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!)

Simplest Regression: Can we get accurate polynomial coefficients? Vandermonde matrix, multicolinearity problem

Quadratic Programming and Gaussian Belief Propagation: revisit nodes correspondence

Gaussian Belief Propagation under a Bayesian viewpoint

[Regularization: Ridge, Lasso, Tikhonov, Ivanov, Morozov, Mixed-Integer Quadratic Programming (MIQP), Mixed-Integer Linear Programming (MILP), GUROBI]

Meanwhile, Sai has some preferred naming of the above psets, which I’ve also included here:

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