Professor Pedro Ferreira

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:

Current cosmological data seem to show that dark energy is evolving in time and that it possibly crossed the phantom divide in the past. So far the only theories that lead to such a behavior involve a nontrivial coupling between dark energy, in the form of a scalar field, and the gravitational or matter sector. We show that there is another possibility involving both a nontrivial kinetic sector in a cubic Galileon theory and a scalar field potential that breaks the Galileon shift symmetry, which can lead to a similar phenomenology on large scales. We perform a full Bayesian analysis using the latest cosmological data, including DESI DR2 baryonic acoustic oscillation measurements, type Ia SNe measurements from DESY5, Union3, and Pantheon+, and cosmic microwave background data from Planck and ACT. We find that it is statistically strongly favored over a universe dominated by a cosmological constant (with a Bayes factor of log B ≃ 6.5). Yet, as with other nonminimally coupled theories, it has severe ancillary gravitational effects. These can be mitigated to some extent, but as with other viable theories, the penalty is ever more elaborate scalar field models of dark energy.