In recent years, graph neural networks (GNNs) have shown tremendous promise in solving problems in high energy physics, materials science, and fluid dynamics. In this work, we introduce a new application for GNNs in the physical sciences: instrumentation design. As a case study, we apply GNNs to simulate models of the Laser Interferometer Gravitational-Wave Observatory (LIGO) and show that they are capable of accurately capturing the complex optical physics at play, while achieving runtimes 815 times faster than state of the art simulation packages. We discuss the unique challenges this problem provides for machine learning models. In addition, we provide a dataset of high-fidelity optical physics simulations for three interferometer topologies, which can be used as a benchmarking suite for future work in this direction.
Understanding the magnetic field environment around Mars and its response to upstream solar wind conditions provide key insights into the processes driving atmospheric ion escape. To date, global models of Martian induced magnetosphere have been exclusively physics-based, relying on computationally intensive simulations. For the first time, we develop a data-driven model of the Martian induced magnetospheric magnetic field using Physics-Informed Neural Network (PINN) combined with MAVEN observations and physical laws. Trained under varying solar wind conditions, including B_IMF, P_SW, and θ_cone, the data-driven model accurately reconstructs the three-dimensional magnetic field configuration and its variability in response to upstream solar wind drivers. Based on the PINN results, we identify key dependencies of magnetic field configuration on solar wind parameters, including the hemispheric asymmetries of the draped field line strength in the Mars-Solar-Electric coordinates. These findings demonstrate the capability of PINNs to reconstruct complex magnetic field structures in the Martian induced magnetosphere, thereby offering a promising tool for advancing studies of solar wind-Mars interactions.
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 summarise 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 emphasise 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.