[ChrisRackauckas]

Oh another thing, in the chaotic regime which is of interest, standard automatic differentiation schemes don't even apply as you require shadow adjoints given the shadow trajectory leads to inaccurate calculations for the gradient. Julia's system is the only one that I know of that has shadow adjoints for differentiation of ergodic properties.

https://frankschae.github.io/post/shadowing/

So unless the purpose is to only differentiate the simulator for short time periods or in the absence of chaos, I cannot see differentiation as a good justification because AD will not give a stable algorithm on that type of problem.