I have a problem composed of around 6 mathematical expressions - i.e. (f(g(z(y(x))))) where x are two independent arrays.
I can divide this expression into multiple explicit comps with analytical derivatives or use an algorithmic differentiation method to get the derivatives which reduces the system to a single explicit component.
As far as i understand it is not easy to tell in advance the possible computational performance difference between these 2 approaches. It might depend on the algorithmic differentiation tools capabilities on the reverse mode case but maybe the system will be very large with multiple explicit components that it would still be ok to use algo diff.
my questions is :
Is algo diff. a common tool being used by any of the developers/users ? I found AlgoPY but not sure about other python tools.
As of OpenMDAO v2.4 the OpenMDAO development team has not heavily used AD tools on any pure-python components. We have experimented with it a bit and found roughly a 2x increase in computational vs hand differentiated components. While some computational cost increase is expected, I do not want to indicate that I expect 2x to be the final rule of thumb. We simply don't have enough data to provide such an estimate.
Python based AD tools are much less well developed than those for compiled languages. The dynamic typing and general language flexibility both make it much more challenging to write good AD tools.
We have interfaced OpenMDAO with compiled codes that use AD, such as CFD and FEA tools. In these cases you're always using the matrix-free derivative APIs for OpenMDAO (apply_linear and compute_jacvec_product).
If your component is small enough to fit in memory and fast enough to run on a single process, I suggest you hand differentiate your code. That will give you the best overall performance for now.
AD support for small serial components is something we'll look into supporting in the future, but we don't have anything to offer you in the near term (as of OpenMDAO v2.4)