Zack Li

We should insert the c_s^2 k^2 \delta_{b} term into the current `hierarchy!`. This is a really nice catch! I'll add a c_s function in `ionization.jl`. We can get the matter...

Should close this when we finish adding it in.

https://gist.github.com/xzackli/7c8819f3e7b43f16481e5d909c0b7764

However, maybe iterative methods like #57 will be better? Nevertheless, our background and RECFAST are basically like the example above -- we need gradients through ODE solves.

@jmsull that's a really interesting thread! I'm glad to learn there are CS people at the julialab working on Enzyme BLAS support. Yeah, let's just leave this aside for a...

Just to add on to Jamie's comment, my understanding is that for *n* ODEs and *p* parameters, forward-mode AD will scale like O(*np*) whereas adjoint methods scale like O(*n+p*) but...

It occurs to me due to this discussion that perhaps people were saying that we should use Enzyme only for ODE internal vjps, i.e. in the [sensitivity docs](https://diffeq.sciml.ai/stable/analysis/sensitivity/#Internal-Automatic-Differentiation-Options-(ADKwargs)). We would...

Here's a somewhat realistic demo. Consider a future hierarchy-less situation where we have a small, stiff ODE system (+ some iterative methods) and some number of parameters we want to...

Thanks @ChrisRackauckas, this is exciting stuff -- I think there will be a substantial (order of magnitude?) performance improvement for us. We'll play with the workaround for now and watch...

This PR is at a very exciting step! I'm finding your code to be very clear, especially for a first draft. For my own understanding, I still need to do...