatz # TODO: write code here a = torch.nn.Parameter(torch.zeros(1, requires_grad=True)) b = torch.nn.Parameter(torch.zeros(1, requires_grad=True)) # define boundary points, for the boundary loss t_boundary = torch.tensor(0.).view(-1,1).requires_grad_(True) # define training points over the entire domain, for the physics loss t_physics = torch.linspace(0,1,60).view(-1,1).requires_grad_(True) # train the PINN d, w0 = 2, 80# note w0 is higher! mu, k = 2*d, w0**2 t_test = torch.linspace(0,1,300).view(-1,1) u_exact = exact_solution(d, w0, t_test) # add a,b to the optimiser # TODO: write code here optimiser = torch.optim.Adam(list(pinn.parameters())+[a]+[b],lr=1e-3) for i in range(15001): optimiser.zero_grad() # compute each term of the PINN loss function above # using the following hyperparameters: lambda1, lambda2 = 1e-1, 1e-4 # compute boundary loss # TODO: write code here (change to ansatz formulation) u = pinn(t_boundary)*torch.sin(a*t_boundary+b) loss1 = (torch.squeeze(u) - 1)**2 dudt = torch.autograd.grad(u, t_boundary, torch.ones_like(u), create_graph=True)[0] loss2 = (torch.squeeze(dudt) - 0)**2 # compute physics loss # TODO: write code here (change to ansatz formulation) u = pinn(t_physics)*torch.sin(a*t_physics+b) dudt = torch.autograd.grad(u, t_physics, torch.ones_like(u), create_graph=True)[0] d2udt2 = torch.autograd.grad(dudt, t_physics, torch.ones_like(dudt), create_graph=True)[0] loss3 = torch.mean((d2udt2 + mu*dudt + k*u)**2) # backpropagate joint loss, take optimiser step # TODO: write code here loss = loss1 + lambda1*loss2 + lambda2*loss3 loss.backward() optimiser.step() # plot the result as training progresses if i % 5000 == 0: #print(u.abs().mean().item(), dudt.abs().mean().item(), d2udt2.abs().mean().item()) u = (pinn(t_test)*torch.sin(a*t_test+b)).detach() plt.figure(figsize=(6,2.5)) plt.scatter(t_physics.detach()[:,0], torch.zeros_like(t_physics)[:,0], s=20, lw=0, color="tab:green", alpha=0.6) plt.scatter(t_boundary.detach()[:,0], torch.zeros_like(t_boundary)[:,0], s=20, lw=0, color="tab:red", alpha=0.6) plt.plot(t_test[:,0], u_exact[:,0], label="Exact solution", color="tab:grey", alpha=0.6) plt.plot(t_test[:,0], u[:,0], label="PINN solution", color="tab:green") plt.title(f"Training step {i}") plt.legend() plt.show()

Very informational. Got a lot of insight on this !

This was a very nice conversation with insight about their idea of solving one of the the millennium prize problems.😎👍

Thanks for sharing this recording from the workshop. Thanks, Ben!

👍👍👍

This is a great resource for FEA beginners. Thank you for all your work Jousef and Dominic! You are both great ambassadors of engineering and simulation.

Thank you very much fot the y+ explanation.

Whats her name 😮

Thanks Aidan @fluidmechanics101, Very useful as always!! Thanks very much

nice tutorial. thank you.

Thermo final coming up... love the music!

And also where can I find part 2?

I am a CFD noob and trying to figure out how to set up my meshes in a way that will give me good results. A lot of information online is over my head. This was good to give me a good base understanding. Thank you

could you please provide the example code of PINN?. Link in the comments not working.

Thank you for the video. It was very informational. Can you give the references of the authors and books you found this information from?

+1 for Oxford PhD saying "timesing" instead of multiplying... respect! :D

I wonder if this give better results with PDE for option pricing

well done,the trend information is also very important,and it can be involved by a partial differential equation.i think maybe the parameters of the partial differential equation can also be the parameters of the neural network PINNS

🙋🏼‍♀️ sir! Keep thinking about the circle stuff kzfaq.info/get/bejne/e99dipap3LSuhWw.htmlsi=MhBoLEI273o3TdWf and how my stomach is making the same sound now. 🤭🤭🤭

Oh! 🤭🤭🤭 the question is if air is a fluid that can be hydrodynamic? Or whatever? 🤭🤭🤭

🙋🏼‍♀️ excuse me sir! So ... air is a fluid hyper whatever?

But isn't all reduce to know what fluid is it? 🤔 I don't think I understand.

🤭🤭🤭 my stomach does the same when it's hungry 🤭🤭🤭

🤭 excuse me sir 🤭🤭🤭 was his stomach hungry 😋 @:36 or so? 🤭🤭🤭

Great discussion, thanks for sharing Jousef!

Fantastic introduction, much appreciated!