Dr Harry Desmond

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:

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:

Measuring galaxy rotation curves is critical for inferring the properties of dark-matter haloes in the Lambda cold dark matter (CDM) paradigm. We present H i rotation curves and mass models for 20 galaxies from the MIGHTEE survey. Using extended H i kinematics, we construct resolved mass models that include stellar, gaseous, and dark-matter components. Stellar masses are derived using 3.6 m imaging under fixed mass-to-light ratio () assumptions and are complemented, for the first time for a H i-selected sample, by spatially resolved , obtained from multiwavelength spectral energy distribution fitting. We examine the ratio of baryonic to observed rotation velocity () at the characteristic radius . Adopting a fixed yields a clear dependence of on galaxy luminosity, while adopting substantially weakens this trend. In contrast, the resolved analysis preserves the luminosity dependence while modifying the stellar contribution on a galaxy-by-galaxy basis, providing a more accurate representation of the underlying relation. We model the dark-matter haloes using Navarro–Frenk–White profiles and find that the different assumptions for a fixed a systematically shift galaxies relative to the theoretical stellar-to-halo mass and baryonic-to-halo mass relations, while the spatially varying yields the closest agreement with theoretical benchmarks within CDM. We therefore demonstrate that future investigations of the dark matter properties of galaxies using rotation curves need to account for varying across individual galaxy profiles and between galaxies in order to obtain accurate measurements of the dark matter, and therefore test CDM.

Abstract:

If dark matter annihilates into standard model particles with a cross section which is velocity dependent, then Local Group dwarf galaxies will not be the best place to search for the resulting gamma ray emission. A greater flux would be produced by more distant and massive halos, with larger velocity dispersions. We construct full-sky predictions for the gamma ray emission from galaxy- and cluster-mass halos within $\sim 200\mathrm{Mpc}$ using a suite of constrained $N$ -body simulations () based on the Bayesian Origin Reconstruction from Galaxies algorithm. Comparing to observations from the Large Area Telescope and marginalizing over reconstruction uncertainties and other astrophysical contributions to the flux, we obtain constraints on the cross section which are 2 (7) orders of magnitude tighter than those obtained from dwarf spheroidals for $p$ -wave ( $d$ -wave) annihilation. We find no evidence for either type of annihilation from dark matter particles with masses in the range $m_{\chi }=2–500\mathrm{GeV}/c^2$ , for any channel. As an example, for annihilations producing bottom quarks with $m_{\chi }=10\mathrm{GeV}/c^2$ , we find $a_1<2.4\times {10}^{-21}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ and $a_2<3.0\times {10}^{-18}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ at 95% confidence, where the product of the cross section, $\sigma$ , and relative particle velocity, $v$ , is given by $\sigma v=a_{\ell }(v/c{)}^{2\ell }$ and $\ell =1$ , 2 for $p$ - and $d$ -wave annihilation, respectively. Our bounds, although failing to exclude the thermal relic cross section for velocity-dependent annihilation channels, are among the tightest to date.

Abstract:

Abstract Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the Special issue on symbolic regression for the physical sciences, motivated by the Royal Society discussion meeting held in April 2025. The contributions collected here span applications from automated equation discovery and emergent-phenomena modelling to the construction of compact emulators for computationally expensive simulations. The introductory review outlines the conceptual foundations of SR, contrasts it with conventional regression approaches and surveys its main use cases in the physical sciences, including the derivation of effective theories, empirical functional forms and surrogate models. We summarize methodological considerations such as search-space design, operator selection, complexity control, feature selection and integration with modern AI approaches. We also highlight ongoing challenges, including scalability, robustness to noise, overfitting and computational complexity. Finally, we emphasize emerging directions, particularly the incorporation of symmetry constraints, asymptotic behaviour and other theoretical information. Taken together, the papers in this Special issue illustrate the accelerating progress of SR and its growing relevance across the physical sciences. This article is part of the discussion meeting issue ‘Symbolic regression in the physical sciences’.