M.Sc Thesis

M.Sc StudentWiegner Aviad
SubjectData Driven Koopman Operator Analysis Based on Noisy
Augmented Observations
DepartmentDepartment of Electrical and Computer Engineering
Supervisor ASSOCIATE PROF. Ronen Talmon
Full Thesis textFull thesis text - English Version


Data driven modelling of complex systems has recently become an evolving field with many scientific applications.  Many systems of interest in a broad range of fields may be characterized as high-dimensional, nonlinear dynamical systems that exhibit rich multi-scale propagation in both space and time.  DMD is a popular data driven algorithm which is based on the Koopman operator theory.  Despite the fact that the DMD analysis has an informative spectral representation of the underlying dynamics of the system, it is highly sensitive to noise and requires a relatively large amount of observations in order to achieve good performance.  Solving these two problems can significantly broaden the scope to which DMD can be applied. In this thesis we present methods that attempt to alleviate the two inherent problems in DMD analysis mentioned above. We use an augmentation method that overcomes the lack of observations, and propose a new alignment method, which consists of phase alignment between the augmented modes and an appropriate modification of the amplitude of the mode according to the decay rate of the spectral components. In addition, we present a new metric that approximates the augmentation error, which in turn is used for determining the most informative dynamic modes.  This way, we show that we are able to cope with high level of observation noise. The proposed method is applied to synthetic data and to real Brain Computer Interface (BCI) data, demonstrating the improvement attained by using the proposed method and metric.