Fitting parameters in partial differential equations from partially observed noisy data

We describe a new method for parameter estimation in systems with nonlinear spatiotemporal dynamics. The technique is able to reliably determine parameter estimates from noisy data and is even applicable in cases with unobserved components. In a simulation study we investigate its performance in comparison to standard methods and show its superiority. As numerical example we analyze in detail a complex Ginzburg–Landau equation under realistic conditions.