[IlyaOrson]

That actual content of that work was good but very misleading with an excess of backpropaganda and a poor literature review. The training procedure makes sense as continuous time backprop but it is mostly a special case of adjoint sensitivity analysis. The use of a NN as defining an ODE system seems fair to be named Neural ODE, imho its a good name, although again it was not completely novel as the writing style through the paper makes it look.

[orbifold]

I agree that it is a good name and evaluating this on "ML tasks" was novel. However this and subsequent papers did a really poor job in delineating what is novel, from what is well known. Moreover this is a pattern in almost all subsequent papers, where people literally pretend that they were the first to consider parameter gradient computation of controlled differential equations, hybrid dynamical systems, etc., while in fact this has been worked out in full generality since essentially the 60s.