Machine Learning on Dynamical Systems

I’ve started taking an off-cycle course 12.S592 on machine learning taught by Sai Ravela, with a focus on (non-Gaussian) dynamical systems. My desired final project is on extratropical cyclone downscaling, using a reduced stochastic model. Here are some PSet notes and schematic solutions, because they are very interesting problems to think about.

Loading using Google Colab is recommended.

L0 vs L1 Problem: Particle Tracking in Non-Gaussian Flow. Hungarian Algo (L0 Method), and Sinkhorn Algo (Doubly Stochastic)

Subset Selection Problem: What to do when nonlinear functional mapping is expensive? (Resampling and mapping approximation, to identify most damaging cyclones from massive input features)

Sparse Recovery: How to identify particles with spike in wavelength spectra, convoluted and added by noises, as siganls received in telescopes? Retrieving 4 particles from a 1000by1000 space and identify their weight!

Earthquake Sourcing: How to identify source location and onset time for multiple earthqukes (with spurious noises like local ppl stamping on the groud!)

Meanwhile, Sai has some preferred naming of the above psets, which I’ve also included their correspodent Sai-standard names:

• L0 vs L1 Problem: Correspodent Problem
• Subset Selection Problem: Where’s Waldo
• Sparse Recovery: All mixed up
• Earthquake Sourcing: Boom!