  The Helioseismic and Magnetic Imager (HMI) onboard NASA's Solar Dynamics
Observatory (SDO) produces estimates of the photospheric magnetic field which
are a critical input to many space weather modelling and forecasting systems.
The magnetogram products produced by HMI and its analysis pipeline are the
result of a per-pixel optimization that estimates solar atmospheric parameters
and minimizes disagreement between a synthesized and observed Stokes vector. In
this paper, we introduce a deep learning-based approach that can emulate the
existing HMI pipeline results two orders of magnitude faster than the current
pipeline algorithms. Our system is a U-Net trained on input Stokes vectors and
their accompanying optimization-based VFISV inversions. We demonstrate that our
system, once trained, can produce high-fidelity estimates of the magnetic field
and kinematic and thermodynamic parameters while also producing meaningful
confidence intervals. We additionally show that despite penalizing only
per-pixel loss terms, our system is able to faithfully reproduce known
systematic oscillations in full-disk statistics produced by the pipeline. This
emulation system could serve as an initialization for the full Stokes inversion
or as an ultra-fast proxy inversion. This work is part of the NASA Heliophysics
DRIVE Science Center (SOLSTICE) at the University of Michigan, under grant NASA
80NSSC20K0600E, and has been open sourced.
