Symbolic Regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of symbolic mathematical constraints) allows for the generation of expressions that are meaningful with respect to theory while also being consistent with data. We specifically examine the addition of constraints to traditional genetic algorithm (GA) based SR (PySR) as well as a Markov-chain Monte Carlo (MCMC) based Bayesian SR architecture (Bayesian Machine Scientist), and apply these to rediscovering adsorption equations from experimental, historical datasets. We find that, while hard constraints prevent GA and MCMC SR from searching, soft constraints can lead to improved performance both in terms of search effectiveness and model meaningfulness, with computational costs increasing by about an order-of-magnitude. If the constraints do not correlate well with the dataset or expected models, they can hinder the search of expressions. We find Bayesian SR is better these constraints (as the Bayesian prior) than by modifying the fitness function in the GA

翻译：符号回归（SR）能够生成拟合给定数据集的可解释、简洁表达式，相较于黑箱方法使人类更易理解其结构。通过引入符号数学约束形式的背景知识，可在生成与理论相关且与数据一致的表达式时发挥重要作用。我们具体研究了在传统遗传算法（GA）基础SR（PySR）和基于马尔可夫链蒙特卡洛（MCMC）的贝叶斯SR架构（贝叶斯机器科学家）中添加约束的效果，并将其应用于从实验历史数据集重发现吸附方程。研究发现：硬约束会阻碍GA和MCMC-SR的搜索过程，而软约束则可提升搜索效率与模型可解释性，但计算成本约增加一个数量级。若约束与数据集或预期模型相关性不佳，反而会抑制表达式搜索。结果表明，贝叶斯SR通过将约束作为贝叶斯先验引入，相较于修改GA中的适应度函数能更有效地利用这些约束。