Course "Data Analysis and Modeling"

Lectures: Eckehard Olbrich, N. Marwan, A. Bergner
Fr 11:00-12:30 Building 28 Room 0.104
Exercises: Udo Schwarz
Do 11:00-12:30 Building 28 Room 0.104
Computer lab: Udo Schwarz, Eckehard Olbrich
Fr 13:30-15:00 Building 28 Room 0.087



The course will consist of four parts. In the first part we will deal with linear models and the related methods such as correlation functions and spektral analysis. At the end of this part we will deal with the Kalman filter, which is important also beyond the area of linear time series analysis.
After an intermezzo devoted to wavelet analysis we will proceed in the second part of the lecture to nonlinear deterministic systems and the corresponding methods, e.g. the estimate of fractal dimensions, dynamical entropies and Ljapunov exponents. Finally we will consider approaches to deal with nonlinear stochastic systems: Fitting Langevin equations or Fokker-Planck equations, respectively, from data.
If time suffices we will look at the end on different approaches to model physical phenomena directly, from cellular automata to partial differential equations.



Literature:

Linear methods:
Nonlinear time series analysis
Stochastic Systems

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