  Non-linear force-free extrapolations are a common approach to estimate the 3D
topology of coronal magnetic fields based on photospheric vector magnetograms.
The force-free assumption is a valid approximation at coronal heights, but for
the dense plasma conditions in the lower atmosphere, this assumption is not
satisfied. In this study, we utilize multi-height magnetic field measurements
in combination with physics-informed neural networks to advance solar magnetic
field extrapolations. We include a flexible height-mapping, which allows us to
account for the different formation heights of the observed magnetic field
measurements. The comparison to analytical and simulated magnetic fields
demonstrates that including chromospheric magnetic field measurements leads to
a significant improvement of our magnetic field extrapolations. We also apply
our method to chromospheric line-of-sight magnetograms, from the Vector
Spectromagnetograph (VSM) on the Synoptic Optical Long-term Investigations of
the Sun (SOLIS) observatory, in combination with photospheric vector
magnetograms, from the Helioseismic Magnetic Imager (HMI) onboard the Solar
Dynamic Observatory (SDO). The comparison to observations in extreme
ultraviolet wavelengths shows that the additional chromospheric information
leads to a better agreement with the observed coronal structures. In addition,
our method intrinsically provides an estimate of the corrugation of the
observed magnetograms. With this new approach, we make efficient use of
multi-height magnetic field measurements and advance the realism of coronal
magnetic field simulations.
