Dynamic optimization of dissipative PDE systems using empirical eigenfunctions

We propose a computationally efficient method for the solution of dynamic constraint optimization problems arising in the context of spatially-distributed processes governed by highly-dissipative nonlinear partial differential equations (PDEs). The method is based on spatial discretization using a combination of the method of weighted residuals with spatially-global empirical eigenfunctions as basis functions. We use a diffusion-reaction process with nonlinearities and spatially-varying coefficients to demonstrate the implementation and evaluate the effectiveness of the proposed optimization method.