Numerical simulations of particle systems in Statistical Physics require a tremendous amount of computer time because of the many degrees of freedom and the possible interactions between individual particles. For this reason simplifications are necessary for numerical simulations, wherever possible. One possibility are, for example, multiscale simulations: Instead of the simulation of ``real'' particles in a well-defined realistic setting, the "real'' particles are merged into fictitious particles (so-called *beads*) on a coarser scale, whose posititions are subsequently computed using adequate effective potentials. In the end, the result is transformed back to the "real'' scale using, what is called *backmapping*.

In other situations the effective potentials are known for some coarse scale, whereas the real potentials on the atomistic level are ownly partly known. In such a case the distribution of the beads can be analyzed, and one can ask oneselve, which "real'' potentials are consistent to this given distribution on the coarse scale.

These problems are typical examples of so-called *inverse problems*; in general they don't have a unique solution (if they have solutions at all), and different approximate solutions can be "arbitrarily far off'' from each other. In this project we want to study, whether nevertheless reasonable answers can be provided to these questions. The viewpoint will be taken from the mathematical theory of inverse problems.