Identification of Dynamical Systems using Symbolic Regression

TL;DR

This paper presents a novel method combining symbolic regression with gradient-based optimization to identify dynamical system models from data, improving accuracy over traditional approaches.

Contribution

It introduces a hybrid approach that integrates genetic programming and automatic differentiation for more accurate dynamical system modeling.

Findings

Gradient optimization enhances model predictive accuracy.

Fitting to numeric differences followed by IVP solution fitting yields best results.

Method tested successfully on diverse simulated and real mechanical systems.

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.