Spectropolarimetric Inversion in Four Dimensions with Deep Learning, A Physics-informed Machine Learning Method for 3D Solar Photosphere Reconstruction

Reconstructing the three-dimensional  (3D) solar atmosphere is a critical task for advancing our understanding of the magnetic and electric current structures 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, including both the fully disambiguated vector magnetic fields and the geometric height associated with each optical depth. Traditional disambiguation techniques typically resolve the azimuth ambiguity on a single, assumed-flat layer, thereby ignoring the intrinsic non-planar geometry of optical depth surfaces (e.g., the Wilson depression in sunspots), which is usually corrected only after magnetic field disambiguation. In contrast, our approach enforces the divergence-free condition across layers while mapping optical depth to physical height. Tests on magnetohydrodynamic simulations of quiet Sun, plage, and sunspot regions demonstrate that our method reliably recovers the horizontal magnetic field orientation in strongly magnetized pixels. By coupling the disambiguated vector magnetic fields with the inferred layer heights, we achieve self-consistent 3D reconstructions of the vector electric currents in the solar photosphere, paving the way for deeper insights into the dynamic processes of the lower solar atmosphere.