While particle-field simulations are maturing both in terms of mathematical foundations and open-source software implementation, the parameterization of the particle-field force field remains challenging. On top of being coarse-grained, which targets the more elusive potential of mean force instead of the potential energy surface of all-atom simulations, the determination of the non-standard particle-field interactions are not straightforwardly amenable to traditional techniques, such as iterative Boltzmann inversion or force-matching. The key challenge resides in calibrating the χkl -parameter matrix, which describes the mixing energy between the density of two species k and l.