Ha, yeah I knew that analysis of how to do second order adjoints fast :), in what is basically documentation no less. I figured someone would probably do a ML paper on that eventually. I have had a hard time judging, what is non-trivial in the past, aswell. The next thing that they will probably discover is Jet spaces and Hopf algebras.

I'm also slightly salty because a recent paper (https://arxiv.org/pdf/2011.03902.pdf) claimed "Differentiable event handling generalizes many numerical methods that often have specialized methods for gradient computation,...", citing one of our results. We instead went through the trouble to find a semi-complete list of prior work, which would make it abundantly clear that what they claim as new is in fact traceable to a paper by Rozenvasser in ~1965 (we translated it from Russian to make sure), with a long history of more recent work. In fact I think DifferentialEquations.jl just supports this out of the box and has non-broken event-handling (their implementation tests against a product of jump conditions).

I am aware of those benchmarks :). I will probably adopt your library for this very reason, although I have to say that I really don't like Julia as a language. It is pretty clear that besides Sundials, PETSC and other C++ based libraries, you are rapidly becoming the only game in town. As much as I am tempted I really shouldn't be handwriting integration routines :). I don't think you need a random internet stranger to tell you that, but it is abundantly clear that DifferentialEquations.jl provides far more long-term value than these types of machine learning papers.