Hintze Centre for Astrophysical Surveys

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 extensive ultraviolet to optical photometric and optical to near-infrared (NIR) spectroscopic follow-up observations of the nearby intermediate-luminosity (MV = −16.81 ± 0.19 mag) Type Iax supernovae (SNe Iax) 2024pxl in NGC 6384. SN 2024pxl exhibits a faster light curve than the high-luminosity members of this class, and slower than low-luminosity events. The observationally well-constrained rise time of ∼11 days and an estimated synthesized 56Ni mass of 0.03 M⊙, based on analytical modeling of the integrated spectral energy distribution light curve, are consistent with models of the weak deflagration of a carbon-oxygen white dwarf. Our optical spectral sequence of SN 2024pxl shows weak Si ii lines and spectral evolution similar to other high-luminosity SNe Iax, but also a prominent early-time C ii line, like lower-luminosity SNe Iax. The late-time optical spectrum of SN 2024pxl closely matches that of SN 2014dt, and its NIR spectral evolution aligns with that of other well-studied, high-luminosity SNe Iax. The spectral-line expansion velocities of SN 2024pxl are at the lower end of the SNe Iax velocity distribution, and the velocity distribution of iron-group elements compared to intermediate-mass elements suggests that the ejecta are mixed on large scales, as expected in pure deflagration models. SN 2024pxl exhibits characteristics intermediate between those of high-luminosity and low-luminosity SNe Iax, further establishing a link across this diverse class.

Abstract:

Extragalactic fast X-ray transients (eFXTs) represent a rapidly growing class of high-energy phenomena, whose physical origins remain poorly understood. With its wide-field, sensitive all-sky monitoring, the Einstein Probe (EP) has greatly increased the discovery rate of eFXTs. The search for and identification of the optical counterparts of eFXTs are vital for understanding their classification and constraining their physical origin. Yet, a considerable fraction of eFXTs still lack secure classifications due to the absence of timely follow-up observations. We carry out a systematic search of publicly available optical survey data and transient databases (including the Zwicky Transient Facility and the Transient Name Server) for optical counterparts to eFXT candidates detected by EP. In this paper, we describe our ongoing program and report the first results. Specifically, we identified the eFXT EP240506a to be associated with a UV/optical counterpart, AT 2024ofs. Spectroscopy of its host galaxy with the Very Large Telescope yields a redshift of z = 0.120 ± 0.002. By combining archival survey data with early-time multiwavelength observations, we find that the luminosity and light-curve evolution of AT 2024ofs are consistent with a core-collapse supernova origin. From detectability simulations, we estimate a local event rate density ρ0=8.8−3.9+21.2yr−1Gpc−3 for EP240506a-like events, and completeness-corrected rate of about 36–78 yr−1 Gpc−3 for EP-detected X-ray transients associated with supernovae. Our results demonstrate the potential of EP to uncover prompt high-energy emission from core-collapse supernovae and underscore the critical importance of timely follow-up of future eFXT events.