  We formulate and compute a class of mean-field information dynamics for
reaction-diffusion equations. Given a class of nonlinear reaction-diffusion
equations and entropy type Lyapunov functionals, we study their gradient flows
formulations with generalized optimal transport metrics and mean-field control
problems. We apply the primal-dual hybrid gradient algorithm to compute the
mean-field control problems with potential energies. A byproduct of the
proposed method contains a new and efficient variational scheme for solving
implicit in time schemes of mean-field control problems. Several numerical
examples demonstrate the solutions of mean-field control problems.
