  We study the modeling and prediction of dynamical systems based on
conventional models derived from measurements. Such algorithms are highly
desirable in situations where the underlying dynamics are hard to model from
physical principles or simplified models need to be found. We focus on symbolic
regression methods as a part of machine learning. These algorithms are capable
of learning an analytically tractable model from data, a highly valuable
property. Symbolic regression methods can be considered as generalized
regression methods. We investigate two particular algorithms, the so-called
fast function extraction which is a generalized linear regression algorithm,
and genetic programming which is a very general method. Both are able to
combine functions in a certain way such that a good model for the prediction of
the temporal evolution of a dynamical system can be identified. We illustrate
the algorithms by finding a prediction for the evolution of a harmonic
oscillator based on measurements, by detecting an arriving front in an
excitable system, and as a real-world application, the prediction of solar
power production based on energy production observations at a given site
together with the weather forecast.
