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We design and compute a class of optimal control problems forreaction-diffusion systems. They form mean field control problems related tomulti-density reaction-diffusion systems. To solve proposed optimal controlproblems numerically, we first apply high-order finite element methods todiscretize the space-time domain and then solve the optimal control problemusing augmented Lagrangian methods (ALG2). Numerical examples, includinggeneralized optimal transport and mean field control problems between Gaussiandistributions and image densities, demonstrate the effectiveness of theproposed modeling and computational methods for mean field control problemsinvolving reaction-diffusion equations/systems.

Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation