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.

本论文提出了一种维度分析的方法，将未知单位作为“小丑”传播并返回单位违规的数量。我们提出了三种方法，即进化修剪、修复机制和多目标方法，以将维度分析集成到遗传编程算法中。对于有完整真实数据的数据集，实验证明进化修剪和多目标方法与无维度分析的基准方法具有可比较的性能。对于没有完整真实数据的数据集，对结果进行广泛分析表明，单位感知的算法在保持较高准确性的同时产生单位合规的解决方案。总体而言，我们提出了一种有前景的新方法，用于开发单位合规的经验方程。

单位感知遗传编程用于经验方程的发展