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.

submitted to Phys. Rev. E

References in corpus (1)

• Closed-loop separation control using machine learning

Cited by in corpus (26)

• Chaos as an Intermittently Forced Linear System
• Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks
• Symbolic Regression in Materials Science
• Model selection for dynamical systems via sparse regression and information criteria
• Sparse Identification of Nonlinear Dynamics for Rapid Model Recovery
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• A Bayesian machine scientist to aid in the solution of challenging scientific problems
• A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge
• Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensors
• Model selection for hybrid dynamical systems via sparse regression
• Derivative-based SINDy (DSINDy): Addressing the challenge of discovering governing equations from noisy data
• Sparse dynamical system identification with simultaneous structural parameters and initial condition estimation
• Inferring the dynamics of oscillatory systems using recurrent neural networks
• Sparse Methods for Automatic Relevance Determination
• Symbolic Regression via Neural Networks
• Learning Optimal Control of Synchronization in Networks of Coupled Oscillators using Genetic Programming-based Symbolic Regression
• Curriculum learning for data-driven modeling of dynamical systems
• Neural-Guided Symbolic Regression with Asymptotic Constraints
• Predicting the long-term collective behaviour of fish pairs with deep learning
• Model Structural Inference using Local Dynamic Operators
• Grammar-based Representation and Identification of Dynamical Systems
• A Tree Adjoining Grammar Representation for Models Of Stochastic Dynamical Systems
• Explainable Machine Learning Control -- robust control and stability analysis
• Physics-informed Spline Learning for Nonlinear Dynamics Discovery
• Inferring the Structure of Ordinary Differential Equations
• Exploration and Exploitation in Symbolic Regression using Quality-Diversity and Evolutionary Strategies Algorithms