There are three issues I can think he might be talking about: 1) if you get a solution, can you be sure that it's right? in this case, the neural network might

There are three issues I can think he might be talking about: 1) if you get a solution, can you be sure that it's right? in this case, the neural network might spit out a wrong solution to the integral. However, this solution is easy to verify by just differentiating (which they do in the paper), so I don't think there's a problem here. 2) will the method always return a good answer? I don't think this is a requirement; Mathematica sometimes fails to integrate but people accept that. 3) Does the method work for larger, more interesting families of functions than the limited families tried in the paper? I think this is what Gibou is talking about, and seems like the strongest objection. This technique might just fail in some circumstances for reasons that are hard to anticipate.