How to perform adjoint sensitivity in Python (preferably through CVODE)

Question

I want to implement the adjoint sensitivity analysis in python, in order to determine the gradient of my objective function with respect to some parameters. In specific the objective function depends on the solution of a differential equation which in turn depends on said parameters which I am looking to find the optimum of.

To perform this there are numerous good packages both in Julia (see here), as well as CVODES from SUNDIALS, however the latter which does apparently have a wrapper made for python, does not include sensitivity analysis capabilities according to this link. Furthermore, I have looked into SALib for sensitivity analysis, but as far as I understand this refers to some other type of 'sensitivity analysis' and therefore adjoint or even forward sensitivity analysis is not included (correct me if I am wrong on this one).

Thus my question is, does a version of CVODES exist in python with sensitivity analysis capabilities, or is there there any other package where one can use in order to perform adjoint sensitivity analys?

Answer 1

You can easily call Julia code / packages from Python with pyjulia. https://github.com/JuliaPy/pyjulia

Answer 2

You can try Assimulo, which is a Python wrapper of the SUNDIALS suite. I've been using it for some years now and it works pretty robustly. So far, I have performed forward sensitivity analysis on ODE systems with moderate number of states/parameters using CVODEs (less than 20 states, less than 10 parameters). It works pretty well in terms of robustness (can handle stiff problems, and also supports a variety of linear solvers for sparse problems) and speed, and also supports DAEs through IDAs.

I have installed Assimulo using conda, which deals with all the dependency tree (including SUNDIALS in its more recent version). Finally, I'm not aware whether adjoint sensitivity analysis can be performed using Assimulo. If you find something, let us all know.