Skip to main content
SpringerLink
Log in

An Improved Prediction of Solar Cycle 25 Using Deep Learning Based Neural Network

  • Research
  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

A deep-learning Vanilla, or single layer, Long Short-Term Memory model is proposed for improving the prediction of Solar Cycle 25. WDC-SILSO the Royal Observatory of Belgium, Brussels provides the 13-month smoothed sunspot-number data that were used to make this prediction. The root mean square error (RMSE) obtained by the proposed model, which is improved in comparison to the existing stacked LSTM model, lies within the range of 1.65 – 4.92, according to analysis on a number of temporal intervals taken into consideration in this study. The model performance has been validated by forecasting the peak amplitude of Solar Cycles 21 – 24. It is shown that for Cycles 21 and 22, the prediction error in estimating the peak is 1.159% and 0.423%, while the RMSE is estimated to be 4.149 and 3.274, respectively. For Cycle 23, the relative error and RMSE are 1.054% and 2.985, respectively, whereas for Cycle 24 they are 1.117% and 3.406, respectively. The current proposed model has exactly predicted the timing when the SSN reached its maximum for Cycle 23. While for Cycle 21, the prediction has a 1-month delay from the actual timing. For Cycles 22 and 24, the year during which the SSN reached maximum coincides with the observed year, although their month of peak occurrence showed a difference of three months and one month, respectively. The current proposed model suggests that the Cycle 25 will peak in April 2023 with an amplitude value of 136.9, which will be approximately 17.68% stronger compared with Cycle 24.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12

Similar content being viewed by others

Data Availability

The SSN version 2.0 has been taken from WDC-SILSO, Royal Observatory of Belgium, Brussels (www.sidc.be/silso/datafiles).

References

  • Ahluwalia, H.S., Ygbuhay, R.C.: 2009, Preliminary forecast for the peak of solar activity cycle 24. Adv. Space Res. 44, 611. DOI.

    Article  ADS  Google Scholar 

  • Ajabshirizadeh, A., Jouzdani, N.M., Abbassi, S.: 2011, Neural network prediction of solar cycle 24. Res. Astron. Astrophys. 11, 491. DOI.

    Article  ADS  Google Scholar 

  • Attia, A.F., Ismail, H.A., Basurah, H.M.: 2013, A neuro-fuzzy modeling for prediction of solar cycles 24 and 25. Astrophys. Space Sci. 344, 5. DOI.

    Article  ADS  Google Scholar 

  • Benson, B., Pan, W.D., Prasad, A., Gary, G.A., Hu, Q.: 2020, Forecasting solar cycle 25 using deep neural networks. Solar Phys. 295, 65. DOI.

    Article  ADS  Google Scholar 

  • Bhatt, N.J., Jain, R., Aggarwal, M.: 2009, Prediction of the maximum amplitude and timing of sunspot cycle 24. Solar Phys. 260, 225. DOI.

    Article  ADS  Google Scholar 

  • Bhowmik, P., Nandy, D.: 2018, Prediction of the strength and timing of sunspot cycle 25 reveal decadal-scale space environmental conditions. Nat. Commun. 9, 5209. DOI.

    Article  ADS  Google Scholar 

  • Bisoi, S.K., Janardhan, P., Ananthakrishnan, S.: 2020, Another mini solar maximum in the offing: a prediction for the amplitude of solar cycle 25. J. Geophys. Res. Space Phys. 125, e2019JA027508. DOI.

    Article  ADS  Google Scholar 

  • Bizzarri, I., Barghini, D., Mancuso, S., Alessio, S., Rubinetti, S., Taricco, C.: 2022, Forecasting the solar cycle 25 using a multistep Bayesian neural network. Mon. Not. Roy. Astron. Soc. 515, 5062. DOI.

    Article  ADS  Google Scholar 

  • Cao, J., Li, Z., Li, J.: 2019, Financial time series forecasting model based on CEEMDAN and LSTM. Physica A 519, 127. DOI.

    Article  ADS  Google Scholar 

  • Chang, Z., Zhang, Y., Chen, W.: 2018, Effective Adam-optimized LSTM neural network for electricity price forecasting. In: Wenzheng, L., Babu, M.S.P. (eds.) 9th Internat. Conf. Software Eng. Service Sci., ICSESS2018, IEEE. DOI.

    Chapter  Google Scholar 

  • Charbonneau, P.: 2010, Dynamo models of the solar cycle. Living Rev. Solar Phys. 7, 3. DOI.

    Article  ADS  Google Scholar 

  • Chen, Z., Gao, Y., Liu, Z.: 2005, Evaluation of solar radio bursts’ effect on GPS receiver signal tracking within International GPS Service network. Radio Sci. 40, 1. DOI.

    Article  Google Scholar 

  • Choudhuri, A.R.: 1992, Stochastic fluctuations of the solar dynamo. Astron. Astrophys. 253, 277.

    ADS  MATH  Google Scholar 

  • Choudhuri, A.R., Chatterjee, P., Jiang, J.: 2007, Predicting solar cycle 24 with a solar dynamo model. Phys. Rev. Lett. 98, 131103. DOI.

    Article  ADS  Google Scholar 

  • Chowdhury, P., Jain, R., Ray, P.C., Burud, D., Chakrabarti, A.: 2021, Prediction of amplitude and timing of solar cycle 25. Solar Phys. 296, 69. DOI.

    Article  ADS  Google Scholar 

  • Coban, G.C., Raheem, A.U., Cavus, H., Asghari-Targhi, M.: 2021, Can solar cycle 25 be a new Dalton minimum? Solar Phys. 296, 156. DOI.

    Article  ADS  Google Scholar 

  • Courtillot, V., Lopes, F., Le Mouël, J.L.: 2021, On the prediction of solar cycles. Solar Phys. 296, 21. DOI.

    Article  ADS  Google Scholar 

  • Covas, E., Peixinho, N., Fernandes, J.: 2019, Neural network forecast of the sunspot butterfly diagram. Solar Phys. 294, 24. DOI.

    Article  ADS  Google Scholar 

  • Dabas, R.S., Sharma, K., Das, R.M., Pillai, K.G.M., Chopra, P., Sethi, N.K.: 2008, A prediction of solar cycle 24 using a modified precursor method. Solar Phys. 250, 171. DOI.

    Article  ADS  Google Scholar 

  • Dikpati, M., De Toma, G., Gilman, P.A.: 2006, Predicting the strength of solar cycle 24 using a flux-transport dynamo-based tool. Geophys. Res. Lett. 33, L05102. DOI.

    Article  ADS  Google Scholar 

  • Du, Z.L.: 2020a, The solar cycle: predicting the peak of solar cycle 25. Astrophys. Space Sci. 365, 104. DOI.

    Article  ADS  Google Scholar 

  • Du, Z.: 2020b, Predicting the shape of solar cycle 25 using a similar-cycle method. Solar Phys. 295, 134. DOI.

    Article  ADS  Google Scholar 

  • Echer, E., Rigozo, N., Nordemann, D., Vieira, L.: 2004, Prediction of solar activity on the basis of spectral characteristics of sunspot number. Ann. Geophys. 22, 2239. DOI.

    Article  ADS  Google Scholar 

  • Feynman, J., Gabriel, S.B.: 1990, Period and phase of the 88-year solar cycle and the Maunder minimum: evidence for a chaotic Sun. Solar Phys. 127, 393. DOI.

    Article  ADS  Google Scholar 

  • Gholipour, A., Lucas, C., Araabi, B.N., Shafiee, M.: 2005, Solar activity forecast: spectral analysis and neurofuzzy prediction. J. Atmos. Solar-Terr. Phys. 67, 595. DOI.

    Article  ADS  Google Scholar 

  • Gonçalves, Í.G., Echer, E., Frigo, E.: 2020, Sunspot cycle prediction using warped Gaussian process regression. Adv. Space Res. 65, 677. DOI.

    Article  ADS  Google Scholar 

  • Guo, W., Jiang, J., Wang, J.X.: 2021, A dynamo-based prediction of solar cycle 25. Solar Phys. 296, 136. DOI.

    Article  ADS  Google Scholar 

  • Han, Y.B., Yin, Z.Q.: 2019, A decline phase modeling for the prediction of solar cycle 25. Solar Phys. 294, 107. DOI.

    Article  ADS  Google Scholar 

  • Hathaway, D.H., Wilson, R.M.: 2006, Geomagnetic activity indicates large amplitude for sunspot cycle 24. Geophys. Res. Lett. 33, L18101. DOI.

    Article  ADS  Google Scholar 

  • Hawkes, G., Berger, M.A.: 2018, Magnetic helicity as a predictor of the solar cycle. Solar Phys. 293, 109. DOI.

    Article  ADS  Google Scholar 

  • Hiremath, K.M.: 2008, Prediction of solar cycle 24 and beyond. Astrophys. Space Sci. 314, 45. DOI.

    Article  ADS  Google Scholar 

  • Hochreiter, S., Schmidhuber, J.: 1997, Long short-term memory. Neural Comput. 9, 1735. DOI.

    Article  Google Scholar 

  • Jiang, J., Chatterjee, P., Choudhuri, A.R.: 2007, Solar activity forecast with a dynamo model. Mon. Not. Roy. Astron. Soc. 381, 1527. DOI.

    Article  ADS  Google Scholar 

  • Kakad, B.: 2011, A new method for prediction of peak sunspot number and ascent time of the solar cycle. Solar Phys. 270, 393. DOI.

    Article  ADS  Google Scholar 

  • Kane, R.P.: 1999, Prediction of the sunspot maximum of solar cycle 23 by extrapolation of spectral components. Solar Phys. 189, 217. DOI.

    Article  ADS  Google Scholar 

  • Kane, R.P.: 2007, A preliminary estimate of the size of the coming solar cycle 24, based on Ohl’s precursor method. Solar Phys. 243, 205. DOI.

    Article  ADS  Google Scholar 

  • Karak, B.B., Mandal, S., Banerjee, D.: 2018, Double peaks of the solar cycle: an explanation from a dynamo model. Astrophys. J. 866, 17. DOI.

    Article  ADS  Google Scholar 

  • Kim, M.Y., Wilson, J.W., Cucinotta, F.A.: 2006, A solar cycle statistical model for the projection of space radiation environment. Adv. Space Res. 37, 1741. DOI.

    Article  ADS  Google Scholar 

  • Kitiashvili, I.N.: 2016, Data assimilation approach for forecast of solar activity cycles. Astrophys. J. 831, 15. DOI.

    Article  ADS  Google Scholar 

  • Kitiashvili, I.N.: 2020, Application of synoptic magnetograms to global solar activity forecast. Astrophys. J. 890, 36. DOI.

    Article  ADS  Google Scholar 

  • Kitiashvili, I., Kosovichev, A.G.: 2008, Application of data assimilation method for predicting solar cycles. Astrophys. J. 688, L49. DOI.

    Article  ADS  Google Scholar 

  • Labonville, F., Charbonneau, P., Lemerle, A.: 2019, A dynamo-based forecast of solar cycle 25. Solar Phys. 294, 82. DOI.

    Article  ADS  Google Scholar 

  • Lantos, P.: 2006, The skewness of a solar cycle as a precursor of the amplitude of the next. Solar Phys. 236, 199. DOI.

    Article  ADS  Google Scholar 

  • Lantos, P., Richard, O.: 1998, On the prediction of maximum amplitude for solar cycles using geomagnetic precursors. Solar Phys. 182, 231. DOI.

    Article  ADS  Google Scholar 

  • Le, X.H., Ho, H.V., Lee, G., Jung, S.: 2019, Application of long short-term memory (LSTM) neural network for flood forecasting. Water 11, 1387. DOI.

    Article  Google Scholar 

  • Lee, T.: 2020, EMD and LSTM hybrid deep learning model for predicting sunspot number time series with a cyclic pattern. Solar Phys. 295, 82. DOI.

    Article  ADS  Google Scholar 

  • Li, Y., Cao, H.: 2018, Prediction for tourism flow based on LSTM neural network. Proc. Comput. Sci. 129, 277. DOI.

    Article  Google Scholar 

  • Li, F.Y., Kong, D.F., Xie, J.L., Xiang, N.B., Xu, J.C.: 2018, Solar cycle characteristics and their application in the prediction of cycle 25. J. Atmos. Solar-Terr. Phys. 181, 110. DOI.

    Article  ADS  Google Scholar 

  • Maris, G., Oncica, A.: 2006, Solar cycle 24 forecasts. Sun Geosph. 1, 8.

    ADS  Google Scholar 

  • Miao, J., Wang, X., Ren, T.L., Li, Z.T.: 2020, Prediction verification of solar cycles 18 – 24 and a preliminary prediction of the maximum amplitude of solar cycle 25 based on the Precursor Method. Res. Astron. Astrophys. 20, 004. DOI.

    Article  ADS  Google Scholar 

  • Muñoz-Jaramillo, A., Balmaceda, L.A., DeLuca, E.E.: 2013, Using the dipolar and quadrupolar moments to improve solar-cycle predictions based on the polar magnetic fields. Phys. Rev. Lett. 111, 041106. DOI.

    Article  ADS  Google Scholar 

  • Nandy, D.: 2021, Progress in solar cycle predictions: sunspot cycles 24 – 25 in perspective. Solar Phys. 296, 54. DOI.

    Article  ADS  Google Scholar 

  • Nikou, M., Mansourfar, G., Bagherzadeh, J.: 2019, Stock price prediction using DEEP learning algorithm and its comparison with machine learning algorithms. Intell. Syst. Account. Finance Manag. 26, 164. DOI.

    Article  Google Scholar 

  • Okoh, D.I., Seemala, G.K., Rabiu, A.B., Uwamahoro, J., Habarulema, J.B., Aggarwal, M.: 2018, A hybrid regression-neural network (HR-NN) method for forecasting the solar activity. Space Weather 16, 1424. DOI.

    Article  ADS  Google Scholar 

  • Pala, Z., Atici, R.: 2019, Forecasting sunspot time series using deep learning methods. Solar Phys. 294, 50. DOI.

    Article  ADS  Google Scholar 

  • Passos, D.: 2011, Evolution of solar parameters since 1750 based on a truncated dynamo model. Astrophys. J. 744, 172. DOI.

    Article  ADS  Google Scholar 

  • Pesnell, W.D.: 2008, Predictions of solar cycle 24. Solar Phys. 252, 209. DOI.

    Article  ADS  Google Scholar 

  • Pesnell, W.D.: 2012, Solar cycle predictions (invited review). Solar Phys. 281, 507. DOI.

    Article  ADS  Google Scholar 

  • Pesnell, W.D.: 2016, Predictions of solar cycle 24: how are we doing? Space Weather 14, 10. DOI.

    Article  ADS  Google Scholar 

  • Pesnell, W.D.: 2020, Lessons learned from predictions of solar cycle 24. J. Space Weather Space Clim. 10, 60. DOI.

    Article  ADS  Google Scholar 

  • Pesnell, W.D., Schatten, K.H.: 2018, An early prediction of the amplitude of solar cycle 25. Solar Phys. 293, 1. DOI.

    Article  Google Scholar 

  • Petrovay, K.: 2010, Solar cycle prediction. Liv. Rev. Solar Phys. 7, 6. DOI.

    Article  ADS  Google Scholar 

  • Petrovay, K.: 2020, Solar cycle prediction. Liv. Rev. Solar Phys. 17, 2. DOI.

    Article  ADS  Google Scholar 

  • Petrovay, K., Nagy, M., Gerják, T., Juhász, L.: 2018, Precursors of an upcoming solar cycle at high latitudes from coronal green line data. J. Atmos. Solar-Terr. Phys. 176, 15. DOI.

    Article  ADS  Google Scholar 

  • Pishkalo, M.I.: 2010, Prediction of amplitude of solar cycle 24 based on polar magnetic field of the Sun at cycle minimum. Sun Geosph. 5, 47.

    ADS  Google Scholar 

  • Podladchikova, T., Van der Linden, R.: 2011, An upper limit prediction of the peak sunspot number for solar cycle 24. J. Space Weather Space Clim. 1, A01. DOI.

    Article  Google Scholar 

  • Podladchikova, T., Van der Linden, R., Veronig, A.M.: 2017, Sunspot number second differences as a precursor of the following 11-year sunspot cycle. Astrophys. J. 850, 81. DOI.

    Article  ADS  Google Scholar 

  • Prasad, A., Roy, S., Sarkar, A., Panja, S.C., Patra, S.N.: 2022, Prediction of solar cycle 25 using deep learning based long short-term memory forecasting technique. Adv. Space Res. 69, 798. DOI.

    Article  ADS  Google Scholar 

  • Quassim, M.S., Attia, A.F., Elminir, H.K.: 2007, Forecasting the peak amplitude of the 24th and 25th sunspot cycles and accompanying geomagnetic activity. Solar Phys. 243, 253. DOI.

    Article  ADS  Google Scholar 

  • Sabarinath, A., Anilkumar, A.K.: 2018, Sunspot cycle prediction using multivariate regression and binary mixture of Laplace distribution model. J. Earth Syst. Sci. 127, 84. DOI.

    Article  ADS  Google Scholar 

  • Sarp, V., Kilcik, A., Yurchyshyn, V., Rozelot, J.P., Ozguc, A.: 2018, Prediction of solar cycle 25: a non-linear approach. Mon. Not. Roy. Astron. Soc. 481, 2981. DOI.

    Article  ADS  Google Scholar 

  • Schatten, K.: 2005, Fair space weather for solar cycle 24. Geophys. Res. Lett. 32, L21106. DOI.

    Article  ADS  Google Scholar 

  • Sello, S.: 2019, Solar cycle activity: an early prediction for cycle 25. arXiv.

  • Singh, A.K., Bhargawa, A.: 2017, An early prediction of 25th solar cycle using Hurst exponent. Astrophys. Space Sci. 362, 199. DOI.

    Article  ADS  Google Scholar 

  • Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: 2014, Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15, 1929.

    MathSciNet  MATH  Google Scholar 

  • Svalgaard, L., Cliver, E.W., Kamide, Y.: 2005, Sunspot cycle 24: smallest cycle in 100 years? Geophys. Res. Lett. 32, L01104. DOI.

    Article  ADS  Google Scholar 

  • Thompson, R.J.: 1993, A technique for predicting the amplitude of the solar cycle. Solar Phys. 148, 383. DOI.

    Article  ADS  Google Scholar 

  • Upton, L.A., Hathaway, D.H.: 2018, An updated solar cycle 25 prediction with AFT: the modern minimum. Geophys. Res. Lett. 45, 8091. DOI.

    Article  ADS  Google Scholar 

  • Uwamahoro, J., McKinnell, L.A., Cilliers, P.J.: 2009, Forecasting solar cycle 24 using neural networks. J. Atmos. Solar-Terr. Phys. 71, 569. DOI.

    Article  ADS  Google Scholar 

  • Velankar, S., Valecha, S., Maji, S.: 2018, Bitcoin price prediction using machine learning. In: 20th Internat. Conf. Adv. Commun. Tech., ICACT 2018, IEEE. DOI.

    Chapter  Google Scholar 

  • Wang, Q.J., Li, J.C., Guo, L.Q.: 2021, Solar cycle prediction using a long short-term memory deep learning model. Res. Astron. Astrophys. 21, 012. DOI.

    Article  ADS  Google Scholar 

  • Wang, Y.M., Sheeley, N.R.: 2009, Understanding the geomagnetic precursor of the solar cycle. Astrophys. J. Lett. 694, L11. DOI.

    Article  ADS  Google Scholar 

  • Wang, J.L., Zong, W.G., Le, G.M., Zhao, H.J., Tang, Y.Q., Zhang, Y.: 2009, Predicting the start and maximum amplitude of solar cycle 24 using similar phases and a cycle grouping. Res. Astron. Astrophys. 9, 133. DOI.

    Article  ADS  Google Scholar 

  • Wilson, R.M., Hathaway, D.H., Reichmann, E.J.: 1998, An estimate for the size of cycle 23 based on near minimum conditions. J. Geophys. Res. Space Phys. 103, 6595. DOI.

    Article  ADS  Google Scholar 

  • Xiong, Y., Lu, J., Zhao, K., Sun, M., Gao, Y.: 2021, Forecasting solar cycle 25 using comprehensive precursor combination and multiple regression technique. Mon. Not. Roy. Astron. Soc. 505, 1046. DOI.

    Article  ADS  Google Scholar 

  • Xu, T., Wu, J., Wu, Z.S., Li, Q.: 2008, Long-term sunspot number prediction based on EMD analysis and AR model. Chin. J. Astron. Astrophys. 8, 337. DOI.

    Article  ADS  Google Scholar 

  • Yan, Y., Stenning, D.C., Kashyap, V.L., Yu, Y.: 2021, Forecasting solar cycle 25 with a principled Bayesian two-stage statistical model. Res. Notes AAS 5, 192. DOI.

    Article  ADS  Google Scholar 

  • Zięba, S., Nieckarz, Z.: 2012, Sunspot time series – relations inferred from the location of the longest spotless segments. Solar Phys. 278, 457. DOI.

    Article  ADS  Google Scholar 

Download references

Acknowledgments

We thank to the WDC-SILSO, Royal Observatory of Belgium, Brussels for the sunspot-number data. We sincerely acknowledge the support extended by Jadavpur University, West Bengal India.

Author information

Authors and Affiliations

  1. Dept. of Mechanical Engineering, Jadavpur University, Kolkata, 700032, India

    Amrita Prasad & Subhash Chandra Panja

  2. Dept. of Applied Electronics & Instrumentation Engineering, Haldia Institute of Technology, Haldia, 721657, India

    Soumya Roy

  3. Dept. of Computer Science & Electronics, Ramakrishna Mission Vidyamandira, Belur Math, 711202, India

    Arindam Sarkar

  4. Dept. of Instrumentation & Electronics Engineering, Jadavpur University, Kolkata, 700106, India

    Sankar Narayan Patra

Authors
  1. Amrita Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Soumya Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arindam Sarkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Subhash Chandra Panja
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sankar Narayan Patra
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Amrita Prasad did the conceptualization of the article, performed the experimental analysis of the article, and wrote the original draft. Soumya Roy contributed in editing the manuscript, writing-review and software. Arindam Sarkar did the conceptualization of the article, supervised the work and helped in formal analysis. Subhash. C. Panja helped in editing of the manuscript as well as writing-review. Sankar Narayan Patra provided the resources for carrying out the experimental work, helped in the writing and editing of the article.

Corresponding author

Correspondence to Amrita Prasad.

Ethics declarations

Competing Interests

The authors declare no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prasad, A., Roy, S., Sarkar, A. et al. An Improved Prediction of Solar Cycle 25 Using Deep Learning Based Neural Network. Sol Phys 298, 50 (2023). https://doi.org/10.1007/s11207-023-02129-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11207-023-02129-2

Keywords

Search

Navigation