Prediction of dynamical systems by symbolic regression
- 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 anWe 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.…
Author details: | Markus QuadeORCiD, Markus AbelORCiDGND, Kamran Shafi, Robert K. Niven, Bernd R. Noack |
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DOI: | https://doi.org/10.1103/PhysRevE.94.012214 |
ISSN: | 2470-0045 |
ISSN: | 2470-0053 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/27575130 |
Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
Publisher: | American Society for Pharmacology and Experimental Therapeutics |
Place of publishing: | Bethesda |
Publication type: | Article |
Language: | English |
Year of first publication: | 2016 |
Publication year: | 2016 |
Release date: | 2020/03/22 |
Volume: | 94 |
Number of pages: | 15 |
Funding institution: | German Federal Ministry for Economic Affairs and Energy, the ZIM project "Green Energy Forecast" [KF2768302ED4] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |