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Abstract Inferring the three-dimensional (3D) solar atmospheric structures from observations is a critical task for advancing our understanding of the magnetic-fields and electric currents that drive solar activity. In this work, we introduce a novel, physics-informed machine learning method to reconstruct the 3D structure of the lower solar atmosphere based on the output of optical-depth-sampled spectropolarimetric inversions, wherein both the fully disambiguated vector magnetic fields and the geometric height associated with each optical depth are returned simultaneously. Traditional techniques typically resolve the 180° azimuthal ambiguity assuming a single layer, either ignoring the intrinsic nonplanar physical geometry of constant optical-depth surfaces (e.g., the Wilson depression in sunspots) or correcting the effect as a postprocessing step. In contrast, our approach simultaneously maps the optical depths to physical heights, and enforces the divergence-free condition for magnetic fields fully in 3D. Tests on magnetohydrodynamic simulations of quiet Sun, plage, and a sunspot demonstrate that our method reliably recovers the horizontal magnetic-field orientation in locations with appreciable magnetic field strength. By coupling the resolutions of the azimuthal ambiguity and the geometric height problems, we achieve a self-consistent reconstruction of the 3D vector magnetic fields and, by extension, the electric current density and Lorentz force. This physics-constrained, label-free training paradigm is a generalizable, physics-anchored framework that extends across solar magnetic environments while improving the understanding of various solar puzzles. 

Abstract The National Science Foundation’s Daniel K. Inouye Solar Telescope (DKIST) will provide high-resolution, multiline spectropolarimetric observations that are poised to revolutionize our understanding of the Sun. Given the massive data volume, novel inference techniques are required to unlock its full potential. Here, we provide an overview of our “SPIn4D” project, which aims to develop deep convolutional neural networks (CNNs) for estimating the physical properties of the solar photosphere from DKIST spectropolarimetric observations. We describe the magnetohydrodynamic (MHD) modeling and the Stokes profile synthesis pipeline that produce the simulated output and input data, respectively. These data will be used to train a set of CNNs that can rapidly infer the four-dimensional MHD state vectors by exploiting the spatiotemporally coherent patterns in the Stokes profile time series. Specifically, our radiative MHD model simulates the small-scale dynamo actions that are prevalent in quiet-Sun and plage regions. Six cases with different mean magnetic fields have been explored; each case covers six solar-hours, totaling 109 TB in data volume. The simulation domain covers at least 25 × 25 × 8 Mm, with 16 × 16 × 12 km spatial resolution, extending from the upper convection zone up to the temperature minimum region. The outputs are stored at a 40 s cadence. We forward model the Stokes profile of two sets of Feilines at 630 and 1565 nm, which will be simultaneously observed by DKIST and can better constrain the parameter variations along the line of sight. The MHD model output and the synthetic Stokes profiles are publicly available, with 13.7 TB in the initial release. 

This white paper is on the HMCS Firefly mission concept study. Firefly focuses on the global structure and dynamics of the Sun's interior, the generation of solar magnetic fields, the deciphering of the solar cycle, the conditions leading to the explosive activity, and the structure and dynamics of the corona as it drives the heliosphere.