I had a thesis on this for applying to conjugate heat transfer problems. This family of models is surprisingly easy to train both computationally and architecturally. Definitely the easiest to start with from an operator standpoint imo
This could be very interesting from a computational standpoint. A full analytic computation is usually expensive, so we derive setpoints around them. As the mesh is variable we have a tradeoff of detail and compute. Sounds promising to update setpoints, or as part of a controller.
Are these figures (@6:53 * Zero-shot Super Resolution) calculated on a torus? Maybe you mention the topology later, but I'm curious as to boundary conditions and such.
I read more about the neural operators. Can neural operators be used for inverse problems in image processing? Especially when we have clear physical understanding of the model? For example, MRI image restoration
FYI, I think that around video 16-24 are in reverse order in the playlist. In particular video 22 (Fourier Neural Op) mentions that it follows 23 (Deep Operator Networks). Great series, though. I find all your work very interesting.
there is some joke flying around having to do with convolutions in the frequency domain and reversing order of your signal here, but im not nerdy enough to catch it.
![Deep Operator Networks (DeepONet) [Physics Informed Machine Learning]](http://i.ytimg.com/vi/CDCyOHXDRcI/mqdefault.jpg)
![Deep Operator Networks (DeepONet) [Physics Informed Machine Learning]](/img/tr.png)
![Lagrangian Neural Network (LNN) [Physics Informed Machine Learning]](http://i.ytimg.com/vi/HLUIx6FqAvg/mqdefault.jpg)
I had a thesis on this for applying to conjugate heat transfer problems. This family of models is surprisingly easy to train both computationally and architecturally. Definitely the easiest to start with from an operator standpoint imo
1:41
@eigensteve
Are those resources whic are mentioned still available ?
They could not be found in the description.
thanks.
Very interesting. Please make more videos with the FNO!
This could be very interesting from a computational standpoint. A full analytic computation is usually expensive, so we derive setpoints around them. As the mesh is variable we have a tradeoff of detail and compute. Sounds promising to update setpoints, or as part of a controller.
Are these figures (@6:53 * Zero-shot Super Resolution) calculated on a torus? Maybe you mention the topology later, but I'm curious as to boundary conditions and such.
"Periodic boundary conditions" @10:04. Ok, thanks, nevermind, thanks for the video!
Fantastic as always. Looking forward the code in the description.
Awesome discussion
Cool! Great job
Where are the code and tutorials links?
Nice lecture. Highly appreciate it. Could you please also introduce Laplace Neurual Operator? Thank you.
I read more about the neural operators. Can neural operators be used for inverse problems in image processing? Especially when we have clear physical understanding of the model? For example, MRI image restoration
Awesome! Would you cover the Laplace neural operator at a high level like this too?
You can use this one, just rotate it 90 degrees. 😎
@@adamkucera9094 hmmm, good idea that might just work
Great subject! I wonder if trained fourier neural operators are efficient compared to fft? .
Lovely pictures. The sample-est edge still isn’t there so maybe the sample’s relevant state is not yet fully spanned
But as always great vid ❤ the question for me is where i can try this is there any space were a example is coded?
Did not knew that boeing is the Sponsor of this video:)
Great content!
Would be very interesting to see if Wavelets could be utilized in that context 🤔.
Same thought here.
there exists a paper that had similar SOTA performance using wavelet compression actually. It's just way harder to train and use
Thanks Mr Brunton, i follow you since 2020, always interesting …
FYI, I think that around video 16-24 are in reverse order in the playlist. In particular video 22 (Fourier Neural Op) mentions that it follows 23 (Deep Operator Networks). Great series, though. I find all your work very interesting.
there is some joke flying around having to do with convolutions in the frequency domain and reversing order of your signal here, but im not nerdy enough to catch it.
Im thinking how this can be applied to LLM research
I would like to see a network about KAN-kolmogorov-Arnolnd nn
These don't work well unfortunately. XD nets' work way better.
Can you provide a reference or repo? Thanks.