Identification of Dynamical Systems Using Symbolic Regression

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Abstract

We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential equations (ODE). The novelty is that we add a step of gradient-based optimization of the ODE parameters. For this we calculate the sensitivities of the solution to the initial value problem (IVP) using automatic differentiation. The proposed approach is tested on a set of 19 problem instances taken from the literature which includes datasets from simulated systems as well as datasets captured from mechanical systems. We find that gradient-based optimization of parameters improves predictive accuracy of the models. The best results are obtained when we first fit the individual equations to the numeric differences and then subsequently fine-tune the identified parameter values by fitting the IVP solution to the observed variable values.

Original languageEnglish
Title of host publicationComputer Aided Systems Theory – EUROCAST 2019 - 17th International Conference, Revised Selected Papers
EditorsRoberto Moreno-Díaz, Alexis Quesada-Arencibia, Franz Pichler
PublisherSpringer
Pages370-377
Number of pages8
ISBN (Print)9783030450922
DOIs
Publication statusPublished - 2020
Event17th International Conference on Computer Aided Systems Theory, EUROCAST 2019 - Las Palmas de Gran Canaria, Spain
Duration: 17 Feb 201922 Feb 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12013 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference17th International Conference on Computer Aided Systems Theory, EUROCAST 2019
Country/TerritorySpain
CityLas Palmas de Gran Canaria
Period17.02.201922.02.2019

Keywords

  • Genetic programming
  • Symbolic regression
  • System dynamics

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