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arxiv: 2606.18464 · v1 · pith:2DUFMVGSnew · submitted 2026-06-16 · 🌌 astro-ph.IM · astro-ph.EP· cs.LG

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

Isidro G\'omez-Vargas , Xavier Dumusque , Yinan Zhao , Khaled Al Moulla , Michael Cretignier This is my paper

Pith reviewed 2026-06-26 22:14 UTC · model grok-4.3

classification 🌌 astro-ph.IM astro-ph.EPcs.LG
keywords deep learningradial velocityexoplanet detectionDoppler shiftstellar activityneural networksHARPS-Nspectral representations
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The pith

A neural network trained on solar spectra recovers planetary Doppler signals down to 25 cm/s amplitude

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper trains artificial neural networks on HARPS-N solar spectra that contain artificially injected planetary signals. It uses spectral representations grounded in flux and line-formation temperature together with their velocity gradients. Under a cross-validation strategy the best model recovers the amplitudes, phases, and orbital periods of signals whose amplitudes are at least 25 cm/s and whose periods lie between 10 and 550 days. The recovered signals always coincide with the strongest peaks in the corresponding periodograms, and temperature-based representations outperform flux-based ones. The work also releases a Python package that implements the full pipeline.

Core claim

The central claim is that a neural network trained on solar spectra with injected planetary signals can reliably retrieve the amplitudes, phases, and orbital periods of those signals when their amplitudes are greater than or equal to 25 cm/s and their periods fall between 10 and 550 days, provided a cross-validation training strategy is used; temperature-based spectral shells consistently give better results than flux-based shells, and the recovered signals match the most significant peaks in the periodograms of the predictions.

What carries the argument

Physically motivated spectral representations (flux and line-formation temperature shells plus velocity gradients) passed to artificial neural networks whose hyperparameters are tuned by genetic algorithm and whose uncertainty is estimated by Monte Carlo dropout.

If this is right

  • 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.
  • Predictive uncertainty can be quantified for every detection via Monte Carlo dropout.
  • The full pipeline is released as the open-source package doppleriann.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the method generalizes beyond solar spectra, it could be applied directly to existing radial-velocity surveys of other stars.
  • The same spectral-representation approach might be combined with activity indicators to further separate stellar noise from planetary signals.
  • Extending the training set to include spectra from a wider range of stellar types would test whether the 25 cm/s threshold holds for non-solar hosts.

Load-bearing premise

Performance measured on solar spectra that contain artificially injected signals will carry over to the detection of genuine planetary signals in spectra of other stars that are dominated by natural stellar activity.

What would settle it

Apply the trained model to radial-velocity time series of a star that hosts an independently confirmed planet with amplitude at least 25 cm/s and check whether the planetary parameters are recovered at the correct period.

Figures

Figures reproduced from arXiv: 2606.18464 by Isidro G\'omez-Vargas, Khaled Al Moulla, Michael Cretignier, Xavier Dumusque, Yinan Zhao.

Figure 1
Figure 1. Figure 1: Example of a single HARPS-N solar spectrum. The top panel shows the flux, normalized to its continuum level, as a function of wave￾length. The bottom panel shows the corresponding average formation temperature, T1/2, corresponding to the same wavelengths. flux variation relative to the master spectrum is recorded. This transformation retains localized spectral variations with respect to the master spectrum… view at source ↗
Figure 2
Figure 2. Figure 2: Shell representations for flux and temperature at the time of a maximum DS of 20 m/s. The masked shell is defined as the element-wise product between the spectral shell and the associated density-weight map. In the shell construction, a cell is assigned zero only when no spectral pixels populate the corresponding bin. Although the same selected spectral pixels are used for both the flux- and temperature-ba… view at source ↗
Figure 3
Figure 3. Figure 3: Schematic of the 1D CNN architecture used to predict RV and DS from shell inputs. 4. Deep-Learning Framework We train supervised convolutional neural networks that receive as input a physics-informed shell representation, based on flux or temperature, with dimensions of 9 × 9. The neural network is designed to predict two outputs: the total RV estimated from the CCF, and the DS manually injected into the s… view at source ↗
Figure 4
Figure 4. Figure 4: Schematic workflow of the methodology. HARPS-N solar spectra (293,401 wavelengths, 2036 spectra in a time series) are processed through a line-selection mask to select spectral regions of interest (strong lines with minimum blending). Planetary signals with specified DS and periods (P) are injected to augment the dataset, and their radial velocities (RVs) are calculated using the CCF method. Both flux and … view at source ↗
Figure 5
Figure 5. Figure 5: Detection maps grouped by metric (rows) and model configuration (columns). From top to bottom: detection probability, relative amplitude difference, phase difference, and absolute period difference. From left to right: Flux+HO, Temp+HO, Flux+CV, and Temp+CV. All quantities, except detection probability, correspond to mean values over the successful realizations. Period recovery remains strong for both trai… view at source ↗
Figure 6
Figure 6. Figure 6: Example of a 20 cm/s planetary signal recovery using the cross-validation temperature-based model (CV-Temp). The top panels show periodograms of the mean raw CCF RVs (left) and the predicted Doppler shifts (DS; right), with the dashed line indicating the 0.1% FAP threshold. The injected period at 350 days is clearly detected in the DS periodogram, while it remains obscured in the RVs. The middle panels dis… view at source ↗
read the original abstract

Detecting the tiny Doppler shifts induced by Earth-mass planets in stellar radial-velocity measurements remains extremely challenging due to stellar activity. 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 and cross-validation. Model robustness is enhanced through genetic-algorithm-based hyperparameter optimization, and predictive uncertainty is quantified using 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. We also release doppleriann, a Python package implementing the proposed framework. 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript describes a deep-learning approach to extract planetary Doppler shifts from stellar spectra by training neural networks on HARPS-N solar observations with artificially injected planetary signals. Using flux- and temperature-based spectral representations and their velocity gradients, the authors explore hold-out and cross-validation training strategies, employ genetic-algorithm hyperparameter tuning, and quantify uncertainty via Monte Carlo dropout. They report that their best model recovers amplitudes, phases, and periods for injected signals with amplitudes ≥ 25 cm/s and periods 10–550 days under cross-validation, with temperature-based representations outperforming flux-based ones, and release the doppleriann package.

Significance. If the reported performance generalizes beyond the solar-injection testbed, the work would represent a meaningful step toward Earth-mass planet detection by integrating physically motivated spectral features with modern deep-learning techniques, including built-in uncertainty estimation and automated hyperparameter search. The public release of the doppleriann package further strengthens the contribution by enabling reproducibility and community use.

major comments (1)
  1. [Abstract] Abstract: the central claim that the framework 'generalizes to real, unseen spectra' and provides a pathway 'toward the detection of Earth-mass planets in radial-velocity data from real observations' rests on experiments performed exclusively on solar spectra with artificial injections; no hold-out tests on non-solar stars, no recovery of genuine (non-injected) planetary signals, and no comparison against intrinsic stellar activity from other spectral types are described, leaving the generalization assertion unsupported.
minor comments (2)
  1. The statement that 'in all cases tested here, the successfully recovered signals correspond to the most significant peaks in the periodograms' would be strengthened by inclusion of the periodogram figures and quantitative recovery statistics (e.g., fraction recovered per amplitude bin or false-alarm probabilities).
  2. Notation for the temperature-based versus flux-based spectral shells and the precise definition of the velocity-gradient inputs should be clarified with explicit equations or pseudocode to improve reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We agree that the scope of the experiments must be stated more precisely and will revise the abstract and discussion accordingly to avoid overstating generalization.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the framework 'generalizes to real, unseen spectra' and provides a pathway 'toward the detection of Earth-mass planets in radial-velocity data from real observations' rests on experiments performed exclusively on solar spectra with artificial injections; no hold-out tests on non-solar stars, no recovery of genuine (non-injected) planetary signals, and no comparison against intrinsic stellar activity from other spectral types are described, leaving the generalization assertion unsupported.

    Authors: We agree with the referee. All reported results use HARPS-N solar spectra with injected signals; cross-validation is performed across different solar epochs, not across stellar types. No tests on non-solar stars or recovery of genuine planetary signals appear in the manuscript. The phrase 'generalizes to real, unseen spectra' was intended to refer only to held-out solar spectra. We will revise the abstract, introduction, and conclusions to (1) explicitly state that validation is limited to solar data with injections, (2) replace 'generalizes to real, unseen spectra' with 'generalizes across unseen solar spectra under cross-validation', and (3) rephrase the final sentence to indicate that the framework 'provides a promising pathway' rather than claiming it already supports detection in real observations of arbitrary stars. These changes will be incorporated in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; evaluation uses external held-out benchmarks

full rationale

The paper trains neural networks on solar spectra with injected signals and reports performance via cross-validation and hold-out testing against known injected amplitudes/phases/periods. This is a standard external benchmark, not a reduction of the reported metric to the model's own fitted values. No self-citation chains, self-definitional steps, or ansatzes imported from prior author work are load-bearing for the central claims. The derivation relies on standard ML training plus physics-motivated inputs and is self-contained against the injected-signal test sets.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the injection procedure as a proxy for real planets and on the assumption that the chosen spectral representations isolate planetary Doppler information from stellar activity; the neural-network weights themselves are fitted parameters but are not enumerated in the abstract.

free parameters (2)
  • neural network weights and biases
    Learned from the training spectra during supervised optimization.
  • genetic-algorithm hyperparameters
    Tuned to maximize validation performance on the injected-signal task.
axioms (2)
  • domain assumption Artificially injected planetary signals produce spectral perturbations statistically similar to those from real planets.
    Underlies the entire training and evaluation strategy described in the abstract.
  • domain assumption Flux, line-formation temperature, and velocity-gradient representations together contain the information needed to separate planetary Doppler shifts from stellar activity.
    Explicitly used to construct the network inputs.

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discussion (0)

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