Prediction of Dynamical Systems by Symbolic Regression

TL;DR

This paper explores symbolic regression techniques, specifically fast function extraction and genetic programming, to model and predict dynamical systems from data, including physical, biological, and real-world energy systems.

Contribution

It compares two symbolic regression algorithms for modeling dynamical systems and demonstrates their effectiveness on various physical and real-world prediction tasks.

Findings

Both algorithms successfully model the harmonic oscillator.

They detect fronts in excitable systems.

They predict solar power production effectively.

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.