# Unit-Aware Genetic Programming for the Development of Empirical Equations

arXiv: https://arxiv.org/abs/2405.18896 · HTML: https://mlsanity.com/paper/2405.18896/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 29 May 2024.

## Builds on (most cited first, 8 of 8)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge](https://mlsanity.com/paper/2209.06257/) (2022)
- [Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition](https://mlsanity.com/paper/2304.01117/) (2023)
- [Consistent Feature Construction with Constrained Genetic Programming for Experimental Physics](https://mlsanity.com/paper/1908.08005/) (2019)
- [Introducing Thermodynamics-Informed Symbolic Regression -- A Tool for Thermodynamic Equations of State Development](https://mlsanity.com/paper/2309.02805/) (2023)
- [Shape-constrained Symbolic Regression with NSGA-III](https://mlsanity.com/paper/2209.13851/) (2022)

## Built on by (most cited first, 3 of 3)

- [Improving Genetic Programming for Symbolic Regression with Equality Graphs](https://mlsanity.com/paper/2501.17848/) (2025)
- [rEGGression: an Interactive and Agnostic Tool for the Exploration of Symbolic Regression Models](https://mlsanity.com/paper/2501.17859/) (2025)
- [Equality Graph Assisted Symbolic Regression](https://mlsanity.com/paper/2511.01009/) (2025)

## Abstract (arXiv)

When developing empirical equations, domain experts require these to be accurate and adhere to physical laws. Often, constants with unknown units need to be discovered alongside the equations. Traditional unit-aware genetic programming (GP) approaches cannot be used when unknown constants with undetermined units are included. This paper presents a method for dimensional analysis that propagates unknown units as ''jokers'' and returns the magnitude of unit violations. We propose three methods, namely evolutive culling, a repair mechanism, and a multi-objective approach, to integrate the dimensional analysis in the GP algorithm. Experiments on datasets with ground truth demonstrate comparable performance of evolutive culling and the multi-objective approach to a baseline without dimensional analysis. Extensive analysis of the results on datasets without ground truth reveals that the unit-aware algorithms make only low sacrifices in accuracy, while producing unit-adherent solutions. Overall, we presented a promising novel approach for developing unit-adherent empirical equations.