Pith. sign in

REVIEW 2 major objections 6 minor 48 references

Neural networks can emulate FASTWIND line synthesis to ~0.1% accuracy and accelerate stellar fitting 360,000-fold.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

A neural-network emulator of FASTWIND reproduces OB-star line profiles to about 0.01–1% and fits stellar parameters roughly 360,000 times faster than direct FASTWIND calculations.

T0 review reviewed 2026-08-01 challenge →

load-bearing objection Useful, well-executed FASTWIND emulator with a genuinely reusable fitting package; the main caveat is a real but unquantified systematic in independent CNO abundance fitting, plus a slightly oversold 52-star validation. the 2 major comments →

arxiv 2607.17348 v1 pith:GMUH4RLB submitted 2026-07-19 astro-ph.SR astro-ph.IM

SpecFANN: Spectral Fitting via Artificial Neural Networks I. A deep learning based fastwind emulator and fitting suite

M. Abdul-Masih , C. Hawcroft , T. Lechien , S. Simon-Diaz , H. Sana , K. Deshmukh , J. Vrancken , J. I. Villase\~nor
show 9 more authors
J. M\"uller-Horn A. J. Kalita B. Ludwig J. Bodensteiner D. M. Bowman A. Escorza G. Holgado J. Puls A. de Vicente
This is my paper
classification astro-ph.SR astro-ph.IM
keywords neural network emulatorFASTWINDmassive starsspectral fittingOB starsstellar parametersBayesian inference
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper aims to establish that a collection of simple feed-forward neural networks can replace the non-LTE radiative transfer code FASTWIND for synthesizing spectral lines of massive OB stars, accurately enough for quantitative spectroscopy. The authors compute 50,147 FASTWIND models spanning effective temperature, surface gravity, radius, helium, and a joint CNO/Si abundance, and train a separate network for each of 140 spectral lines. Most networks reproduce line profiles to better than ~0.01–0.1% for photospheric lines and ~0.1–1% for wind lines. Using the accompanying SpecFANN package, the same fitting procedures (genetic algorithm, MCMC, nested sampling) recover stellar parameters consistent with the literature, at a speed-up of about 360,000 relative to on-the-fly FASTWIND calculations. The result matters because upcoming multi-object spectroscopic surveys will produce far more massive-star spectra than can be analyzed with current synthesis codes.

Core claim

The central claim is that a per-line multi-layer perceptron, mapping the five stellar parameters (effective temperature, surface gravity, radius, helium fraction, and a joint CNO/Si abundance) to the 161 wavelength points of a line profile, can serve as a drop-in emulator for FASTWIND. After training on 40,147 models and testing on 10,000, global mean absolute errors are below 0.1% for most photospheric lines and below ~1% for the most difficult wind lines, with errors reduced by roughly half once a 30 km/s rotational broadening is applied. SpecFANN, built around these networks, fits the standard star 10 Lac and 52 further early-type stars, recovering effective temperatures, gravities, heliu

What carries the argument

The central object is the line-by-line neural network emulator: for each of 140 spectral lines, a fully connected feed-forward network with 5 input neurons, four hidden layers (64, 1024, 1024, 1024 nodes) with ReLU activations, and 161 output neurons producing normalized flux across the line. Training data come from 50,147 FASTWIND models randomly drawn from a physically motivated region of parameter space; wavelengths are homogenized onto a master array per line, and each network is trained with mean-squared error and RMSprop. The line-by-line design carries the argument: it makes the networks modular (poorly reproduced wind lines can be improved independently), keeps storage at ~2 GB versu

Load-bearing premise

The training set sets carbon, nitrogen, oxygen, and silicon to a single abundance value, assuming that changing the abundance of one element does not affect the line profiles of another; if this coupling is not negligible for real OB stars, the independently fitted CNO abundances are biased.

What would settle it

Generate a set of FASTWIND spectra with independently varied carbon, nitrogen, oxygen, and silicon abundances, then fit them with SpecFANN's single-abundance networks; if the recovered elemental abundances deviate from the input values by more than the reported fitting uncertainties, the central assumption is falsified.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Full MCMC and nested-sampling fits with FASTWIND-quality models become practical for whole survey samples: a 50,000-star sample that would take 342 years on a 500-core cluster with on-the-fly FASTWIND can be run in about 4.2 hours with SpecFANN using the genetic algorithm, and in roughly four days with MCMC.
  • The sub-percent network accuracy transfers to fitted stellar parameters: for 10 Lac, results from GA, MCMC, and nested sampling agree with previously published values within uncertainties, and the correlation between helium and nitrogen abundances in the 52-star sample matches expectations from CNO-cycle processing.
  • Line-by-line retraining enables incremental upgrades: additional lines, revised atomic data, or new physics (mass-loss rate, wind clumping, microturbulence) can be added by retraining only the affected networks without altering the rest of the bundle.
  • The emulator compresses the information in a 750 GB grid into 2 GB of network weights with comparable or better interpolation accuracy, reducing storage and evaluation costs for large samples.
  • Because MCMC and nested sampling return well-calibrated posterior uncertainties (differing by about a factor of ten from the GA-based estimates), the availability of cheap likelihood evaluation makes sampling-based error bars the practical standard.

Where Pith is reading between the lines

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

  • If the ~0.1% network accuracy holds, fitting precision will be limited by data quality (signal-to-noise, normalization, atomic data) rather than by the synthesis; a natural test is to fit synthetic spectra with known parameters and check whether recovered parameter scatter matches the quoted uncertainties.
  • The single shared CNO/Si abundance parameter is a simplifying assumption that may bias fitted C, N, and O abundances if cross-abundance coupling is significant; a direct extension would be to train a bundle with separate abundance inputs and compare recovered abundances on stars with independent abundance determinations.
  • The reported error floor in line centers, which is smoothed by 30 km/s rotational broadening, suggests that for narrow-lined, high-S/N targets the emulator's own noise may set the parameter precision; quantifying the unbroadened error floor after only instrumental convolution would clarify this limit.
  • The speed-up changes survey strategy: rather than fitting stars one at a time, it becomes feasible to fit entire clusters or repeat observations jointly, or to use the emulator for forward modelling in population-synthesis or binary studies.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This paper presents SpecFANN, a neural-network emulator of FASTWIND line profiles for OB stars, trained on ~50,000 models varying Teff, logg, radius, helium abundance, and a common CNOSi abundance. 140 individual line networks are trained and validated on a held-out test set; global mean absolute errors are typically 1e-4 to 1e-3 in normalized flux for photospheric lines and up to ~1-2% for wind lines. The SpecFANN package provides GA, MCMC, and nested-sampling fitting. The authors apply it to the standard star 10 Lac, recovering literature Teff, logg, helium, and radial velocity, and to 52 single O-type stars from MELCHIORS, obtaining parameters consistent with spectral-type expectations and a N-He correlation. The claimed speed-up over on-the-fly FASTWIND fitting is roughly 360,000 for the GA setup.

Significance. If the reported emulator accuracy holds, this is a significant contribution: it provides a fast, accurate surrogate for a widely used non-LTE code and makes full posterior sampling for massive stars practical. The held-out test-set validation and the public SpecFANN package are clear strengths, and the 10 Lac comparison with an independent FASTWIND grid analysis is a good external check. The central emulator is not circular: it is trained on FASTWIND and validated on held-out FASTWIND spectra. However, the abundance-return capability is under-validated: the single-parameter training design for CNO/Si abundances is not sufficient to support the independent C, N, and O abundance fits reported in Section 5.1, and the sample-level claim of consistency with the literature in Section 5.2 is stronger than the presented evidence.

major comments (2)
  1. [2.1, 5.1] The training set uses a single heavy-element abundance coordinate epsilon_CNOSi, with C, N, O, and Si always equal. In the fitting of 10 Lac (and the MELCHIORS sample) epsilon_C, epsilon_N, and epsilon_O are freed independently, and for a C line the network's abundance input is set to epsilon_C, for an N line to epsilon_N, etc. The networks were never trained on models with unequal CNO abundances, so they cannot represent cross-abundance coupling (e.g., the effect of changing N on a C line). The paper explicitly acknowledges this in Section 2.1 and cites Puls et al. (2000) for exceptions, but the resulting bias in the derived abundances and in the MCMC/NS posterior widths is not quantified. Since Table 1 reports epsilon_C, epsilon_N, and epsilon_O as results, this is a load-bearing issue for the abundance-return claim. Please add a test set of FASTWIND models with independently varied CN
  2. [Abstract and 5.2] The abstract states that SpecFANN obtains 'robust and accurate stellar parameters that are consistent with the literature for a sample of 52 early-type stars.' Section 5.2, however, validates the MELCHIORS sample only by comparing Teff/logg with spectral-type expectations in a Kiel diagram and by showing the expected N-He correlation; no quantitative comparison to literature stellar parameters or abundances is made. The phrase 'consistent with the literature' overstates the evidence. Either add a quantitative comparison (e.g., against published Teff/logg for overlapping stars) or change the abstract and Section 5.2 to 'consistent with spectral-type expectations.'
minor comments (6)
  1. [1] The text 'WEA VE' should read 'WEAVE'.
  2. [6.4] Typos: 'incoorporating' should be 'incorporating' and 'uncertaity' should be 'uncertainty'.
  3. [Figure 3, B.1, B.2] The residual panels labeled 'Residuals' would be clearer with an explicit unit/scale annotation, especially for the C IV line whose residual range is ±0.1.
  4. [Table 1] The literature vsini value of 13 km/s from Holgado et al. differs because a different method (Fourier transform) was used; adding a table footnote stating this would help, since the text only explains it in Section 5.1.1.
  5. [5.1.2] The fuzz term log f is introduced; please state the prior assumed for log f, since the width of the posterior depends on it.
  6. [5.2] The sentence 'we fit the sample with the GA using the same set up and line list as described above' should specify whether all free parameters used for 10 Lac (including vsini, gamma, and the three abundances) were free for the 52 stars, or whether some were fixed.

Circularity Check

0 steps flagged

No significant circularity: the emulator is validated on held-out FASTWIND spectra and against external literature analyses; the single-CNOSi-abundance assumption is an explicit modeling limitation, not a circular reduction.

full rationale

The paper's central derivation chain is not circular. The neural-network emulator is trained on ~50,000 FASTWIND models and validated on a held-out test set of 10,000 models (Section 2.2, Section 3): the reported accuracies are MAEs between network predictions and FASTWIND line profiles for models not used during training. This is standard surrogate-model validation, not a fitted input being renamed a prediction. The application to 10 Lac uses an observed HERMES spectrum (Section 5.1) and recovers parameters consistent with the independent grid-based FASTWIND analysis of Holgado et al. (2025); the 52 MELCHIORS stars are likewise fitted from observed spectra and checked against spectral-type expectations. Observed data are not used to train the networks, so the fitted stellar parameters are genuine predictions rather than re-statements of training inputs. The speed-up claim compares measured SpecFANN runtimes with estimated on-the-fly FASTWIND computation times (Section 6.2) and is an empirical benchmark, not a definitional identity. The most plausible concern is the single ε_CNOSi training parameter: Section 2.1 states, 'This inherently assumes that changing the abundance of one element does not significantly affect the line profiles of another element, which is an acceptable assumption in most cases (however, see e.g., Puls et al. 2000, for exceptions).' When Section 5.1 frees ε_C, ε_N, and ε_O independently, each line's network is queried with an abundance value it never saw in training, and cross-abundance coupling is neglected. This is a substantive correctness/limitation issue that could bias the reported CNO abundances and should be quantified, but it is not circularity: the fitted abundances are not defined in terms of the network outputs, nor is any target result equivalent by construction to the training input. Self-citations (e.g., pyGA, Abdul-Masih et al. 2021) are tool citations and are not load-bearing; the comparison to Holgado et al. (2025), despite overlapping authorship, is an external published grid analysis and does not by itself make the validation circular. No uniqueness theorem or ansatz is smuggled in via self-citation. Therefore the honest finding is no significant circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

No new physical entities are introduced. The load-bearing assumptions are standard astrophysical modeling choices plus the paper-specific CNO abundance decoupling.

free parameters (2)
  • Neural network weights (all 140 line networks) = Trained by MSE on 40,147 FASTWIND models
    The emulator output is entirely determined by these fitted weights; accuracy claims are empirical and depend on the training set.
  • log f (fuzz term) for 10 Lac MCMC/NS fits = -3.085 +/- 0.003 (10 Lac)
    Nuisance parameter in the likelihood that absorbs underestimated per-point errors; not part of the emulator itself.
axioms (5)
  • domain assumption FASTWIND v10.6.5 is an accurate non-LTE model for OBA stars.
    FASTWIND is used as ground truth for training and validation; no independent physical check is performed in the paper.
  • ad hoc to paper C, N, O, and Si abundances can be represented by a single epsilon_CNOSi input without significant cross-abundance effects.
    This dimensionality reduction is explicit in Section 2.1 and is load-bearing for the independent C/N/O abundance fits; the paper notes exceptions (Puls et al. 2000).
  • domain assumption Fixed wind/physical prescriptions (Vink et al. 2001 mass loss, beta=0.8, unclumped wind, solar metallicity, vmicro=10 km/s) are adequate for the target OB stars.
    These settings constrain the training set and are not varied; real stars may differ.
  • domain assumption Uniform random sampling of the 5D parameter space with Brott-track cuts covers the realistic OB-star main-sequence region.
    The trained networks cannot be trusted outside the sampled region, and the cuts may exclude some stars.
  • standard math Interpolating each line onto a median master wavelength array introduces negligible error.
    Necessary to homogenize wavelength grids across FASTWIND models; the accuracy impact is not separately tested.

reviewed 2026-08-01 · how reviews work

0 comments
Cite this review

Pith. "Pith review of SpecFANN: Spectral Fitting via Artificial Neural Networks I. A deep learning based fastwind emulator and fitting suite." pith.science (2026). https://pith.science/paper/GMUH4RLB

@misc{pith2026260717348,
  author       = {Pith},
  title        = {Pith review of: SpecFANN: Spectral Fitting via Artificial Neural Networks I. A deep learning based fastwind emulator and fitting suite},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GMUH4RLB}},
  note         = {Machine review of arXiv:2607.17348}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

The importance of massive stars cannot be overstated: they are powerful probes of the early universe, play a vital role in the chemical and mechanical evolution of their host environments and their end products allow us to study the most extreme physics in the universe. Obtaining accurate stellar and surface parameters for large samples of massive stars is vital to our understanding of how they evolve, and how their births, lives and deaths affect their surroundings. With the large volume of data expected from upcoming spectroscopic surveys, computational limitations will likely be the most important bottleneck impeding our progress. To address this and dramatically decrease computing times, we aim to develop a robust emulator for the FASTWIND radiative transfer and spectral synthesis code. Additionally, we aim to explore alternative fitting methods that have not been feasible until now due to computational costs. We calculate a set of FASTWIND synthetic spectra of OB-type stars, and we train a collection of neural networks to emulate these models. We also develop the open-source python package SpecFANN, which provides users with a suite of fitting methods that can be used with these or other user-generated neural networks. The majority of the trained neural networks reach average accuracies of better than ~0.01-0.1% for photospheric lines and better than ~0.1-1% for wind lines. SpecFANN is able to obtain robust and accurate stellar parameters that are consistent with the literature for a sample of 52 early-type stars. Using SpecFANN we find that we can achieve the same fit in ~1/360,000 of the time when compared to alternative techniques that rely on on-the-fly FASTWIND computations. We have demonstrated that neural networks offer a viable path forward to address the computational limitations of our current atmosphere analysis and stellar parameter determination methods for hot stars.

Figures

Figures reproduced from arXiv: 2607.17348 by A. de Vicente, A. Escorza, A. J. Kalita, B. Ludwig, C. Hawcroft, D. M. Bowman, G. Holgado, H. Sana, J. Bodensteiner, J. I. Villase\~nor, J. M\"uller-Horn, J. Puls, J. Vrancken, K. Deshmukh, M. Abdul-Masih, S. Simon-Diaz, T. Lechien.

Figure 1
Figure 1. Figure 1: Parameter space covered by the fastwind model set in surface gravity versus temperature (left), radius versus temperature (middle) and radius versus surface gravity (right). Non-rotating evolutionary tracks from Brott et al. (2011a) are over-plotted in black for reference, with the mass of each track indicated in solar masses. González et al. 2012; Carneiro et al. 2016; Sundqvist & Puls 2018), cmfgen (Hill… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic representation of the structure of the neural networks used for each line in our line list. (Teff = 60 kK, R = 5 R⊙). With these limits in mind, samples are randomly drawn from a uniform distribution across our 5- dimensional parameter space. Our final sample consists of 50147 fastwind models, which is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Top left: result of the validation of the test set for the HeI λ4471 line. Each point represents one model, and the symbol color shows the mean absolute error, with worse fitting models plotted on top. Non-rotating evolutionary tracks from Brott et al. (2011a) are over-plotted in grey, with the mass of each track being the same as in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of global MAEs for each line in the master line list as a function of the central wavelength. Global MAE is plotted in purple, while the global MAE after applying a 30 km s−1 rotation rate is plotted in orange. Article number, page 4 of 14 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Results of the GA fit for 10 Lac. The top panels show each of the 16 fitted lines with the observed spectrum plotted in black and the synthetic spectrum of the best-fitting model plotted in red. The shaded red regions represent all models that fall within the 1σ confidence interval. The bottom panels show the fitness as a function of each of the free parameters in our parameter set. The color of each point… view at source ↗
Figure 6
Figure 6. Figure 6: Results of the MCMC fit for 10 Lac. This figure is the same as the top panels in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Corner plot showing the posterior distribution and contours of the MCMC fit in black with the Nested Sampling contours overplotted in red for 10 Lac. The top panel in each column shows the distribution for the parameter indicated above the plot, and the off-diagonal panels show the parameter correlations. the parameter space that the bundle is sensitive to. To do this, we use the MELCHIORS database (Royer … view at source ↗
Figure 8
Figure 8. Figure 8: Results of the GA fit for the single O-type stars in the Melchiors database in a Kiel diagram (left) with Brott et al. (2011b) tracks plotted in dark grey, and in the nitrogen abundance versus helium abundance plane (right). Error bars are indicated in light grey, spectral subtypes are indicated by the color of each point, and the luminosity classes are indicated by the symbol type as indicated in the lege… view at source ↗
Figure 9
Figure 9. Figure 9: Comparison between the results of the GA fits (orange) and MCMC fits (purple) for 38 independent observations of 10 Lac. ln L = − 1 2 X n " (On − Cn) 2 s 2 n + ln(2πs 2 n ) # , (3) where On and Cn are the observed and calculated fluxes and s 2 n is defined as: s 2 n = σ 2 n + f 2C 2 n , (4) where σn is the per point observational errors and f is the fuzz term described above. In the case where the fuzz ter… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

48 extracted references · 4 linked inside Pith

  1. [1]

    2016, arXiv e-prints, arXiv:1603.04467

    Abadi, M., Agarwal, A., Barham, P., et al. 2016, arXiv e-prints, arXiv:1603.04467

    Pith/arXiv arXiv 2016

  2. [2]

    2021, A&A, 651, A96

    Abdul-Masih, M., Sana, H., Hawcroft, C., et al. 2021, A&A, 651, A96

    2021

  3. [3]

    Agarap, A. F. 2018, arXiv e-prints, arXiv:1803.08375

    Pith/arXiv arXiv 2018

  4. [4]

    & Przybilla, N

    Aschenbrenner, P. & Przybilla, N. 2026, A&A, 709, A124

    2026

  5. [5]

    2023, A&A, 671, A36 Astropy Collaboration, Price-Whelan, A

    Aschenbrenner, P., Przybilla, N., & Butler, K. 2023, A&A, 671, A36 Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, ApJ, 935, 167 Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, B. M., et al. 2018, AJ, 156, 123 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33

    2023

  6. [6]

    A., & Puls, J., eds

    Bresolin, F., Crowther, P. A., & Puls, J., eds. 2008, IAU Symposium, V ol. 250, Massive Stars as Cosmic Engines

    2008

  7. [7]

    2016, Statistics and Computing, 26, 383

    Buchner, J. 2016, Statistics and Computing, 26, 383

    2016

  8. [8]

    2019, PASP, 131, 108005

    Buchner, J. 2019, PASP, 131, 108005

    2019

  9. [9]

    2021, The Journal of Open Source Software, 6, 3001

    Buchner, J. 2021, The Journal of Open Source Software, 6, 3001

    2021

  10. [10]

    P., Puls, J., Sundqvist, J

    Carneiro, L. P., Puls, J., Sundqvist, J. O., & Hoffmann, T. L. 2016, A&A, 590, A88

    2016

  11. [11]

    & others

    Chollet, F. & others. 2018, Keras: The Python Deep Learning library, Astro- physics Source Code Library, record ascl:1806.022

    2018

  12. [12]

    2020, The Messenger, 180, 10

    Cirasuolo, M., Fairley, A., Rees, P., et al. 2020, The Messenger, 180, 10

    2020

  13. [13]

    J., Szalay, A

    Connolly, A. J., Szalay, A. S., Bershady, M. A., Kinney, A. L., & Calzetti, D. 1995, AJ, 110, 1071

    1995

  14. [14]

    C., et al

    Dalton, G., Trager, S., Abrams, D. C., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, V ol. 9147, Ground- based and Airborne Instrumentation for Astronomy V , ed. S. K. Ramsay, I. S. McLean, & H. Takami, 91470L de Jong, R. S., Agertz, O., Berbel, A. A., et al. 2019, The Messenger, 175, 3

    2014

  15. [15]

    2015, arXiv e-prints, arXiv:1501.04726

    Evans, C., Puech, M., Afonso, J., et al. 2015, arXiv e-prints, arXiv:1501.04726

    Pith/arXiv arXiv 2015

  16. [16]

    W., Lang, D., & Goodman, J

    Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306 Giudici Michilini, F. N., Gamen, R., Ferrero, G., Morrell, N., & Barbá, R. 2025, ApJS, 281, 18 Gräfener, G., Koesterke, L., & Hamann, W.-R. 2002, A&A, 387, 244

    2013

  17. [17]

    R., Senchyna, P., et al

    Gull, M., Weisz, D. R., Senchyna, P., et al. 2022, ApJ, 941, 206

    2022

  18. [18]

    & Loeb, A

    Haiman, Z. & Loeb, A. 1997, ApJ, 483, 21

    1997

  19. [19]

    & Gräfener, G

    Hamann, W.-R. & Gräfener, G. 2003, A&A, 410, 993

    2003

  20. [20]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357

    2020

  21. [21]

    Hillier, D. J. & Miller, D. L. 1998, ApJ, 496, 407

    1998

  22. [22]

    2012, rmsprop: Divide the gradient by a running average of its recent magnitude

    Hinton, G. 2012, rmsprop: Divide the gradient by a running average of its recent magnitude

    2012

  23. [23]

    2025, A&A, 703, A175

    Holgado, G., Simón-Díaz, S., & Herrero, A. 2025, A&A, 703, A175

    2025

  24. [24]

    F., Kereš, D., Oñorbe, J., et al

    Hopkins, P. F., Kereš, D., Oñorbe, J., et al. 2014, MNRAS, 445, 581

    2014

  25. [25]

    & Mihalas, D

    Hubeny, I. & Mihalas, D. 2014, Theory of Stellar Atmospheres

    2014

  26. [26]

    J., et al

    Hunter, I., Brott, I., Lennon, D. J., et al. 2008, ApJ, 676, L29

    2008

  27. [27]

    L., Smartt, S

    Hunter, I., Dufton, P. L., Smartt, S. J., et al. 2007, A&A, 466, 277

    2007

  28. [28]

    J., & Proffitt, C

    Jin, H., Langer, N., Lennon, D. J., & Proffitt, C. R. 2024, A&A, 690, A135

    2024

  29. [29]

    A., Rix, H.-W., Aerts, C., et al

    Kollmeier, J. A., Rix, H.-W., Aerts, C., et al. 2026, AJ, 171, 52

    2026

  30. [30]

    Kurucz, R. L. 2005, Memorie della Societa Astronomica Italiana Supplementi, 8, 14

    2005

  31. [31]

    & Hubeny, I

    Lanz, T. & Hubeny, I. 2003, ApJS, 146, 417

    2003

  32. [32]

    & Hubeny, I

    Lanz, T. & Hubeny, I. 2007, ApJS, 169, 83

    2007

  33. [33]

    & Bodensteiner, J

    Marchant, P. & Bodensteiner, J. 2024, ARA&A, 62, 21

    2024

  34. [34]

    2000, A&AS, 141, 23

    Puls, J., Springmann, U., & Lennon, M. 2000, A&AS, 141, 23

    2000

  35. [35]

    A., Venero, R., et al

    Puls, J., Urbaneja, M. A., Venero, R., et al. 2005, A&A, 435, 669

    2005

  36. [36]

    2011, A&A, 526, A69

    Raskin, G., van Winckel, H., Hensberge, H., et al. 2011, A&A, 526, A69

    2011

  37. [37]

    Rasmussen, C. E. & Williams, C. K. I. 2006, Gaussian Processes for Machine Learning Rivero González, J. G., Puls, J., Massey, P., & Najarro, F. 2012, A&A, 543, A95

    2006

  38. [38]

    2024, A&A, 681, A107

    Royer, P., Merle, T., Dsilva, K., et al. 2024, A&A, 681, A107

    2024

  39. [39]

    2015, A&A, 577, A13

    Sander, A., Shenar, T., Hainich, R., et al. 2015, A&A, 577, A13

    2015

  40. [40]

    E., Puls, J., & Herrero, A

    Santolaya-Rey, A. E., Puls, J., & Herrero, A. 1997, A&A, 323, 488

    1997

  41. [41]

    J., & Wang, C

    Schootemeijer, A., Langer, N., Grin, N. J., & Wang, C. 2019, A&A, 625, A132 SDSS Collaboration, Adamane Pallathadka, G., Aghakhanloo, M., et al. 2025, arXiv e-prints, arXiv:2507.07093

    Pith/arXiv arXiv 2019

  42. [42]

    2024, A&A, 690, A289 Simón-Díaz, S

    Shenar, T., Bodensteiner, J., Sana, H., et al. 2024, A&A, 690, A289 Simón-Díaz, S. & Herrero, A. 2007, A&A, 468, 1063 Simón-Díaz, S. & Herrero, A. 2014, A&A, 562, A135

    2024

  43. [43]

    Sundqvist, J. O. & Puls, J. 2018, A&A, 619, A59

    2018

  44. [44]

    H., Avila, G., Buchhave, L., et al

    Telting, J. H., Avila, G., Buchhave, L., et al. 2014, Astronomische Nachrichten, 335, 41

    2014

  45. [45]

    2019, ApJ, 879, 69

    Ting, Y .-S., Conroy, C., Rix, H.-W., & Cargile, P. 2019, ApJ, 879, 69

    2019

  46. [46]

    Urbaneja, M. A. 2026, A&A, 707, A249

    2026

  47. [47]

    S., de Koter, A., & Lamers, H

    Vink, J. S., de Koter, A., & Lamers, H. J. G. L. M. 2001, A&A, 369, 574

    2001

  48. [48]

    E., et al

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Medicine, 17, 261 Article number, page 12 of 14 M. Abdul-Masih et al.: SpecFANN: FASTWIND emulator and fitting suite Appendix A: Mean Absolute Errors per line Table A.1.MAE for each spectral line in the master line list. Line MAE MAE 30 km s−1 CII1010 7.45e-03 1.63e-03 CII1036 8.29e-03 3.00e-...

    2020

This paper was first reviewed by deepseek-v4-flash on August 1, 2026.