Introduction to machine learning, Part 5: The proper-orthogonal decomposition (POD)

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To conclude this first introduction series to ML, we derive and describe in detail a widely used method for analysis of high-dimensional fluid-flow systems: the proper-orthogonal decomposition (POD).

I also acknowledge Scott Dawson for his input on this material.
  1. Ricardo Vinuesa
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Thanks as always for the videos on machine learning!

rcorpchannel
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Great series. Thanks. Can you please elaborate a little bit how can we interpret the POD mode shapes? I mean by looking at the highest energy mode shape, let's say, what can we understand about the turbulent flow?

usmannaseerfm
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Great series of videos. If we have a PIV dataset which is not temporal and each velocity snapshot is u(x, y), the A matrix would define what property of the velocity field? Is it still temporal or \Phi defines variables in y direction and A defines streamwise variable?
Many thanks

roozbehehsani