  We propose a mean-field optimal control problem for the parameter
identification of a given pattern. The cost functional is based on the
Wasserstein distance between the probability measures of the modeled and the
desired patterns. The first-order optimality conditions corresponding to the
optimal control problem are derived using a Lagrangian approach on the
mean-field level. Based on these conditions we propose a gradient descent
method to identify relevant parameters such as angle of rotation and force
scaling which may be spatially inhomogeneous. We discretize the first-order
optimality conditions in order to employ the algorithm on the particle level.
Moreover, we prove a rate for the convergence of the controls as the number of
particles used for the discretization tends to infinity. Numerical results for
the spatially homogeneous case demonstrate the feasibility of the approach.

Optimization and Control;Numerical Analysis;Analysis of PDEs;Numerical Analysis