  Both NASA's Solar Dynamics Observatory (SDO) and the JAXA/NASA Hinode mission
include spectropolarimetric instruments designed to measure the photospheric
magnetic field. SDO's Helioseismic and Magnetic Imager (HMI) emphasizes
full-disk high-cadence and good spatial resolution data acquisition while
Hinode's Solar Optical Telescope Spectro-Polarimeter (SOT-SP) focuses on high
spatial resolution and spectral sampling at the cost of a limited field of view
and slower temporal cadence. This work introduces a deep-learning system named
SynthIA (Synthetic Inversion Approximation), that can enhance both missions by
capturing the best of each instrument's characteristics. We use SynthIA to
produce a new magnetogram data product, SynodeP (Synthetic Hinode Pipeline),
that mimics magnetograms from the higher spectral resolution Hinode/SOT-SP
pipeline, but is derived from full-disk, high-cadence, and lower
spectral-resolution SDO/HMI Stokes observations. Results on held-out data show
that SynodeP has good agreement with the Hinode/SOT-SP pipeline inversions,
including magnetic fill fraction, which is not provided by the current SDO/HMI
pipeline. SynodeP further shows a reduction in the magnitude of the 24-hour
oscillations present in the SDO/HMI data. To demonstrate SynthIA's generality,
we show the use of SDO/AIA data and subsets of the HMI data as inputs, which
enables trade-offs between fidelity to the Hinode/SOT-SP inversions, number of
observations used, and temporal artifacts. We discuss possible generalizations
of SynthIA and its implications for space weather modeling. This work is part
of the NASA Heliophysics DRIVE Science Center (SOLSTICE) at the University of
Michigan under grant NASA 80NSSC20K0600E, and will be open-sourced.
