Physics-informed neural networks for advanced solar magnetic field extrapolations

Physics-informed neural networks (PINNs) provide a novel approach for data-driven numerical simulations, tackling challenges of discretization and enabling seamless integration of noisy data and physical models (e.g., partial differential equations). In this presentation, we discuss the results of our recent studies where we apply PINNs for coronal magnetic field extrapolations of the solar atmosphere, which are essential to understand the genesis and initiation of solar eruptions and to predict the occurrence of high-energy events from our Sun.We utilize our PINN to estimate the 3D coronal magnetic fields based on photospheric vector magnetograms and the force-free physical model. This approach provides state-of-the-art coronal magnetic field extrapolations in quasi real-time. We simulate the evolution of Active Region NOAA 11158 over 5 continuous days, where the derived time profile of the free magnetic energy unambiguously relates to the observed flare activity.We extend this approach by utilizing multi-height magnetic field measurements and combine them in a single magnetic field model. Our evaluation shows that the additional chromospheric field information leads to a more realistic approximation of the solar coronal magnetic field. In addition, our method intrinsically provides an estimate of the height corrugation of the observed magnetograms.We provide an outlook on our ongoing work where we use PINNs for global force-free magnetic field extrapolations. This approach enables a novel understanding of the global magnetic topology with a realistic treatment of current carrying fields.In summary, PINNs have the potential to greatly advance the field of numerical simulations, accelerate scientific research, and enable advanced space weather monitoring.