I think that there is good online material to start. Read articles, try to look at code repositories and implement things yourself. Applied experience is good experience! Good luck!!

Thank you very much!!

Thanks for your support!

Thank you!!

Excellent question! Yes, we made some comparisons with other methods, see here: www.nature.com/articles/s41467-024-45578-4 www.sciencedirect.com/science/article/pii/S0142727X23001534

Thank you very much!!

Happy that you enjoyed it!

Just to understand better: if the dataset is not temporal, what are the different snapshots? Aren’t they taken at different instants? You can have 2D snapshots (2D modes in Phi) and then temporal coefficients ai(t). Can you explain the dataset in more detail?

@@rvinuesa Snapshots are 2D images of the velocity field taken at different instants. Each snapshot is independent of the others, and the ensemble average of the statistics is compared with the statistics of a canonical boundary layer. In this dataset, we aimed to study coherent structures of wall turbulence, such as Uniform Momentum Zones (UMZs). I wonder if we can recognize these structures using the POD method instead of histogram-based approaches. If I have just one image (no temporal sequence) and want to decompose this image using the POD method, can I recognize UMZs by selecting the largest eigenvalues?

@@roozbehehsani1468 Here you need to be careful with one thing: when you do UMZs you basically do feature selection, whereas POD is a method of feature extraction. In feature extraction, the new features (i.e. the POD modes) are different from the original ones. If you want to find an alternative way to identify UMZs, I would suggest some method based on image segmentation, there are many methods within computer vision that can be helpful (See e.g. U-nets). I hope this helps, and feel free to email me if you have questions

@@VinuesaLab Thanks a lot for the reply. Since all ML models need labeled datasets and histogram-based approach for the detection of UMZ and making a labeled dataset has flaws, I am thinking more about some fundamental models that detect UMZ(Like POD). ML models basically just map the input into output. If you know any ML model that would be helpful, I would appreciate it if you tell me.

Thanks for following the series!!

It depends on the case, but a clear example is how you can interpret the structures in the wake of a cylinder based on POD modes

Thank you so much!!

The next one is POD 🙂. DMD will come in the future!! 👌

@@rvinuesa Many thanks

Great to have you in the session!!

I think it is important to have a very strong foundation in fluid mechanics and CFD. Then you can dive into ML and apply methods from the fundamental understanding. Hope this helps!

We will probably have a couple more videos on SVD🙂

This is exactly the topic of a lecture coming up very soon! Stay tuned 🙂

Those are interesting topics! After the ML series I am thinking about creating one on numerics and CFD. Stay tuned!

Muchas gracias!! 🙂

Have a look at this paper: www.nature.com/articles/s43588-022-00264-7

@@rvinuesa thank you.

Good question! POD is based on the SVD algorithm. Full video on this coming up soon!!

As many times as you want 😜

Thanks!

Thank you!!

Fantastic!