Dynamic optimization of dissipative PDE systems using nonlinear order reduction

In this work, 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 combination of the method of weighted residuals with spatially-global basis functions and approximate inertial manifolds. We use the Kuramoto-Sivashinsky equation, a model that describes incipient instabilities in a variety of physical and chemical systems, to demonstrate the implementation and evaluate the effectiveness of the proposed optimization method.