SOLARNET Conference: The Many Scales of the Magnetic Sun

Physics-informed neural networks (PINNs) provide a novel approach for 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 highlight the new opportunities for solar magnetic field modelling that are enabled through physics-informed machine learning.
We present a novel approach for coronal magnetic field extrapolation using physics informed neural networks. The neural network is optimized to match observations of the photospheric magnetic field vector at the bottom-boundary, while simultaneously satisfying the force-free and divergence-free equations in the entire simulation volume. We demonstrate that our method can account for noisy data and deviates from the physical model where the force-free magnetic field assumption cannot be satisfied.
We utilize meta-learning concepts to simulate the evolution of the active region 11158. Our simulation of 5 days of observations at full cadence, requires about 12 hours of total computation time. The derived evolution of the free magnetic energy and helicity in the active region, shows that our model captures flare signatures, and that the depletion of free magnetic energy spatially aligns with the observed EUV emission. With this we present the first method that can perform realistic magnetic field extrapolations in quasi real-time, which enables advanced space weather monitoring.
We conclude with an outlook on our ongoing work where we extend this approach to create a new class of MHD simulations, that can flexibly incorporate additional observational constraints and perform fast computations.