# Identification of Dynamical Systems using Symbolic Regression

arXiv: https://arxiv.org/abs/2107.06131 · HTML: https://mlsanity.com/paper/2107.06131/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 615 references that are in the map.
- First posted on arXiv 6 Jul 2021.

## Builds on (most cited first, 15 of 15)

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- [Undefined By Data: A Survey of Big Data Definitions](https://mlsanity.com/paper/1309.5821/) (2013)
- [Runtime Distributions and Criteria for Restarts](https://mlsanity.com/paper/1709.10405/) (2017)
- [Data Mining using Unguided Symbolic Regression on a Blast Furnace Dataset](https://mlsanity.com/paper/1309.5931/) (2013)
- [EduCTX: A blockchain-based higher education credit platform](https://mlsanity.com/paper/1710.09918/) (2017)
- [Effects of forecast errors on optimal utilisation in aggregate production planning with stochastic customer demand](https://mlsanity.com/paper/1812.00773/) (2018)
- [String Solving with Word Equations and Transducers: Towards a Logic for Analysing Mutation XSS (Full Version)](https://mlsanity.com/paper/1511.01633/) (2015)
- [The Stochastic Container Relocation Problem](https://mlsanity.com/paper/1703.04769/) (2017)
- [Resource-constrained multi-project scheduling with activity and time flexibility](https://mlsanity.com/paper/1902.09244/) (2019)

## Built on by (most cited first, 1 of 1)

- [Steel Phase Kinetics Modeling using Symbolic Regression](https://mlsanity.com/paper/2212.10284/) (2022)

## Abstract (arXiv)

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.