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

astro-ph.SRApr 11, 2026

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

Authors: Zhenduo Wang, Yasser Abduallah, Jason T. L. Wang, Haimin Wang, Yan Xu, Vasyl Yurchyshyn, Vincent Oria, Khalid A. Alobaid,

Organizations: Institute for Space Weather Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA · Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, USA · Center for Solar-Terrestrial Research, New Jersey Institute of Technology, Newark, NJ 07102, USA · Big Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA 92314, USA ·

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.

Figures & tables

Figure 1: Illustration of the time series data sets for F10.7 (top) and F30 (bottom) used in our study.

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, $d-30+1$ , $d-30+2$ , $\ldots$ , $d-1$ , $d$ . represented by orange rectangles, to predict the F10.7 values on days $d+1$ , $d+2$ , $\ldots$ , $d+59$ , $d+60$ , represented by gray rectangles. (b) The rolling prediction approach uses a sliding window method, where each predicted value is appended iteratively to generate new predictions one day at a time, ultimately achieving a 60-day ahead forecast. Orange rectangles represent true historical F10.7 values, while yellow rectangles represent predicted synthetic F10.7 values that are used subsequently to make new predictions. See text for detailed descriptions of the rolling prediction approach.

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.

Layer	Input Dimension	Kernel Size	Output Dimension
InConvBlock 1	$30\times 32$	$1\times 1$	$30\times 64$
InConvBlock 2	$30\times 32$	$3\times 3$	$30\times 64$
InConvBlock 3	$30\times 32$	$5\times 5$	$30\times 64$
InConvBlock 4	$30\times 32$	$7\times 7$	$30\times 64$
InConvBlock 5	$30\times 32$	$9\times 9$	$30\times 64$
InConvBlock 6	$30\times 32$	$11\times 11$	$30\times 64$

Table 1: Configuration Details of the Dual-Inception Model Structure in SINet

Loss Function	Optimizer	Learning Rate	Dropout Rate	Batch Size	Epoch
MSE	Adam	0.001	0.3	32	10

Table 2: Model Training Conditions of SINet

Forecast	SINet ${}_{\mbox{f}}$	SINet ${}_{\mbox{r}}$	ARIMA	LSTM	CNN	LSTM+	TCN
$1^{st}$ Day	2.3 $\pm 0.1$	2.3 $\pm 0.1$	2.4 $\pm 0.0$	2.8 $\pm 0.1$	3.0 $\pm 0.2$	2.5 $\pm 0.1$	2.4 $\pm 0.1$
$27^{th}$ Day	8.0 $\pm 0.1$	8.8 $\pm 0.2$	9.1 $\pm 0.1$	8.9 $\pm 0.2$	8.5 $\pm 0.2$	8.7 $\pm 0.1$	8.6 $\pm 0.1$
$45^{th}$ Day	9.1 $\pm 0.1$	9.3 $\pm 0.1$	11.3 $\pm 0.1$	11.0 $\pm 0.4$	9.6 $\pm 0.1$	9.6 $\pm 0.2$	9.4 $\pm 0.1$
$60^{th}$ Day	10.1 $\pm 0.1$	10.9 $\pm 0.3$	11.6 $\pm 0.0$	11.1 $\pm 0.5$	10.7 $\pm 0.5$	10.4 $\pm 0.1$	10.4 $\pm 0.3$

Table 3: Average and Standard Deviation of MAPE (%) Obtained by SINet and Related Methods on F10.7 Prediction in the 5-Fold Validation Experiment

Figure 4: Comparison of three forecasting methods: SINet ${}_{\mbox{f}}$ , TCN and SINet ${}_{\mbox{r}}$ , 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.

Figure 5: Comparison of three forecasting methods: SINet ${}_{\mbox{f}}$ , TCN and SINet ${}_{\mbox{r}}$ , on the 60-day ahead prediction of F10.7 in the solar maximum (2014). The figure shows the quarterly comparison results and the overall comparison results in 2014.

Figure 6: Daily predictions of the F10.7 solar index made by our SINet ${}_{\mbox{f}}$ method with four forecast horizons: 1, 27, 45, and 60 days, respectively, in the period between 2009 and 2021.

Forecast	SINet ${}_{\mbox{f}}$	SINet ${}_{\mbox{r}}$	ARIMA	LSTM	CNN	LSTM+	TCN
$1^{st}$ Day	2.0 $\pm 0.0$	2.0 $\pm 0.0$	2.1 $\pm 0.0$	2.6 $\pm 0.2$	3.4 $\pm 0.2$	2.4 $\pm 0.2$	2.4 $\pm 0.2$
$27^{th}$ Day	7.1 $\pm 0.1$	7.9 $\pm 0.1$	7.6 $\pm 0.1$	8.5 $\pm 0.1$	8.2 $\pm 0.1$	7.6 $\pm 0.1$	7.5 $\pm 0.2$
$45^{th}$ Day	8.7 $\pm 0.1$	8.9 $\pm 0.2$	10.5 $\pm 0.1$	10.6 $\pm 0.1$	9.0 $\pm 0.3$	9.9 $\pm 0.2$	9.2 $\pm 0.3$
$60^{th}$ Day	9.5 $\pm 0.1$	10.2 $\pm 0.3$	10.7 $\pm 0.0$	10.3 $\pm 0.1$	10.2 $\pm 0.1$	9.6 $\pm 0.1$	9.6 $\pm 0.1$

Table 4: Average and Standard Deviation of MAPE (%) Obtained by SINet and Related Methods on F30 Prediction in the 5-Fold Validation Experiment

Figure 7: Comparison of three forecasting methods: SINet ${}_{\mbox{f}}$ , TCN and SINet ${}_{\mbox{r}}$ , on the 60-day ahead prediction of F30 in the period between 2009 and 2021. The figure shows the annual comparison results and the overall comparison results in this period.

Figure 8: Comparison of three forecasting methods: SINet ${}_{\mbox{f}}$ , TCN and SINet ${}_{\mbox{r}}$ , 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.

Figure 9: Daily predictions of the F30 solar index made by our SINet ${}_{\mbox{f}}$ method with four forecast horizons: 1, 27, 45, and 60 days, respectively, in the period between 2009 and 2021.

Figure 10: Prediction errors made by SINet ${}_{\mbox{f}}$ 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).

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.

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.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

	SINet ${}_{\mbox{f}}$	SINet ${}_{\mbox{r}}$	ARIMA	LSTM	CNN	LSTM+	TCN
Fold 1	2.2	2.2	2.4	2.8	2.4	2.4	2.3
$p$ -value		—	2.9E-2	8.3E-70	1.3E-31	7.1E-26	1.7E-39
Fold 2	2.3	2.3	2.4	3.1	2.4	2.6	2.4
$p$ -value		—	9.5E-2	1.5E-83	9.6E-10	1.7E-62	5.9E-15
Fold 3	2.3	2.3	2.4	2.6	2.8	2.6	2.4
$p$ -value		—	1.3E-1	2.3E-50	1.9E-90	7.8E-47	3.9E-16

Appendix

Table 5: MAPE (%) of SINet and Related Methods on F10.7 Prediction (at

1^{st}

Day of Forecast)

	SINet ${}_{\mbox{f}}$	SINet ${}_{\mbox{r}}$	ARIMA	LSTM	CNN	LSTM+	TCN
Fold 1	8.1	8.7	9.2	8.7	8.7	8.8	8.7
$p$ -value		4.6E-25	2.8E-10	2.7E-15	9.8E-30	1.8E-51	7.7E-105
Fold 2	8.0	8.8	9.1	8.8	8.5	8.7	8.7
$p$ -value		1.6E-23	1.6E-11	3.8E-19	2.4E-44	7.7E-27	3.1E-21
Fold 3	8.1	9.0	9.1	8.9	8.4	8.8	8.5
$p$ -value		2.6E-18	1.5E-9	1.8E-18	3.5E-24	1.1E-69	4.9E-55

Appendix

Table 6: MAPE (%) of SINet and Related Methods on F10.7 Prediction (at

27^{th}

Day of Forecast)

	SINet ${}_{\mbox{f}}$	SINet ${}_{\mbox{r}}$	ARIMA	LSTM	CNN	LSTM+	TCN
Fold 1	9.1	9.2	11.4	11.3	9.7	9.8	9.4
$p$ -value		1.4E-1	5.5E-16	3.7E-207	1.5E-10	3.7E-70	8.1E-45
Fold 2	9.1	9.3	11.3	10.7	9.7	9.3	9.3
$p$ -value		8.3E-1	2.2E-18	2.4E-142	1.7E-7	1.1E-83	1.7E-36
Fold 3	9.2	9.3	11.3	11.3	9.7	9.5	9.4
$p$ -value		4.7E-3	2.6E-16	2.4E-175	1.1E-17	1.3E-154	3.7E-50

Appendix

Table 7: MAPE (%) of SINet and Related Methods on F10.7 Prediction (at

45^{th}

Day of Forecast)

	SINet ${}_{\mbox{f}}$	SINet ${}_{\mbox{r}}$	ARIMA	LSTM	CNN	LSTM+	TCN
Fold 1	10.2	10.4	11.6	10.6	11.6	10.6	10.8
$p$ -value		2.3E-13	6.9E-10	1.9E-48	1.1E-7	4.8E-13	5.0E-7
Fold 2	10.0	10.7	11.6	10.8	10.5	10.6	10.5
$p$ -value		7.9E-5	1.1E-10	2.9E-111	9.8E-9	8.1E-10	1.5E-32
Fold 3	10.1	11.0	11.6	10.9	10.6	10.4	10.0
$p$ -value		1.3E-11	1.0E-10	2.7E-71	3.3E-8	4.6E-8	1.0E-11

Appendix

Table 8: MAPE (%) of SINet and Related Methods on F10.7 Prediction (at

60^{th}

Day of Forecast)

	SINet ${}_{\mbox{f}}$	SINet ${}_{\mbox{r}}$	ARIMA	LSTM	CNN	LSTM+	TCN
Fold 1	2.0	2.0	2.1	2.4	3.7	2.1	2.2
$p$ -value		—	1.2E-2	2.0E-78	1.9E-299	7.8E-26	1.6E-44
Fold 2	2.0	2.0	2.1	2.7	3.3	2.2	2.7
$p$ -value		—	1.1E-1	2.7E-127	3.4E-235	2.5E-23	2.9E-146
Fold 3	2.0	2.0	2.1	2.7	3.4	2.5	2.1
$p$ -value		—	2.5E-2	1.0E-149	1.1E-279	1.0E-96	5.9E-23

Appendix

Table 9: MAPE (%) of SINet and Related Methods on F30 Prediction (at

1^{st}

Day of Forecast)

	SINet ${}_{\mbox{f}}$	SINet ${}_{\mbox{r}}$	ARIMA	LSTM	CNN	LSTM+	TCN
Fold 1	7.1	7.9	7.7	8.4	8.2	7.8	7.4
$p$ -value		1.5E-29	2.9E-2	5.0E-43	1.4E-49	2.1E-140	5.2E-187
Fold 2	7.2	7.9	7.6	8.7	8.0	7.5	7.6
$p$ -value		1.0E-25	3.8E-2	8.1E-65	1.2E-62	2.3E-65	1.5E-265
Fold 3	7.1	7.9	7.5	8.5	8.2	7.6	7.7
$p$ -value		2.0E-26	5.8E-3	3.0E-53	2.3E-105	8.3E-37	1.5E-151

Appendix

Table 10: MAPE (%) of SINet and Related Methods on F30 Prediction (at

27^{th}

Day of Forecast)

	SINet ${}_{\mbox{f}}$	SINet ${}_{\mbox{r}}$	ARIMA	LSTM	CNN	LSTM+	TCN
Fold 1	8.7	8.8	10.6	10.4	8.7	10.0	9.0
$p$ -value		1.2E-1	6.8E-15	4.8E-67	—	1.4E-160	2.5E-219
Fold 2	8.7	9.0	10.6	10.6	9.0	10.2	9.2
$p$ -value		1.4E-2	2.1E-17	1.5E-145	5.6E-41	1.4E-131	4.4E-28
Fold 3	8.8	8.9	10.5	10.5	8.8	10.0	9.0
$p$ -value		1.8E-2	8.1E-16	1.9E-195	—	2.1E-172	1.4E-187

Appendix

Table 11: MAPE (%) of SINet and Related Methods on F30 Prediction (at

45^{th}

Day of Forecast)

	SINet ${}_{\mbox{f}}$	SINet ${}_{\mbox{r}}$	ARIMA	LSTM	CNN	LSTM+	TCN
Fold 1	9.5	9.6	10.7	10.3	10.3	9.6	9.6
$p$ -value		7.4E-32	6.1E-10	3.3E-85	9.6E-37	9.0E-25	1.4E-11
Fold 2	9.6	10.4	10.7	10.2	10.1	9.7	9.6
$p$ -value		1.6E-9	2.5E-8	7.9E-71	2.2E-35	1.1E-20	—
Fold 3	9.5	10.2	10.7	10.2	10.2	9.6	9.4
$p$ -value		4.8E-22	8.9E-9	1.9E-298	9.3E-46	4.2E-18	8.8E-26

Appendix

Table 12: MAPE (%) of SINet and Related Methods on F30 Prediction (at

60^{th}

Day of Forecast)

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F10.7 Index Prediction: A Multiscale Decomposition Strategy with Wavelet Transform for Performance Optimization

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Time Series Forecasting Wavelet Methods

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In this study, we construct Dataset A for training, validation, and testing, and Dataset B to evaluate generalization. We propose a novel F10.7 index forecasting method using wavelet decomposition, which feeds F10.7 together with its decomposed approximate and detail signals into the iTransformer model. We also incorporate the International Sunspot Number (ISN) and its wavelet-decomposed signals to assess their influence on prediction performance. Our optimal method is then compared with the latest method from S. Yan et al. (2025) and three operational models (SWPC, BGS, CLS). Additionally, we transfer our method to the PatchTST model used in H. Ye et al. (2024) and compare our method with theirs on Dataset B. Key findings include: (1) The wavelet-based combination methods overall outperform the baseline using only F10.7 index. The prediction performance improves as higher-level approximate and detail signals are incrementally added. The Combination 6 method integrating F10.7 with its first to fifth level approximate and detail signals outperforms methods using only approximate or detail signals. (2) Incorporating ISN and its wavelet-decomposed signals does not enhance prediction performance. (3) The Combination 6 method significantly surpasses S. Yan et al. (2025) and three operational models, with RMSE, MAE, and MAPE reduced by 18.22%, 15.09%, and 8.57%, respectively, against the former method. It also excels across four different conditions of solar activity. (4) Our method demonstrates superior generalization and prediction capability over the method of H. Ye et al. (2024) across all forecast horizons. To our knowledge, this is the first application of wavelet decomposition in F10.7 prediction, substantially improving forecast performance.

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