Authors: Qin Li (New Jersey Institute of Technology), Bo Shen (New Jersey Institute of Technology), Haodi Jiang (Sam Houston State University), Vasyl B. Yurchyshyn (Big Bear Solar Observatory), Taylor Baildon (Big Bear Solar Observatory), Kangwoo Yi (New Jersey Institute of Technology), Wenda Cao (Big Bear Solar Observatory), Haimin Wang (New Jersey Institute of Technology)

We introduce a Physics-Informed Neural Network (PINN) approach tailored for solving the Milne–Eddington (ME) inversion problem, specifically applied to spectropolarimetric observations from the Big Bear Solar Observatory’s Near-InfraRed Imaging Spectropolarimeter (BBSO/NIRIS) at the Fe I 1.56 µm lines. Traditional ME inversion methods, though widely used, are computationally intensive, sensitive to noise, and often struggle to accurately capture complex profile asymmetries resulting from gradients in magnetic field strength, orientation, and line-of-sight velocities. By embedding the ME radiative transfer equations directly into the neural network training as physics-informed constraints, our ME-PINN method robustly and efficiently retrieves magnetic field parameters, significantly outperforming traditional inversion methods in accuracy, noise resilience, and the ability to handle asymmetric and weak polarization signals. Quantitative comparisons demonstrate excellent agreement with well-established magnetic field measurements from the SDO/HMI and Hinode/SP instruments, with correlation coefficients exceeding 0.88. We further analyze the physical significance of profile asymmetries and the limitations inherent to the ME model assumption. Our results illustrate the potential of physics-informed machine learning methods in high-spatial-temporal solar observations, preparing for more sophisticated, real-time magnetic field analysis essential for next-generation solar telescopes and space weather forecasting.