The hell is going on here?
The web article is written VERY amateurishly. I am very annoyed each time they use the word “complex” (six hits in the article) when they mean complicated (complex means real and imaginary parts; any mathematical writing avoids the word with other meanings). The pdf paper even says that sqrt(-2) is an invalid expression! Moreover, 2nd degree ODEs are not that complicated, especially when they chose them to have elementary solutions! It looks like they consider a Bessel function (to cite one special function) to be an invalid solution. They sound awfully proud of themselves for “discovering” that some algebraic expressions (or “equations”, as they call them, even when there’s no equals sign) have a parse tree? wtf? Every CAS uses a parse tree for expressions, so why are you going on about this remedial stuff? And natural language processing often also does parse trees, so why are they saying that this doesn’t look like normal language?
And then there’s their whole “accuracy” bit. Looks like they consider a solution to be innacurate if it involved a special function or if one of the Mas timed out. I mean, okay, so you trained a NN on a specific set hoping for elementary solutions and didn’t get them, and if the solution you got took too long or wasn’t of the right shape, you rejected it. That part of the paper is kind of interesting. But it’s also weird to claim superiority of their model when they handpicked the problems to make sure they had elementary solutions. Sure, the Mas could be improved to give elementary solutions, but this seems to be hyperspecialising and narrowly optimising for one case that doesn’t really arise that often in practice. “Most” ODEs do not have elementary solutions.
This seems to be the impression I’m getting from other people too: the picked problem looks important if you don’t know the field, but if you do, isn’t actually that interesting.
It’s facebook, it’s AI. The article is probably meant for people without specific knowledge of differential equations. Still, you make some good points.