Exhaustive enumeration of functions up to complexity k across operator bases shows the integrability fraction declines with k but rises sharply with logarithms, and the method discovers three integrals that resist SymPy, Mathematica, RUBI, FriCAS, Maxima, and Giac.
Constraining dark matter halo profiles with symbolic regression
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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.
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Exhaustive symbolic regression identifies low-complexity functional forms for luminosity and mass functions that outperform Schechter and Press-Schechter parametrizations while satisfying physical extrapolation and integration constraints.
Bootstrap-based symbolic regression on supernova and BAO data finds mild 2-4 sigma deviations from FLRW consistency relations, which if real would rule out most FLRW-based solutions to cosmological tensions.
citing papers explorer
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Exhaustive Symbolic Integration: Integration by Differentiation and the Landscape of Symbolic Integrability
Exhaustive enumeration of functions up to complexity k across operator bases shows the integrability fraction declines with k but rises sharply with logarithms, and the method discovers three integrals that resist SymPy, Mathematica, RUBI, FriCAS, Maxima, and Giac.
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The functional form of galaxy and halo luminosity and mass functions
Exhaustive symbolic regression identifies low-complexity functional forms for luminosity and mass functions that outperform Schechter and Press-Schechter parametrizations while satisfying physical extrapolation and integration constraints.
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Model-independent constraints on generalized FLRW consistency relations with bootstrap-based symbolic regression
Bootstrap-based symbolic regression on supernova and BAO data finds mild 2-4 sigma deviations from FLRW consistency relations, which if real would rule out most FLRW-based solutions to cosmological tensions.