Regarding theory vs physical, I'm not sure. The article isn't an attempt to be a general machine learning article but to sate some of the things it would be helpful to refer to from other El Nino articles. (I'm too lazy to write Nino correctly on the forum...) That argues physical models are most appropriate, but then there's the sore thumb of the car example. So maybe theory driven is better.
(Incidentally I've stared adding a sparsity example to the text, but I'll wait until you've finished editing to do more.)