Modeling Doppler Shifts in Radial-Velocity Data with Deep Learning toward Earth-mass Exoplanet Detection

Detecting the tiny Doppler shifts induced by Earth-mass planets in stellar radial-velocity measurements remains extremely challenging due to stellar activity. Despite substantial progress in statistical and machine-learning techniques, many deep-learning methods performing well on simulated data remain difficult to apply reliably on real stellar spectra. The aim of this work is to develop a deep-learning framework that generalizes to real, unseen spectra and improves the detectability of Earth-mass planets in radial-velocity data. We train artificial neural networks on HARPS-N solar spectra with injected planetary signals, using physics-motivated spectral representations based on flux and line-formation temperature, together with their velocity gradients. Two training strategies are explored: hold-out testing, which provides a direct assessment of generalization to unseen spectra, and cross-validation, which evaluates performance across multiple folds of the dataset. The robustness of the model is enhanced by optimizing the hyperparameters based on genetic-algorithms, and the predictive uncertainty is quantified using the Monte Carlo dropout. Our most precise neural network model reliably retrieves, under the cross-validation strategy, the amplitudes, phases, and orbital periods of planetary signals with amplitudes greater than or equal to 25 cm/s and periods between 10 and 550 days. In addition, in all cases tested here, the successfully recovered signals correspond to the most significant peaks in the periodograms of the Doppler-shift predictions. Temperature-based spectral-shell representations consistently outperform flux-based shells, particularly in terms of predictive uncertainty and generalization to unseen data. As a byproduct, we release , a Python package that implements the proposed framework. doppleriann Our results demonstrate that combining physically motivated spectral representations with deep learning provides a promising pathway toward the detection of Earth-mass planets in radial-velocity data from real observations, supported by a modeling framework that is both physically grounded and statistically rigorous, incorporating uncertainty quantification and optimized training strategies.