# Constraining dark matter halo profiles with symbolic regression

arXiv: https://arxiv.org/abs/2511.23073 · HTML: https://mlsanity.com/paper/2511.23073/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 28 Nov 2025.

## Builds on (most cited first, 8 of 8)

- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Minimum Description Length Revisited](https://mlsanity.com/paper/1908.08484/) (2019)
- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [Priors for symbolic regression](https://mlsanity.com/paper/2304.06333/) (2023)
- [The Inefficiency of Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2404.17292/) (2024)
- [Optimal Inflationary Potentials](https://mlsanity.com/paper/2310.16786/) (2023)
- [Class Symbolic Regression: Gotta Fit 'Em All](https://mlsanity.com/paper/2312.01816/) (2023)
- [On the functional form of the radial acceleration relation](https://mlsanity.com/paper/2301.04368/) (2023)

## Abstract (arXiv)

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.