Dark matter haloes are typically characterised by radial density profiles with fixed forms motivated by simulations (e.g. NFW). However, simulation predictions depend on uncertain dark matter physics and baryonic modelling. Here, we present a method to constrain halo density profiles directly from observations using Exhaustive Symbolic Regression (ESR), a technique that searches the space of analytic expressions for the function that best balances accuracy and simplicity for a given dataset. We test the approach on mock weak lensing excess surface density (ESD) data of synthetic clusters with NFW profiles. Motivated by real data, we assign each ESD data point a constant fractional uncertainty and vary this uncertainty and the number of clusters to probe how data precision and sample size affect model selection. For fractional errors around 5%, ESR recovers the NFW profile even from samples as small as 20 clusters. At higher uncertainties representative of current surveys, simpler functions are favoured over NFW, though it remains competitive. This preference arises because weak lensing errors are smallest in the outskirts, causing the fits to be dominated by the outer profile. ESR therefore provides a robust, simulation-independent framework both for testing mass models and determining which features of a halo's density profile are genuinely constrained by the data.

翻译：暗物质晕通常由具有固定形式的径向密度轮廓所表征，这些形式受模拟结果启发（例如NFW轮廓）。然而，模拟预测依赖于不确定的暗物质物理和重子模型。本文提出一种方法，通过穷举符号回归（ESR）直接从观测数据约束晕密度轮廓，该技术通过搜索解析表达式空间，寻找在给定数据集中平衡准确性与简洁性的最优函数。我们在具有NFW轮廓的合成星系团模拟弱引力透镜过剩面密度（ESD）数据上测试该方法。基于真实数据特征，我们为每个ESD数据点分配恒定比例误差，并通过改变误差幅度和星系团数量，探究数据精度与样本量如何影响模型选择。当比例误差约为5%时，即使仅使用20个星系团的小样本，ESR仍能准确恢复NFW轮廓。在代表当前巡天观测的更高误差水平下，虽然NFW模型仍具竞争力，但更简单的函数更受青睐。这种偏好源于弱引力透镜误差在外围区域最小，导致拟合结果主要由外部轮廓主导。因此，ESR提供了一个独立于模拟的稳健框架，既能检验质量模型，又能确定晕密度轮廓的哪些特征真正受到数据的约束。