Solar Wind Speed Estimation via Symbolic Knowledge Extraction from Opaque Models

The unprecedented predictive capabilities of machine learning models make them inestimable tools to perform data forecasting and other complex tasks. Benefits of these predictors are even more precious when there is the necessity of surrogating unavailable data due to the lack of dedicated instrumentation on board space missions. For instance, the future ESA space interferometer LISA for low-frequency gravitational wave detection will host, as part of its diagnostics subsystem, particle detectors to measure the galactic cosmic-ray flux and magnetometers to monitor the magnetic field intensity in the region of the interferometer mirrors. No instrumentation dedicated to the interplanetary medium parameter monitoring will be placed on the three spacecraft constituting the LISA constellation. However, important lessons about the correlation between galactic cosmic-ray flux short-term variations and the solar wind speed profile have been learned with the ESA LISA precursor mission, LISA Pathfinder, orbiting around the L1 Lagrange point. In a previous work, we have demonstrated that for LISA Pathfinder it was possible to reconstruct with an uncertainty of 2 nT the interplanetary magnetic field intensity for interplanetary structure transit monitoring. Machine learning models are proposed here to infer the solar wind speed that is not measured on the three LISA spacecraft from galactic cosmic-ray measurements. This work is precious and necessary since LISA, scheduled to launch in 2035, will trail Earth on the ecliptic at 50 million km distance, too far from the orbits of other space missions dedicated to the interplanetary medium monitoring to benefit of their observations.

We built an interpretable machine learning predictor based on galactic cosmic-ray and interplanetary magnetic field observations to obtain a solar wind speed reconstruction within ±65 km s^-1 of uncertainty. Interpretability is achieved by applying the CReEPy symbolic knowledge extractor to the outcomes of a k-NN regressor. The extracted knowledge consists of linear equations aimed at describing the solar wind speed in terms of four statistical indices calculated for the input variables.

Details about the model workflow, performance and validation will be presented at the conference, together with the advantages, drawbacks and possible future enhancements, to demonstrate that our model may provide the LISA mission with an effective and human-interpretable tool to carry out reliable solar wind speed estimates and recognise the transit of interplanetary structures nearby the LISA spacecraft, as a support to the data analysis activity for the monitoring of the external forces acting on the spectrometer mirrors.