Transformers for Stratified Spectropolarimetric Inversion: Proof of Concept

Abstract

Solar spectropolarimetric inversion -- inferring atmospheric conditions from the Stokes vector -- is a key diagnostic tool for understanding solar magnetism, but traditional inversion methods are computationally expensive and sensitive to local minima. Advances in artificial intelligence (AI) offer faster solutions, but are often restricted to shallow models or a few spectral lines. We present a proof-of-concept study using a transformer machine learning (ML) model for multi-line, full-Stokes inversion, to infer stratified parameters from synthetic spectra produced from 3D magnetohydrodynamic simulations. We synthesise a large set of Stokes vectors using forward modelling across 15 spectral lines spanning the deep photosphere towards the chromosphere. The model maps full-Stokes input to temperature, magnetic field strength, inclination, azimuth (encoded as $\sin2\phi$, $\cos2\phi$), and line-of-sight velocity as a function of optical depth. The transformer incorporates an attention mechanism that allows the model to focus on the most informative regions of the spectrum for each inferred parameter, and uses positional embedding to encode wavelength and depth order. We benchmark it against a multilayer perceptron (MLP), test robustness to noise, and assess generalisation. The transformer outperforms the MLP, especially in the higher layers and for magnetic parameters, yielding higher correlations and more regularised stratifications. The model retains strong performance across a range of noise levels typical for real observations, with magnetic parameter inference degrading predictably while temperature and velocity remain stable. We explore attention maps, linking the transformer's learned behaviour to line-formation physics.