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\begin{document}

\title{Physics-informed Neural Networks for the Improvement of Platform
Magnetometer Measurements}



\author[1]{Kevin Styp-Rekowski}%
\author[2]{Ingo Michaelis}%
\author[3]{Monika Korte}%
\author[4]{Claudia Stolle}%
\affil[1]{TU Berlin}%
\affil[2]{GFZ German Research Centre For Geosciences}%
\affil[3]{GFZ German Research Center for Geosciences}%
\affil[4]{Leibniz Institut of Atmospheric Physics at the University of Rostock}%


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  \date{May 16, 2024}


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\begin{abstract}
Space-based measurements of the Earth's magnetic field with a good
spatiotemporal coverage are needed to understand the complex system of
our surrounding geomagnetic field. High-precision magnetic field
satellite missions form the backbone for sophisticated research, but
they are limited in their coverage. Many satellites carry so-called
platform magnetometers that are part of their attitude and orbit control
systems. These can be re-calibrated by considering different behaviors
of the satellite system, hence reducing their relatively high initial
noise originating from their rough calibration. These platform
magnetometer data obtained from non-dedicated satellite missions
complement the high-precision data by additional coverage in space,
time, and magnetic local times. In this work, we present an extension to
our previous Machine Learning approach for the automatic in-situ
calibration of platform magnetometers. We introduce a new
physics-informed layer incorporating the Biot-Savart formula for dipoles
that can efficiently correct artificial disturbances due to electric
current-induced magnetic fields evoked by the satellite itself. We
demonstrate how magnetic dipoles can be co-estimated in a neural network
for the calibration of platform magnetometers and thus enhance the
Machine Learning-based approach to follow known physical principles.
Here we describe the derivation and assessment of re-calibrated datasets
for two satellite missions, GOCE and GRACE-FO, which are made publicly
available. We achieved a mean residual of about 7 nT and 4 nT for low-
and mid-latitudes, respectively.%
\end{abstract}%



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