Unit-Aware Genetic Programming for the Development of Empirical Equations
<|reference_start|>Unit-Aware Genetic Programming for the Development of Empirical Equations: 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.<|reference_end|>
@article{reuter2024unit-aware,
    title={Unit-Aware Genetic Programming for the Development of Empirical
  Equations},
    author={Julia Reuter, Viktor Martinek, Roland Herzog, Sanaz Mostaghim},
    journal={arXiv preprint arXiv:2405.18896},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.18896},
    primaryClass={cs.LG cs.SC}
}