A Machine Learning approach for correcting radial velocities using physical observables

Precision radial velocity (RV) measurements continue to be a key tool to detect and characterise extrasolar planets. While instrumental precision keeps improving, stellar activity remains a barrier to obtain reliable measurements below 1-2 m/s accuracy. Using simulations and real data, we investigate the capabilities of a Deep Neural Network approach to produce activity free Doppler measurements of stars. As case studies we use observations of two known stars (Eps Eridani and AUMicroscopii), both with clear signals of activity induced RV variability. Synthetic data using the starsim code are generated for the observables (inputs) and the resulting RV signal (labels), and used to train a Deep Neural Network algorithm. We identify an architecture consisting of convolutional and fully connected layers that is adequate to the task. The indices investigated are mean line-profile parameters (width, bisector, contrast) and multi-band photometry. We demonstrate that the RV-independent approach can drastically reduce spurious Doppler variability from known physical effects such as spots, rotation and convective blueshift. We identify the combinations of activity indices with most predictive power. When applied to real observations, we observe a good match of the correction with the observed variability, but we also find that the noise reduction is not as good as in the simulations, probably due to the lack of detail in the simulated physics. We demonstrate that a model-driven machine learning approach is sufficient to clean Doppler signals from activity induced variability for well known physical effects. There are dozens of known activity related observables whose inversion power remains unexplored indicating that the use of additional indicators, more complete models, and more observations with optimised sampling strategies can lead to significant improvements in our detrending capabilities.