title: Prediction of dynamical systems by symbolic regression.
abstract: 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.
authors: Universität Potsdam, Institut für Physik und Astronomie, Karl-Liebknecht-Straße 24/25, 14476 Potsdam, Germany and Ambrosys GmbH, David-Gilly-Straße 1, 14469 Potsdam, Germany.
authors: Markus
authors: M
authors: Quade
authors: Universität Potsdam, Institut für Physik und Astronomie, Karl-Liebknecht-Straße 24/25, 14476 Potsdam, Germany and Ambrosys GmbH, David-Gilly-Straße 1, 14469 Potsdam, Germany.
authors: Markus
authors: M
authors: Abel
authors: School of Engineering and Information Technology, University of New South Wales, Canberra ACT 2600, Australia.
authors: Kamran
authors: K
authors: Shafi
authors: School of Engineering and Information Technology, University of New South Wales, Canberra ACT 2600, Australia.
authors: Robert K
authors: RK
authors: Niven
authors: Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur LIMSI-CNRS, BP 133, 91403 Orsay cedex, France and Institut für Strömungsmechanik, Technische Universität Braunschweig, Hermann-Blenk-Straße 37, 38108 Braunschweig, Germany.
authors: Bernd R
authors: BR
authors: Noack