Unit-Aware Genetic Programming for the Development of Empirical Equations

TL;DR

This paper introduces a novel unit-aware genetic programming method that incorporates dimensional analysis to discover empirical equations with unknown constants and units, ensuring physical consistency.

Contribution

It proposes three innovative methods to integrate dimensional analysis into genetic programming, enabling the development of physically consistent empirical equations with unknown units.

Findings

Comparable performance to baseline without dimensional analysis

Low accuracy sacrifices with unit-adherent solutions

Effective handling of unknown units in empirical equations

Abstract

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.