Prediction of dynamical systems by symbolic regression
Markus Quade1, Markus Abel1, Kamran Shafi2
1Universität Potsdam, Institut für Physik und Astronomie, Karl-Liebknecht-Straße 24/25, 14476 Potsdam, Germany and Ambrosys GmbH, David-Gilly-Straße 1, 14469 Potsdam, Germany.
Physical Review. E
|August 31, 2016
Summary
This study explores symbolic regression for modeling dynamical systems. Machine learning methods like fast function extraction and genetic programming create accurate, simplified predictive models from data.
Area of Science:
- Dynamical Systems Modeling
- Machine Learning Applications
- Scientific Computing
Background:
- Modeling complex dynamical systems from physical principles is often challenging.
- Simplified, analytically tractable models are highly desirable for prediction and analysis.
- Machine learning offers advanced methods for data-driven model discovery.
Purpose of the Study:
- To investigate symbolic regression methods for modeling and predicting dynamical systems.
- To demonstrate the capability of learning analytical models directly from measurement data.
- To compare the efficacy of fast function extraction and genetic programming.
Main Methods:
- Symbolic regression, a machine learning technique, was employed.
- Two specific algorithms were analyzed: fast function extraction (generalized linear regression) and genetic programming.
- These methods were applied to measurement data to identify predictive models.
Main Results:
- Successfully identified predictive models for dynamical system evolution.
- Demonstrated accurate prediction for a harmonic oscillator and detection of fronts in excitable systems.
- Applied the methods to a real-world problem: predicting solar power production.
Conclusions:
- Symbolic regression provides a powerful approach for discovering analytical models of dynamical systems from data.
- Fast function extraction and genetic programming are effective tools for this purpose.
- These data-driven methods have broad applicability, including in renewable energy forecasting.
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