Before revision:  Prototypical algorithms and numerical implementations of the aforementioned techniques to the approximate identification and predictive simulation of time series models with symmetries and nonlinear structured dynamical systems in theoretical physics, fluid dynamics and weather forecasting are presented.
After revision:  Prototypical algorithms based on the aforementioned techniques to the approximate identification and predictive simulation of time series models with symmetries and nonlinear structured dynamical systems in theoretical physics, fluid dynamics and weather forecasting are presented.