Reuter, JuliaJuliaReuterMartinek, ViktorViktorMartinekHerzog, RolandRolandHerzogMostaghim, SanazSanazMostaghim2024-10-222024-10-222024https://publica.fraunhofer.de/handle/publica/47788110.1007/978-3-031-70055-2_11When 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 multiobjective 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.engenetic programmingunit-awarenessphysics constraintsconference paper