  When a colloid is mixed with a depletant such as a non-adsorbing polymer, one
observes attractive effective interactions between the colloidal particles. If
these particles are anisotropic, analysis of these effective interactions is
challenging in general. We present a method for inference of approximate
(coarse-grained) effective interaction potentials between such anisotropic
particles. Using the example of indented (lock-and-key) colloids, we show how
numerical solutions can be used to integrate out the (hard sphere) depletant,
leading to a depletion potential that accurately characterises the effective
interactions. The accuracy of the method is based on matching of contributions
to the second virial coefficient of the colloids. The simplest version of our
method yields a piecewise-constant effective potential; we also show how this
scheme can be generalised to other functional forms, where appropriate.
