Physics-informed neural networks for fluid mechanics
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- Опубликовано: 11 сен 2024
- Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations. We employ PINNs for solving the Reynolds-averaged Navier-Stokes equations for incompressible turbulent flows without any specific model or assumption for turbulence and by taking only the data on the domain boundaries. We first show the applicability of PINNs for solving the Navier-Stokes equations for laminar flows by solving the Falkner-Skan boundary layer. We then apply PINNs for the simulation of four turbulent-flow cases, i.e., zero-pressure-gradient boundary layer, adverse-pressure-gradient boundary layer, and turbulent flows over a NACA4412 airfoil and the periodic hill. Our results show the excellent applicability of PINNs for laminar flows with strong pressure gradients, where predictions with less than 1% error can be obtained. For turbulent flows, we also obtain very good accuracy on simulation results even for the Reynolds-stress components.
You can find all the data and codes here:
github.com/KTH...
And all the references:
aip.scitation....
iopscience.iop...
arxiv.org/abs/...
![Physics Informed Neural Networks (PINNs) [Physics Informed Machine Learning]](http://i.ytimg.com/vi/-zrY7P2dVC4/mqdefault.jpg)
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Amazing explanation. Finally I have a clear image of PINNs :)
Thank you.
I am happy the video helps! 🙂
Great video. Would be interesting to know more about what properties in model and data will drive computational complexety in PINN's and traditionell simulation. From my understanding PINN's are great for cheap iterative measurements to optimize the setup of an experiment. Once you found points of interesst you can set up expensive traditional experiments.
Very helpful. Thanks for your time and effort.
Geart job sir...
Very productive
@@rvinuesa ❤❤
Great!
Thanks!!@@segundovinuesa9648
Excellent video, Prof. I have been also working in developing PINNs for turbulence modelling. What would you say are the current challenges for PINNs for fluid dynamics. I believe it is difficult for NN to learn the small scales turbulence. Is it true?
thank Ricardo Vinuesa really really thanks can you also for LES for turbulence
This could be an application too, although there are some challenges with PINNs in unsteady problems
Hi professor, I am also working on PINNs to solve the radial flow diffusivity equation. But it keeps failing. Using the same PINNs I solved Burger's and Schrodinger which gave magnificent results. Do you have some recommendations?
Maybe you can email me the details?
Interesting work and nice explanation!
What I don't understand is why you don't need to include a model for the Reynolds stresses. Since the RANS equations are underdetermined, it doesn't seem obvious to me that the model converges to a physically meaningful solution. So, does the model not converge to a different solution each time depending on the initial weights, thus not guaranteeing the physical meaningfulness of the solution?
The boundary conditions ensure that one converges to the right solution. Note that these include boundary conditions for the Reynolds stresses!
@@rvinuesa
Thank you very much for your response! Initially, I didn't realize that you included boundary conditions for the Reynolds stresses as well. However, it's still not clear to me that this boundary value problem should have a unique solution inside the domain, considering there are 6 variables but only 3 field equations.
This is a great video! Thank you very much. I have a question about the input data. I noticed that you used (X, Y) as input, which I think represents the coordinates of the problem. and threfore you made predictions for U, V, and P. However, one thing I noticed is that we didn't provide the model the initial conditions as input for the problem. Could you please explain why we don't need initial conditions?
@@rvinuesa thanks 👍👍👍
Happy to help if you have more questions :) @@elganaelmehdi1697
Great work, Prof.! Can you please explain more about the boundary condition? As I have viewed your code, all test cases use bc loss as MSE between the prediction of bc points (x,y) and bc velocities (u,v) which are observations/measurements/simulated data. Therefore, all boundaries here use the Dirichlet boundary condition? And the data is from either the analytical solution or numerical solver, isn't it?
That's correct, the boundary conditions are Dirichlet, and they are taken from the statistics of the DNS
@@VinuesaLab Thank you for the explaination!
Sehr gut
Will this method work if we use libraries like DeepXDE or Neurodiffeq? Is there a difference in using this library and the traditional method used
This relies on the very basic automatic differentiation, which is needed in the back-propagation algorithm to train any neural network
Thankyou! it was great and really useful. I want to ask a question about 2 terms in loss function which you used. One of them (supervised loss) you used only data in boundaries. While working with experimental data is not better that we expand supervised loss over all points which we have measured? I mean if we have measured data in any points it can help us or not?
@Ricardo Vinuesa Thanks for your kind response.
Happy to answer any other questions you may have!@@user-zu7qv9co6b
Great explanation, could you let me know, is there chance to estimate the value of drag/ coefficient in the the E- E model with this approach
Absolutely! You can calculate it based on the computed pressure and wall-shear stress
Thanks very much for such valuable animation
Would you please share your email
Thanks indeed