# Data-driven Modelling of Dynamical Systems Using Tree Adjoining Grammar and Genetic Programming

## TL;DR

This paper presents a novel data-driven approach for modeling non-linear dynamical systems using Genetic Programming and Tree Adjoining Grammar, tested on real physical systems with varying complexities and data availability.

## Contribution

It introduces a new method combining GP with Tree Adjoining Grammar to improve model structure search in data-driven dynamical system modeling.

## Key findings

- Successfully modeled real physical systems with diverse challenges.
- Demonstrated the effectiveness of the approach across multiple case studies.
- Provided critical analysis of the method's performance.

## Abstract

State-of-the-art methods for data-driven modelling of non-linear dynamical systems typically involve interactions with an expert user. In order to partially automate the process of modelling physical systems from data, many EA-based approaches have been proposed for model-structure selection, with special focus on non-linear systems. Recently, an approach for data-driven modelling of non-linear dynamical systems using Genetic Programming (GP) was proposed. The novelty of the method was the modelling of noise and the use of Tree Adjoining Grammar to shape the search-space explored by GP. In this paper, we report results achieved by the proposed method on three case studies. Each of the case studies considered here is based on real physical systems. The case studies pose a variety of challenges. In particular, these challenges range over varying amounts of prior knowledge of the true system, amount of data available, the complexity of the dynamics of the system, and the nature of non-linearities in the system. Based on the results achieved for the case studies, we critically analyse the performance of the proposed method.