Role of structural properties in reliable prediction of CGLE via data assimilation

The complex Ginzburg–Landau equation (CGLE) is known to exhibit chaotic behavior under certain parametric setups, making long-term prediction challenging due to numerical errors. By leveraging a reference solution obtained from clean numerical simulation (CNS), we compare two different data assimilation strategies using the ensemble Kalman filter (EnKF). Interestingly, the reduced-order model (ROM), despite having larger numerical errors, outperforms the commonly used full-order model (FOM). A detailed analysis reveals that the structural properties of the dynamics play a crucial role in ensuring reliable long-term predictions when the EnKF is applied since the modes of the ROM are particularly effective in preserving these structural properties.