A Physics Informed Neural Network For Deriving MHD State Vectors From Global Active Regions Observations
Accurate early prediction of solar active regions (ARs) requires physically consistent initialization of the tachocline—the sub-photospheric magnetohydrodynamic (MHD) dynamo layer—yet conventional inversion methods lack physical self-consistency. Method: We propose PINNBARDS, a novel physics-informed neural network (PINN) framework that embeds the shallow-water MHD equations as hard constraints to enable end-to-end reconstruction of dynamically evolving, energy- and momentum-conserving tachocline initial states from observed photospheric magnetic ribbon geometry (e.g., SDO/HMI data). Contribution/Results: Applied to 14 February 2024 observations, PINNBARDS successfully reconstructed antisymmetric active band structures with optimal toroidal field strength of 20–30 kG and latitudinal width ≈10°, in excellent agreement with low-order radial-mode excitation theory. This constitutes the first physically grounded, observationally constrained initialization scheme enabling week-scale forecasting of AR emergence and associated flare activity.