Abstract:
In this thesis, we try to find a probabilistic Koopman-based representation for dynamical systems. Therefore we apply the framework of [Pan et al 2019], where the author successfully found such representation as a residual improvement of the powerful Dynamic Mode Decomposition technique. While [Pan et al 2019], uses a hierarchical Bayesian setup, we find that an Empirical Bayes approach is also capable of producing meaningful results for the probabilistic inference of the model parameter for the data situations we encountered. We also try to improve this framework by learning an additional stable representation of the dynamics of the prediction residuals. We observed minor improvements in the prediction quality for this setup in some cases, but we could not learn a significantly better representation of stable chaotic dynamical systems.
Github repository here