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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 present a catalog of 4539 fast radio bursts (FRBs) observed with the Canadian Hydrogen Intensity Mapping Experiment telescope between 2018 July 25 and 2023 September 15. These bursts originate from 3641 unique sources, including 981 bursts from 83 known repeating sources. For each FRB, the catalog provides an O(10′) estimate of sky location along with corresponding measurements of cumulative exposure time and survey sensitivity over the observing period. It includes a total-intensity dynamic spectrum between 400 and 800 MHz at 0.983 ms resolution. From this spectrum, we constrain a model of the burst morphology and measure key parameters such as arrival time, intrinsic temporal width, dispersion measure, scattering time, and flux density. This second catalog includes all FRBs from the first catalog, with every event reprocessed using a uniform and improved analysis framework. We show that previously published inferences remain valid under the updated measurements. We assess consistency of the detection rate across observational parameters, present initial distributions of burst properties, and outline ongoing and future studies that will use this catalog to investigate the nature of FRBs and their utility as astrophysical and cosmological probes.

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.