Parameter Identification Techniques for Partial Differential Equations

Many physical systems exhibiting nonlinear spatiotemporal dynamics can be modeled by partial differential equations. Although information about the physical properties for many of these systems is available, normally not all dynamical parameters are known and, therefore, have to be estimated from experimental data. We analyze two prominent approaches to solve this problem and describe advantages and disadvantages of both methods. Specifically, we focus on the dependence of the quality of the parameter estimates with respect to noise and temporal and spatial resolution of the measurements.