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We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods by inducing a library of abstract textual concepts. Our algorithm, called LaSR, uses zero-shot queries to a large language model (LLM) to discover and evolve concepts occurring in known high-performing hypotheses. We discover new hypotheses using a mix of standard evolutionary steps and LLM-guided steps (obtained through zero-shot LLM queries) conditioned on discovered concepts. Once discovered, hypotheses are used in a new round of concept abstraction and evolution. We validate LaSR on the Feynman equations, a popular SR benchmark, as well as a set of synthetic tasks. On these benchmarks, LaSR substantially outperforms a variety of state-of-the-art SR approaches based on deep learning and evolutionary algorithms. Moreover, we show that LASR can be used to discover a new and powerful scaling law for LLMs. 

Complex astrophysical systems often exhibit low-scatter relations between observable properties (e.g., luminosity, velocity dispersion, oscillation period). These scaling relations illuminate the underlying physics, and can provide observational tools for estimating masses and distances. Machine learning can provide a fast and systematic way to search for new scaling relations (or for simple extensions to existing relations) in abstract high-dimensional parameter spaces. We use a machine learning tool called symbolic regression (SR), which models patterns in a dataset in the form of analytic equations. We focus on the Sunyaev-Zeldovich flux−cluster mass relation ( Y SZ − M ), the scatter in which affects inference of cosmological parameters from cluster abundance data. Using SR on the data from the IllustrisTNG hydrodynamical simulation, we find a new proxy for cluster mass which combines Y SZ and concentration of ionized gas ( c gas ): M ∝ Y conc 3/5 ≡ Y SZ 3/5 (1 − A c gas ). Y conc reduces the scatter in the predicted M by ∼20 − 30% for large clusters ( M ≳ 10 14 h −1 M ⊙ ), as compared to using just Y SZ . We show that the dependence on c gas is linked to cores of clusters exhibiting larger scatter than their outskirts. Finally, we test Y conc on clusters from CAMELS simulations and show that Y conc is robust against variations in cosmology, subgrid physics, and cosmic variance. Our results and methodology can be useful for accurate multiwavelength cluster mass estimation from upcoming CMB and X-ray surveys like ACT, SO, eROSITA and CMB-S4. 

ABSTRACT Feedback from active galactic nuclei (AGNs) and supernovae can affect measurements of integrated Sunyaev–Zeldovich (SZ) flux of haloes (YSZ) from cosmic microwave background (CMB) surveys, and cause its relation with the halo mass (YSZ–M) to deviate from the self-similar power-law prediction of the virial theorem. We perform a comprehensive study of such deviations using CAMELS, a suite of hydrodynamic simulations with extensive variations in feedback prescriptions. We use a combination of two machine learning tools (random forest and symbolic regression) to search for analogues of the Y–M relation which are more robust to feedback processes for low masses ($$M\lesssim 10^{14}\, \mathrm{ h}^{-1} \, \mathrm{ M}_\odot$$); we find that simply replacing Y → Y(1 + M*/Mgas) in the relation makes it remarkably self-similar. This could serve as a robust multiwavelength mass proxy for low-mass clusters and galaxy groups. Our methodology can also be generally useful to improve the domain of validity of other astrophysical scaling relations. We also forecast that measurements of the Y–M relation could provide per cent level constraints on certain combinations of feedback parameters and/or rule out a major part of the parameter space of supernova and AGN feedback models used in current state-of-the-art hydrodynamic simulations. Our results can be useful for using upcoming SZ surveys (e.g. SO, CMB-S4) and galaxy surveys (e.g. DESI and Rubin) to constrain the nature of baryonic feedback. Finally, we find that the alternative relation, Y–M*, provides complementary information on feedback than Y–M. 

Abstract A wealth of cosmological and astrophysical information is expected from many ongoing and upcoming large-scale surveys. It is crucial to prepare for these surveys now and develop tools that can efficiently extract most information. We present HIF low : a fast generative model of the neutral hydrogen (H i ) maps that is conditioned only on cosmology (Ω m and σ 8 ) and designed using a class of normalizing flow models, the masked autoregressive flow. HIF low is trained on the state-of-the-art simulations from the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project. HIF low has the ability to generate realistic diverse maps without explicitly incorporating the expected two-dimensional maps structure into the flow as an inductive bias. We find that HIF low is able to reproduce the CAMELS average and standard deviation H i power spectrum within a factor of ≲2, scoring a very high R 2 > 90%. By inverting the flow, HIF low provides a tractable high-dimensional likelihood for efficient parameter inference. We show that the conditional HIF low on cosmology is successfully able to marginalize over astrophysics at the field level, regardless of the stellar and AGN feedback strengths. This new tool represents a first step toward a more powerful parameter inference, maximizing the scientific return of future H i surveys, and opening a new avenue to minimize the loss of complex information due to data compression down to summary statistics.