Computational Mean-field information dynamics associated with Reaction diffusion equations

We formulate and compute a class of mean-field information dynamics based on reaction diffusion equations. Given a class of nonlinear reaction diffusion and entropy type Lyapunov functionals, we study their gradient flow formulations. We write the mean-field metric space formalisms and derive Hamiltonian flows therein. These Hamiltonian flows follow saddle point systems of the proposed mean-field control problems. We apply primal-dual hybrid-gradient algorithms to compute the mean field information dynamics. Several numerical examples are provided.