We just released v0.86 of Torsten, a PKPD library based on/forked from Stan. In v0.86 we seek an alternative to map_rect
for PMX population models, motivated to
 Avoid using/building boost.mpi and serialization
 Reduce cognitive load of packing & unpacking for
map_rect
by providing a simplified function signature.  Automate (static) load balance by relieving user from “sharding”.
 Prepare for future parallelization planned on our roadmap.
Attempting to achieve above, the MPI support is limited to ODEbased (PKPD) population models, provided through a few group
solvers, based on Torsten’s own implementation of ODE integrators
pmx_integrate_ode_adams
pmx_integrate_ode_bdf

pmx_integrate_ode_rk45
These integrators have same signatures as Stan’s, with additional support for time step being parameters.
The population/group version of these integrators are
pmx_integrate_ode_group_adams
pmx_integrate_ode_group_bdf

pmx_integrate_ode_group_rk45
with signature
matrix pmx_integrate_ode_group_xxx(f, real[ , ] y0, real t0,
int[] len, real[ , ] ts,
real[ , ] theta, real[ , ] x_r, int[ , ] x_i,
real rtol, real atol, int max_step);
namely the corresponding ODE integrator args now become ragged arrays, and array len
giving the record length for each subject within the population. The return is a matrix ragged columnwise.
Similarly, for PMX modeling, population solvers are provided for NONMENcompatible input, as found in previous releases. The PMX population solvers are
pmx_solve_adams
pmx_solve_bdf
pmx_solve_rk45
The above MPI solvers do not use “sharding”. Currently, the population load is distributed statically and evenly.
Some example models for MPI solvers can be found in the examplemodels
folder of the repo. In particular

https://github.com/metrumresearchgroup/Torsten/tree/master/examplemodels/harmonic_oscillator_ode_group_model
fitting an ODE group model for sinusoidal oscillator parameter. 
https://github.com/metrumresearchgroup/Torsten/tree/master/examplemodels/lotka_volterra_ode_group_model
fitting an ODE group model for LotkaVolterra equation, based on @Bob_Carpenter 's case study. 
https://github.com/metrumresearchgroup/Torsten/tree/master/examplemodels/twocpt_population
fitting the standard twocpt model to demonstrate the PMX population solver, on a population of 8.
Note that due to the process management conflict between Torsten’s scheme and map_rect
, Torsten’s MPI solvers cannot be used when STAN_MPI
is turned on.