Optimization algorithms for parameter identification in parabolic partial differential equations

The problem of estimating model parameters from data representing near-equilibrium patterns in PDEs is considered. This problem is formulated as an optimization problem by determining the nearest state on a manifold of equilibria. Algorithms to solve this optimization problem are proposed, by first regularizing the problem and using explicit search directions on the tangent space of the equilibrium manifold. Some rigorous results on local converge are obtained. Several examples of pattern forming systems are used to test the proposed methodology. Comparisons to synthetic data are made showing the ability of obtaining excellent estimates even when significant noise is present.