Tagging @charlesm93, @wds15, @yizhang, and @bbbales2 to start for this question, since I know you guys are working on various things related to the topic.

I was wondering about the general state of priorities right now for ODEs in Stan and what present areas of development focus were. Over the past few months, among the in-progress tasks I’ve seen include variadic arguments into the ODE function, DDEs, and non-linear root solvers. I’ve seen that the ability to use DifferentialEquations.jl is one of the things that is making Julia-native PPL’s more appealing for some whose work is more focused on differential equation system inferences, so general improvement in this area would probably be of interest to a lot of PPL users.

~~Generally, it looks like these angles are being worked on? ~~

Edit: Some of these bullet points are not, so this is now more intended to be taken as a list of ripe areas of contribution for improving Stan’s differential equation functionality.

- Variadic arguments in ODE function
- DDE/SDE/other diff eq type solvers
- Additional ODE solvers (don’t need too many, but having a couple more options other than
`rke45`

and`bdf`

might be useful for versatility). An auto-switching algorithm that automatically switches between stiff and non-stiff would be the most useful addition in this area. - PDE solvers
- Adjoint method for propagating derivatives to ODEs
- Deterministic event handling, as @wds15 mentions below, which would help with forcing function manipulations that happen a lot in ecology and pharmacology.
- Dynamic event handling, also mentioned by @wds15 below. Non-linear root-finding would be a very useful subset of this, as that would help larger ODE models be initiated at a non-analytic steady state prior to a perturbation response.

Of most use to me are introductions of the non-linear root solving, which I think @charlesm93 is working on, and the variadic argument update, which I think is being headed by @bbbales2, as they directly correspond to the next project I’m going to be working on for my PhD thesis, so I figured it was high time I took a look under the Stan hood and learn about contributing to one of those areas. However, I was also just generally interested in the state of what was in the works on the Stan differential equation front. Thanks!