Beecroft Institute for Particle Astrophysics and Cosmology

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’.

Abstract:

We compared the performance of the flat-sky approximation and Limber approximation for the clustering analysis of the photometric galaxy catalogue of Euclid . We studied a 6-bin configuration, representing the first data release (DR1), and a 13-bin configuration, representing the third and final data release (DR3). We find that the Limber approximation is sufficiently accurate for the analysis of the wide bins of DR1. Instead, the 13 bins of DR3 cannot be modelled accurately with the Limber approximation. Instead, the flat-sky approximation is accurate to below 5% in recovering the angular power spectra of galaxy number counts in both cases and can be used to simplify the computation of the full power spectrum in harmonic space for the data analysis of DR3.

Abstract:

Local Universe dwarf galaxies can serve as both cosmological and mass assembly probes. Deep surveys have enabled the study of these objects down to the low surface brightness (LSB) regime. In this paper, we estimate Euclid ’s dwarf detection capabilities as well as limits of its MERge processing function (MER pipeline), which is responsible for producing the stacked mosaics and final catalogues. To do this, we injected mock dwarf galaxies in a real Euclid Wide Survey (EWS) field in the VIS band and compared the input catalogue to the final MER catalogue. The mock dwarf galaxies were generated using simple Sérsic models with structural parameters (including size and surface brightness) drawn from observed dwarf galaxy catalogues. These simulations represent an idealised case in the sense they do not account for additional factors such as ellipticity, morphology, or crowding. To characterise the detected dwarfs, we used the mean surface brightness inside the effective radius SB e (in mag arcsec −2 ). The final MER catalogues achieve a completenesses of 91% for SB e ∈ [21, 24] and 54% for SB e ∈ [24, 28]. These numbers do not take into account possible contaminants, including confusion with background galaxies at the location of the dwarfs. After taking those effects into account, they respectively became 86% and 38%. The MER pipeline performs a final local background subtraction with a small mesh size, leading to a flux loss for galaxies with R e > 10″. By using the final MER mosaics and reinjecting this local background, we obtained an image in which we recover reliable photometric properties for objects under the arcminute scale. This background-reinjected product is thus suitable for the study of Local Universe dwarf galaxies. Euclid ’s data reduction pipeline serves as a test bed for other deep surveys, particularly regarding background subtraction methods, a key issue in LSB science.