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arxiv: 2604.10045 · v1 · submitted 2026-04-11 · 🌌 astro-ph.SR · cs.LG

Daily Predictions of F10.7 and F30 Solar Indices with Deep Learning

Zhenduo Wang , Yasser Abduallah , Jason T. L. Wang , Haimin Wang , Yan Xu , Vasyl Yurchyshyn , Vincent Oria , Khalid A. Alobaid
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Xiaoli Bai
This is my paper

Pith reviewed 2026-05-10 16:08 UTC · model grok-4.3

classification 🌌 astro-ph.SR cs.LG
keywords solar indicesF10.7F30deep learningsolar activitypredictionneural networkspace weather
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The pith

A deep learning model called SINet forecasts daily F10.7 and F30 solar radio indices up to 60 days ahead more accurately than prior methods.

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

The paper introduces SINet, a neural network trained on historical radio flux measurements from multiple stations, to generate medium-term daily predictions of two solar activity indicators. F10.7 serves as a proxy for ultraviolet radiation effects on Earth's upper atmosphere, while the more sensitive F30 index offers potential for refined thermospheric density modeling. Experiments show SINet exceeds five statistical and deep learning baselines on F10.7 forecasts and supplies the first deep learning results for F30, indicating that such networks can extract usable patterns from solar radio time series for practical forecasting.

Core claim

The central claim is that the Solar Index Network (SINet) produces more accurate 1-60 day predictions of the F10.7 solar index than five comparison statistical and deep learning methods, while also delivering the first deep learning forecasts of the F30 index, using training data from NOAA, Toyokawa, and Nobeyama observatories.

What carries the argument

SINet, a deep neural network architecture that ingests sequences of observed solar radio flux values and outputs multi-step ahead daily index predictions.

Load-bearing premise

Historical radio flux records from the listed stations will remain representative of future solar conditions and the trained network will generalize without overfitting to training-period or cycle-specific patterns.

What would settle it

A head-to-head comparison of SINet forecast errors against the five benchmark methods on actual F10.7 and F30 measurements collected during an entire future solar cycle phase absent from the training data.

Figures

Figures reproduced from arXiv: 2604.10045 by Haimin Wang, Jason T. L. Wang, Khalid A. Alobaid, Vasyl Yurchyshyn, Vincent Oria, Xiaoli Bai, Yan Xu, Yasser Abduallah, Zhenduo Wang.

Figure 1
Figure 1. Figure 1: Illustration of the time series data sets for F10.7 (top) and F30 (bottom) used in our study. ing sample contains the true F10.7 values on days d − 30 + 1, d − 30 + 2, . . ., d − 1, d. For fixed prediction, the labels of the training sample contain the true F10.7 values on days d+ 1, d+ 2, . . ., d+ 59, d+ 60 (1-60 days in advance). For rolling prediction, the label of the training sample is the true F10.7… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the two prediction approaches employed by SINet. (a) The fixed prediction approach uses the historical F10.7 values of the previous 30 days, d−30 + 1, d−30 + 2, . . ., d−1, d. represented by orange rectangles, to predict the F10.7 values on days d+ 1, d+ 2, . . ., d + 59, d + 60, represented by gray rectangles. (b) The rolling prediction approach uses a sliding window method, where each pre… view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the SINet model architecture. (a) Overall architecture of SINet, which contains two TimesBlocks. (b) Architecture of a TimesBlock, which contains a dual￾inception model structure with two inception blocks. (c) Architecture of the dual-inception model structure, in which the two inception blocks are connected by a Gelu layer. See text for detailed descriptions of the components of SINet. Sep… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of three forecasting methods: SINetf , TCN and SINetr, on the 60-day ahead prediction of F10.7 in the period between 2009 and 2021. The figure shows the annual comparison results and the overall comparison results in this period. 2009 and 2021. Each dashed blue line represents the observed F10.7 values, while each solid black line represents the synthetic F10.7 values predicted by SINetf . In ge… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of three forecasting methods: SINetf , TCN and SINetr, on the 60-day ahead prediction of F10.7 in the solar maximum (2014). The figure shows the quarterly compari￾son results and the overall comparison results in 2014 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Daily predictions of the F10.7 solar index made by our SINetf method with four forecast horizons: 1, 27, 45, and 60 days, respectively, in the period between 2009 and 2021. –11– [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of three forecasting methods: SINetf , TCN and SINetr, on the 60-day ahead prediction of F30 in the period between 2009 and 2021. The figure shows the annual com￾parison results and the overall comparison results in this period. horizon, the less accurate SINetf is. For 1-day ahead forecasts, SINetf achieves an RMSE of 2.05 sfu, an MAE of 1.40 sfu, and an MAPE of 2.0%. For 60-day ahead forecasts… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of three forecasting methods: SINetf , TCN and SINetr, on the 60-day ahead prediction of F30 in the solar maximum (2014). The figure shows the quarterly comparison results and the overall comparison results in 2014 [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Daily predictions of the F30 solar index made by our SINetf method with four fore￾cast horizons: 1, 27, 45, and 60 days, respectively, in the period between 2009 and 2021. –14– [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Prediction errors made by SINetf for the F10.7 and F30 solar indices in the period between September 1, 2017 and October 30, 2017 (that is, between day 1 and day 60 on the X￾axis). ber 10, 2017 (that is, between day 4 and day 10 on the X-axis) than in the other peri￾ods. This happens probably because there are relatively few training samples related to such a fast magnetic flux emergence as in the dynamic… view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of autocorrelation effects among seven forecasting methods on the 1-day ahead prediction of F10.7 in the period between 2009 and 2021 [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of autocorrelation effects among seven forecasting methods on the 1-day ahead prediction of F30 in the period between 2009 and 2021. methods (ARIMA, LSTM, CNN, LSTM+, TCN). Extensive experiments show that SINetf performs the best while TCN is generally the second best method. When predicting the F10.7 solar index (60 days in advance), TCN achieves an RMSE of 17.19 sfu, MAE of 11.53 sfu, and MAP… view at source ↗
read the original abstract

The F10.7 and F30 solar indices are the solar radio fluxes measured at wavelengths of 10.7 cm and 30 cm, respectively, which are key indicators of solar activity. F10.7 is valuable for explaining the impact of solar ultraviolet (UV) radiation on the upper atmosphere of Earth, while F30 is more sensitive and could improve the reaction of thermospheric density to solar stimulation. In this study, we present a new deep learning model, named the Solar Index Network, or SINet for short, to predict daily values of the F10.7 and F30 solar indices. The SINet model is designed to make medium-term predictions of the index values (1-60 days in advance). The observed data used for SINet training were taken from the National Oceanic and Atmospheric Administration (NOAA) as well as Toyokawa and Nobeyama facilities. Our experimental results show that SINet performs better than five closely related statistical and deep learning methods for the prediction of F10.7. Furthermore, to our knowledge, this is the first time deep learning has been used to predict the F30 solar index.

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

3 major / 2 minor

Summary. The manuscript introduces SINet, a deep learning model for medium-term (1-60 day) daily predictions of the F10.7 and F30 solar radio flux indices. It trains on historical observations from NOAA, Toyokawa, and Nobeyama stations and reports that SINet outperforms five statistical and deep-learning baselines on F10.7 while claiming to be the first deep-learning application to F30.

Significance. If the reported performance gains are shown to arise from genuine generalization rather than cycle-phase overlap, the work would supply a practical forecasting tool with direct relevance to thermospheric density modeling and space-weather applications. The extension of deep learning to F30 is a modest but clear novelty.

major comments (3)
  1. [Abstract] Abstract: the headline claim that SINet 'performs better than five closely related statistical and deep learning methods' is unsupported by any quantitative metrics, error bars, statistical tests, or ablation results, preventing assessment of whether the improvement is load-bearing or practically meaningful.
  2. [Methods] Methods (data preparation and validation): no description is given of the temporal train/test split dates, the solar-cycle phases covered by each set, or any cycle-holdout protocol. Given the strong 11-year modulation of F10.7 and F30, failure to isolate distinct cycle phases risks conflating interpolation with true medium-term forecasting skill.
  3. [Results] Results: the five baseline methods are not characterized (architecture, hyperparameters, or training protocol), so it is impossible to determine whether SINet’s reported advantage reflects architectural improvement or simply better hyperparameter tuning.
minor comments (2)
  1. [Abstract] The abstract states the prediction horizon as '1-60 days in advance' but does not clarify whether this is a single multi-step model or an ensemble of separate lead-time models.
  2. [Introduction] Notation for the two indices is introduced without a brief reminder of their physical definitions or units in the opening paragraph.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive comments on our manuscript. We have carefully considered each point and provide point-by-point responses below. We believe the suggested revisions will improve the clarity and rigor of the paper.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim that SINet 'performs better than five closely related statistical and deep learning methods' is unsupported by any quantitative metrics, error bars, statistical tests, or ablation results, preventing assessment of whether the improvement is load-bearing or practically meaningful.

    Authors: We agree with the referee that the abstract should include quantitative support for the performance claims to allow proper evaluation. In the revised manuscript, we will update the abstract to include key metrics such as the RMSE and correlation coefficients for SINet versus the baselines on F10.7 predictions, along with indications of statistical significance. This will make the headline claim substantiated. revision: yes

  2. Referee: [Methods] Methods (data preparation and validation): no description is given of the temporal train/test split dates, the solar-cycle phases covered by each set, or any cycle-holdout protocol. Given the strong 11-year modulation of F10.7 and F30, failure to isolate distinct cycle phases risks conflating interpolation with true medium-term forecasting skill.

    Authors: This is a valid concern given the periodic nature of solar activity. Although the manuscript mentions training on historical observations, we will revise the Methods section to explicitly detail the temporal train/test splits (specifying exact date ranges), the solar cycle phases represented in each subset, and the use of a cycle-holdout validation strategy to ensure the model is evaluated on unseen cycle phases. We will also add a supplementary figure illustrating the data timeline across solar cycles. revision: yes

  3. Referee: [Results] Results: the five baseline methods are not characterized (architecture, hyperparameters, or training protocol), so it is impossible to determine whether SINet’s reported advantage reflects architectural improvement or simply better hyperparameter tuning.

    Authors: We acknowledge that insufficient detail on the baselines hinders assessment of the results. In the revised manuscript, we will expand the Results and Methods sections to fully characterize the five baseline methods, including their specific architectures (e.g., for LSTM or other DL models), chosen hyperparameters, and the training protocols employed. This will clarify that the comparisons were performed under consistent conditions and highlight the contributions of SINet's design. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical ML prediction task with independent train/test evaluation

full rationale

The paper describes training and evaluating a deep learning model (SINet) on historical solar flux data from NOAA, Toyokawa, and Nobeyama to forecast F10.7 and F30 indices 1-60 days ahead, with performance compared against five statistical and DL baselines. No derivation chain, first-principles equations, or uniqueness theorems are present. Claims rest on standard supervised learning with held-out test data rather than any self-definitional fit, renamed prediction, or self-citation load-bearing step. The work is self-contained against external benchmarks (observed station data) and does not reduce any result to its inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard supervised learning assumptions (i.i.d. training/test split, sufficient data volume, no distribution shift) plus the implicit assumption that neural network capacity is appropriate for the time-series task. No new physical entities or ad-hoc constants are introduced.

free parameters (1)
  • neural network weights and hyperparameters
    All model parameters are fitted to the historical solar flux time series during training.
axioms (1)
  • domain assumption Training and test periods are drawn from the same underlying distribution
    Standard assumption for supervised learning on time series; invoked implicitly when claiming generalization to future days.

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