Mean-field optimal control for biological pattern formation

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