Beecroft Institute for Particle Astrophysics and Cosmology

Abstract:

Symbolic regression (SR) is the machine learning (ML) method for learning functions from data. After a brief overview of the SR landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown (and probably significant) probability of failing to find any given good function, and they suffer from ambiguity and poorly justified assumptions in their function-selection procedure. To address these, I propose an exhaustive search and model selection by the minimum description length (MDL) principle, which allows accuracy and complexity to be directly traded off by measuring each in units of information. I showcase the resulting publicly available Exhaustive Symbolic Regression (ESR) algorithm on three open problems in astrophysics: the expansion history of the universe, the effective behaviour of gravity in galaxies and the potential of the inflaton field. In each case, the algorithm identifies many functions superior to the literature standards. This general-purpose methodology should find widespread utility in science and beyond. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of BSM physics this model has a number (four) of arbitrary parameters, which determine the experimental signals, and cosmological observables such as the dark matter relic density. We show that analysis of the phenomenology can be greatly accelerated by using symbolic expressions derived for the observables in terms of the input parameters. Here we focus on the Higgs mass, the cold dark matter relic density and the contribution to the anomalous magnetic moment of the muon. We find that SR can produce remarkably accurate expressions. Using them we make global fits to derive the posterior probability densities of the CMSSM input parameters which are in good agreement with those performed using conventional methods. Moreover, we demonstrate a major advantage of SR, which is the ability to make fits using differentiable methods rather than sampling methods. We also compare the method with neural network (NN) regression. SR produces more globally robust results, while NNs require data that is focused on the promising regions in order to be equally performant. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

Resolved rotation curves (RCs) are our best probe of the dark matter distribution around individual galaxies. However their acquisition is resource-intensive, rendering them impractical for large-scale surveys and studies at higher redshift. Spatially integrated flux profiles on the other hand are observationally abundant and also probe dynamics across the whole disc. Despite this, they are typically only studied using the highly compressed linewidth summary statistic, discarding much of the available information. Here we construct a Bayesian model to infer halo properties from the full shape of the spatially integrated 21-cm line profile of a galaxy, utilizing all the available information. We validate our model by assessing the consistency of halo parameters obtained from the flux profile with those obtained from RC fits for a sample of 20 galaxies where both are available, finding good agreement provided the profile is not strongly asymmetric. We study the relative constraining power (quantified using the Kullback–Leibler divergence of the posterior from the prior), finding the flux profile inference recovers posteriors on generalized Navarro–Frenk–White halo parameters on average three times tighter than those from the linewidth, and in some cases as tight as those from resolved RCs. Finally we introduce and validate a probabilistic empirical model for the spatial distribution of , enabling our model to be applied to data sets for which no spatially resolved information is available. As the next-generation of observatories comes online, our framework will enable mass modelling in new regimes, with particular utility for constraining the dark matter content of galaxies across cosmic time.

Abstract:

Abstract:

Cosmological inference from weak lensing (WL) surveys is increasingly limited by uncertainties in baryonic physics, which suppress the non-linear matter power spectrum on small scales. Multiprobe analyses that incorporate complementary tracers of the gas distribution around haloes offer a pathway to calibrate these effects and recover unbiased cosmological information. In this work, we forecast the constraining power of a joint analysis combining fiducial data from a Stage-IV WL survey with measurements of the dispersion measure from fast radio bursts (FRBs). We evaluate the ability of this approach to simultaneously constrain cosmological parameters and the astrophysical processes governing baryonic feedback, and we quantify the impact of key FRB systematics, including redshift uncertainties and source clustering. We find that, even after accounting for these effects, a 32-point analysis of WL and FRBs significantly improves cosmological constraints, reducing the degradation factor on by compared to WL alone. We further show that FRBs alone are sensitive only to a degenerate combination of the key baryonic parameters, and , and that the inclusion of WL measurements breaks this degeneracy. Finally, we extend our framework to incorporate galaxy clustering measurements using luminous red galaxy and emission line galaxy samples, performing a unified 62-point analysis of WL, dispersion measures of FRBs, and galaxy clustering. While this combined approach tightens constraints on and , it does not lead to a significant improvement in constraints beyond those obtained from WL and FRBs alone.