It is amazing how Prof. Steve Brunton distills knowledge from various papers and provide insight into physics of Turbulence and applies Deep learning to understand it better. Great lecture sir.
I have had the opportunity to know Dr. Andrew Kurzawski, which is a great person and a very estimated friend. As a scientist, needless to say. Awesome work BTW and very interesting video.
I watched this video hoping to understand what deep learning is, and what the catch phrase physics informed means. I guess I blinked and missed it. All I saw was some pretty graphics that were not compared to exprirment and so may or may not have validity. At a deeper level, physicists and mathematicians have questions about whether the (compressible) Navier--Stokes equations model compressible turbulence correctly. DNS is not nature's truth.
The video explains this work 'Reynolds Averaged Turbulence Modeling using Deep Neural Networks with Embedded Invariance' which appears to be a milestone in using deep learning for turbulent flow, and in using physics informed neural networks. Nvidia SiMnet is commecializing this algorithm; anybody else?
Outstanding explanation and clarity on the concepts. I hope I can also get a same guidance and team to pursue my PhD as most of your lectures are the extensions or the basics of my Master's research.
Hello Steve ! I quite honestly love your videos, they are instructive, well written and tap directly in my interests. I'm currently completing a master's degree in applied math engineering. I was only able to play around with some code I wrote to implement the Lagaris et al. paper. Unfortunately I wasn't taught anything about neural networks and reinforcement learning in my curriculum, but that would defenently be a research interest if I get to persue a PhD. Thank you for your awesome content !
Fantastic video, Steve. The scope that you are covering is amazing. I shared this the rest of my group :). Hopefully someone bites and applies what you have touched on to some of the things we are doing in terms of superresolution methods to help us understand our measurements, model dependent controls (I dislike it intensely when physics is excluded in ML, and it should help it learn way faster if you don't make it so model-free and generalized, just like you reducing the basis for your facial recognition instead of using the whole DFT basis) for the accelerator and beamlines. I really think that what you are doing with this channel deserves the highest praise, I just wish more people would do it.
These are just ways of approximating Navier stokes equations at the end of the day right? So basically just approximate another mathematical function with a neural network. Input into the network is boundary conditions. Maybe you can have channels of output for every point on a grid. I guess a custom neural network to handle this makes sense. I wonder how to quantify the loss. We know how much loss we get from finite difference. How much loss do we get from a neural network? Could you ever trust one enough to design an expensive aircraft with one, if you can't prove the loss is bounded?
hopefully neural networks will be incorporated with design giving more relevance to physical phenomenon happening , and for the time being comparision can be done with actual LES done on problems and tht of result obtained by deep learning...isn't it?... nice video though....also interested in having a series on multiphase flow modelling @ Prof. Steve Brunton.
This is a fascinating topic. I cannot help but think whether inferring micro dynamics inside a cell based on average flow has any relationship to pareidolia. I would think cells in the transitional regions will result in neural net coefficients that make inputs hover over the saturation points of the activation functions. I suspect modeling how a dust devil starts could still pose major challenges. Regardless, for the purposes of design we can stay away from such regimes. Atmospheric scientists do not have this luxury.
Kant says that there are two forms of the sublime, the mathematical and the dynamical, which can be found in formless objects, represented by a "boundlessness". Here, it seems that the both kind of sublime are merged into these beautiful simulations.
