Inspired by @charlesm93 's recent talk on fitting ODE models in Stan (see e.g. Bayesian Model of Planetary Motion: exploring ideas for a modeling workflow when dealing with ordinary differential equations and multimodality | planetary_motion.utf8), I was wondering whether there exists a collation of best practices/tricks to more efficiently fit ODE models in Stan?
Just for the above example (planetary motion of a single body with unknown mass and initial positing around some object) a few things come to mind.
For example, one could limit the model to the first few time steps at first (during warmup?) , to not waste so much time on regions in the parameter space that are hopeless.
Likewise, I assume we might sacrificing accuracy of the numerical solver to speed up the computations. On the other hand, this will surely impact the performance of the HMC method. However, even for moderate accuracies, the flow of the system should not actually change too much. So there might be some potential there, at least for the warmup phase?
I’m sure other people have thought about this longer and with more background knowledge. Is there maybe a collection of resources or papers that I should know about /look at?
I hope this is the appropriate place for this question!