I would like to try using the mixed-dimensional branch of FEniCS with dolfin-adjoint but I have no clues on how to start. So, I first would like to ask if this idea is possible and do I also need to do some additional work when my problem is mixed-dimensional?
As the Mixed dimensional branch is using a custom assembler, it has to be overloaded with adjoint and tlm actions. Thus can be done manually for your application, or as a part of a pull request to dolfin-adjoint: https://github.com/dolfin-adjoint/pyadjoint