Application of Deep Learning to the Classification of Stokes Profiles: From the Quiet Sun to Sunspots

The morphology of circular polarisation profiles from solar spectropolarimetric observations encode information about the magnetic field strength, inclination, and line-of-sight velocity gradients. Previous studies used manual methods or unsupervised machine learning (ML) to classify the shapes of circular polarisation profiles. We trained a multi-layer perceptron (MLP) comparing classifications with unsupervised ML. The method was tested on quiet Sun datasets from DKIST, Hinode, and GREGOR, as well as simulations of granulation and a sunspot. We achieve validation metrics typically close to or above $90\%$. We also present the first statistical analysis of quiet Sun DKIST/ViSP data using inversions and our supervised classifier. We demonstrate that classifications with unsupervised ML alone can introduce systemic errors that could compromise statistical comparisons. DKIST and Hinode classifications in the quiet Sun are similar, despite our modelling indicating spatial resolution differences should alter the shapes of circular polarization signals. Asymmetrical (symmetrical) profiles are less (more) common in GREGOR than DKIST or Hinode data, consistent with narrower response functions in the $1564.85$ nm line. Single-lobed profiles are extremely rare in GREGOR data. In the sunspot simulation, the $630.25$ nm line produces ``double' profiles in the penumbra, likely a manifestation of magneto-optical effects in horizontal fields; these are rarer in the $1564.85$ nm line. We find the $1564.85$ nm line detects more reverse polarity magnetic fields in the penumbra in contradiction to observations. We detect mixed-polarity profiles in nearly one fifth of the penumbra. Supervised ML robustly classifies solar spectropolarimetric data, enabling detailed statistical analyses of magnetic fields.