Estimation of Deterministic and Stochastic Rules Underlying Fluctuating Data

One basic aim of scientific research is to set up reasonable models for considered systems. A suitable model should reproduce the observed quantities and help to gain a deeper understanding of the system. Usually, collected data and known properties of the system, as symmetry relations for example, serve as a basis for this modelling. Very often, nonlinearities and dynamical noise cause fundamental problems. In this contribution, a general, data-drivenmethod for formulating suitable model equations for nonlinear complex systems is presented. The method is validated by application to artificially created time series. Furthermore, the results of an analysis of turbulent flow data and financial data sets are presented.