- author = "Gabriel Kronberger and Lukas Kammerer and Michael Kommenda",
- title = "Identification of Dynamical Systems Using Symbolic Regression",
- booktitle = "International Conference on Computer Aided Systems Theory, EUROCAST 2019",
- year = "2019",
- editor = "Roberto Moreno-Diaz and Franz Pichler and Alexis Quesada-Arencibia",
- volume = "12013",
- series = "Lecture Notes in Computer Science",
- pages = "370--377",
- address = "Las Palmas de Gran Canaria, Spain",
- month = "17-22 " # feb,
- publisher = "Springer",
- keywords = "genetic algorithms, genetic programming, System dynamics, Symbolic regression",
- isbn13 = "978-3-030-45092-2",
-
DOI = "
doi:10.1007/978-3-030-45093-9_45",
-
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.",
