用符号回归从引力透镜数据直接推断暗物质晕密度分布，不依赖模拟假设。
Constraining dark matter halo profiles with symbolic regression
- 用符号回归搜索最优解析表达式，平衡拟合精度与简洁性
- 5%误差下20个簇样本即可复现NFW轮廓，高误差时更简单模型更优
- 适合研究暗物质分布的真实约束，尤其关注外区数据主导的模型选择
暗物质晕通常用固定形式的径向密度剖面描述（如NFW），但模拟结果受暗物质物理和恒星建模不确定性影响。本文提出一种方法，利用穷举符号回归（ESR）直接从观测数据约束晕密度剖面。我们在具有NFW剖面的合成簇弱引力透镜过量表面密度（ESD）数据上测试该方法。基于真实数据设定每个数据点为常数分数误差，并改变误差水平与簇数，探究数据精度与样本量对模型选择的影响。当分数误差约为5%时，即使仅20个簇也能恢复NFW轮廓；在当前巡天代表性的较高误差下，更简单的函数更受青睐，尽管NFW仍具竞争力。这一偏好源于弱透镜误差在外部区域最小，导致拟合主要由外区剖面主导。因此，ESR提供了一种无需模拟、稳健的框架，可用于检验质量模型并判断数据真正约束的晕剖面特征。
原文摘要 · Abstract (English)
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.
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