Constraining dark matter halo profiles with symbolic regression

2025-11-28

AI Summary

Conventional modeling of dark matter halo density profiles relies heavily on N-body simulations and baryonic physics assumptions, introducing theoretical biases. Method: We propose an entirely data-driven approach based on Exhaustive Symbolic Regression (ESR) to infer halo density profiles directly from weak gravitational lensing observations, objectively balancing fitting accuracy and model simplicity without presupposing functional forms. Contribution/Results: Using simulated galaxy cluster surface mass density data, we systematically assess the impact of measurement uncertainty and sample size: with 5% observational error, as few as 20 clusters suffice to robustly recover the Navarro–Frenk–White (NFW) profile at high confidence; under typical current-survey uncertainties, although simpler functions are preferred, the NFW profile remains statistically competitive. This is the first method to construct halo structural models solely from observational data—free of prior functional assumptions—thereby establishing a new paradigm for empirically testing fundamental dark matter properties.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

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.

Problem

• Constraining dark matter halo density profiles directly from observational data
• Testing simulation-independent methods using symbolic regression on weak lensing measurements
• Determining which halo profile features are genuinely constrained by current data precision

Innovation

• Using symbolic regression to constrain halo profiles
• Testing method on mock weak lensing data with NFW profiles
• Providing simulation-independent framework for model selection