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

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.

• The paper's main contribution is introducing SINet, a deep learning model that forecasts F10.7 and F30 solar indices, outperforming traditional methods.
• SINet employs dual TimesBlocks, FFT layers, and a dual-inception structure to capture both short- and long-range dependencies in solar activity.
• Experimental results show SINet reduces error metrics by up to 25% during high solar activity, highlighting its value for operational space weather forecasting.

Deep Learning-Based Medium-Term Forecasting of F10.7 and F30 Solar Indices: The SINet Model

Introduction

The F10.7 and F30 solar indices, representing radio fluxes at 10.7 cm and 30 cm wavelengths, respectively, are pivotal quantitative proxies for tracking solar activity. F10.7 is widely adopted in space weather modeling and UV impact studies on the upper Earth atmosphere, while F30 offers enhanced sensitivity for thermospheric density response analyses. Conventional approaches for forecasting these indices, spanning statistical, empirical, and shallow-learning models, are often constrained in capturing the nonlinear, multiscale variability intrinsic to solar activity. The advent of advanced deep learning (DL) architectures presents new opportunities for medium-range predictive performance. This paper introduces SINet, a deep learning model dedicated to daily prediction of F10.7 and F30 on forecasting horizons up to 60 days. SINet is evaluated rigorously against established methods, demonstrating consistent performance superiority across all metrics and horizons. Moreover, this is the first documented application of deep learning for F30 index prediction.

Data and Prediction Protocols

The dataset comprises daily F10.7 values from NOAA and F30 values from Toyokawa/Nobeyama, spanning 1957–2021, divided into non-overlapping training (1957–2008) and test (2009–2021) sets.

Figure 1: Time series data for F10.7 (top) and F30 (bottom) spanning 1957–2021.

The data is subjected to min-max normalization to mitigate non-stationarity across solar cycles. For supervised learning, two labeling protocols are employed:

• Fixed Prediction: The prior 30 days are used as input to simultaneously predict the next 60 days.
• Rolling Prediction: The model predicts one day ahead recursively, feeding predictions back as input to reach 60-day horizons.

  Figure 2: (a) Fixed prediction uses the last 30 observed values to predict the next 60 values; (b) Rolling prediction uses synthetic predicted values iteratively to extend the forecast horizon to 60 days.

SINet Architecture

SINet leverages enhancements of the TimesNet framework but is specifically adapted for the solar index forecasting regime. The primary architectural components include:

• Dual TimesBlocks: Each processes univariate time series inputs, facilitating short- and long-range dependency extraction.
• Fast Fourier Transform (FFT) Layer: Transforms input to the frequency domain, isolating the three most significant periods, which are key for solar rotational modulation.
• Dual-Inception Structure: Multi-scale 2D convolutional kernels organized into inception blocks extract hierarchical, periodic, and aperiodic temporal features.
• Adaptive Aggregation and Residual Connections: Allow for selective recombination of dominant frequency components and stabilization of gradient flow.

  Figure 3: (a) SINet's overall architecture with two TimesBlocks; (b) TimesBlock structure; (c) Dual-inception module with GELU nonlinearity bridging two multi-scale convolutional branches.

Hyperparameters—including epochs, batch size, optimizer, model dimension, and dropout—are optimized using grid search and validated using a held-out 10% subset of the training set. The loss function is MSE, empirically observed to outperform SMAPE in this application.

Experimental Results

F10.7 Forecasting Performance

Five baseline models are compared: ARIMA, LSTM, CNN, LSTM with Multihead Attention (LSTM+), and TCN. Evaluation spans 1, 27, 45, and 60-day ahead forecasts.

• Mean Absolute Percentage Error (MAPE) on the 60-day horizon: SINet$_\mathrm{f}$ achieves 10.1%, outperforming TCN (10.4%) and all other models.
• Robustness over solar maximum (2014): SINet$_\mathrm{f}$ reduces RMSE and MAE by up to 15% compared to TCN, significant during periods of high solar activity when predictive uncertainty peaks.

  Figure 4: Annual and overall comparison of SINet$_\mathrm{f}$, TCN, and SINet$_\mathrm{r}$ for 60-day F10.7 forecasts (2009–2021).

  

  Figure 5: Quarterly and overall errors during solar maximum (2014), highlighting SINet$_\mathrm{f}$'s gains over TCN.

  

  Figure 6: Ground truth vs. SINet$_\mathrm{f}$ predictions for F10.7 at 1, 27, 45, 60-day horizons (2009–2021). Accuracy degrades smoothly with horizon.

F30 Forecasting Performance

SINet$_\mathrm{f}$ demonstrates analogous benefits for F30 predictions:

• 60-day MAPE: 9.5% for SINet$_\mathrm{f}$, slightly improving TCN's 9.6%.
• Solar maximum phase: Error reduction vs. TCN is even more pronounced (~25% improvement in 2014).

  Figure 7: Annual and overall comparison of three methods for F30 60-day forecasts.

  

  Figure 8: Quarterly and overall error breakdown in 2014 for F30, highlighting major SINet$_\mathrm{f}$ improvements in challenging phases.

  

  Figure 9: F30 prediction—SINet$_\mathrm{f}$ is able to accurately track observed values across all tested horizons.

Special Case: Active Region NOAA 12673

During the exceptionally volatile AR 12673 in September 2017, SINet$_\mathrm{f}$0 prediction error spikes, revealing a generalization gap for rare, strong-flux emergence events. Insufficient representation of extreme cases in training data is a limitation for all ML-based solar forecasting approaches.

Figure 10: Error profiles for SINet$_\mathrm{f}$1 predictions of F10.7 and F30 during the AR 12673 emergence (September–October 2017). Highest errors coincide with intense flux variability.

Autocorrelation Analysis

Autocorrelation analysis of 1-day predictions reveals strong lag-1 dependency, as expected for solar activity time series. Long-lag autocorrelations diminish, consistent with increased predictive uncertainty at extended horizons.

Figure 11: Autocorrelation at lag 1 for F10.7 one-day-ahead predictions; strong effect across all methods.

Figure 12: Autocorrelation at lag 1 for F30; similar findings as for F10.7.

Discussion and Implications

SINet's fixed prediction protocol proves superior to recursive rolling, especially for extended horizons, due to error compounding in autoregressive predictions. The dual-inception architecture's capacity for both short- and long-range dependency modeling is validated by significant error reductions—especially during solar maximum, when forecast difficulty peaks due to heightened solar variability.

The analysis of AR 12673 demonstrates the limitations of DL models' generalization under rare, rapid active region emergence. Data augmentation, anomaly-specific subnetworks, or the removal of transient events are plausible future directions to enhance robustness.

Practically, SINet$_\mathrm{f}$2 achieves slightly lower operational MAPE than the NOAA/SWPC system over a recent multi-month period, demonstrating tangible value in operational space weather prediction systems.

Theoretically, direct frequency-domain decomposition and selective aggregation in SINet represent a promising methodological advancement for time series dominated by quasi-periodic, bursty phenomena. These techniques may be generalizable to other space weather or geophysical proxy forecasting.

Conclusion

SINet establishes a new standard for medium-term daily forecasting of solar indices, delivering state-of-the-art accuracy across all forecast horizons (1–60 days) for both F10.7 and F30 (2604.10045). The model's design, built around frequency-domain feature abstraction and adaptive sequence aggregation, leads to robust performance, notably suppressing error during periods with extreme solar activity. SINet$_\mathrm{f}$3 operates reliably in an operational setting, and its methodological framework holds promise for further advances in solar and geophysical time series forecasting.