Bridging machine learning and diagnostics of the ESA LISA space mission with equation discovery via explainable artificial intelligence

The Laser Interferometer Space Antenna (LISA) of the European Space Agency will be the first interferometer for low-frequency
(10 4–10 1 Hz) gravitational wave detection in space. LISA will detect spurious accelerations of the test masses, the end mirrors of
the interferometer, of the order of femto-g. Amongst spurious signals, Coulomb forces due to stray electric fields coupling with charge
deposited on the test masses by galactic and solar particles and the noise associated to the charging process must be monitored during the
mission lifetime. Precious clues on spurious forces acting on the test masses have been studied with the LISA Pathfinder mission, meant
for the testing of the instrumentation that will be placed on board LISA, in 2016–2017. In this work we present the design and imple-
mentation of a workflow leading to equation discovery for the relationship between solar wind speed, galactic cosmic-ray variations and
interplanetary magnetic field intensity observations for the diagnostics of LISA. The workflow exploits explainable artificial intelligence
tools to build a bridge between the opaque predictions obtained with machine learning (ML) models and data analysis performed by
humans with space mission observations. The core step of the workflow is the implementation, tuning and optimisation of an opaque
ML regressor explicitly designed for the future LISA mission, based on input observations of the galactic cosmic-ray flux and of the
interplanetary magnetic field intensity. The regressor is aimed at reconstructing the solar wind speed, a parameter of fundamental impor-
tance, but not available, for the mission environment monitoring. The workflow ends with the application of explainable clustering tech-
niques to the opaque model in order to  obtain human-interpretable outputs instead of opaque ones without any noticeable loss in the
predictive performance and (ii) discover an equation describing the quantitative relationship between the involved variables, currently missing in the literature. The correlation amongst the transit of interplanetary structures, galactic cosmic-ray variations and LISA test-mass charging is illustrated here.