Sunspot variations are the sun's symptoms of strong magnetic perturbations. In this paper, we use long short-term memory neural network and one-dimensional convolution neural network to detect sunspot variations. Here we use three different datasets, including the yearly mean sunspot number (YSSN) from 1700 to 2020, the monthly mean sunspot number (MSSN) from 1749 to 2021 and the monthly mean sunspot areas (MSSA) from 1874 to 2021. First, based on the YSSN dataset, we obtain YSSN for 2021 and the predicted YSSN in the 25th solar cycle appears at 2025 which equals 163.4; Then, based on the MSSN dataset, we obtain MSSN for June 2021 and the predicted YSSN in the 25th solar cycle appears in October 2024 which equals 245.9; Next, based on the MSSA dataset, the predicted MSSA for June 2021 is 73.1; Finally, the latitude is divided into 13 partitions to predict the butterfly diagram, and still, neural network can reconstruct the butterfly diagram. Therefore, neural network can provide a physical perspective for sunspot investigation.
[1] Okamoto T J, Sakurai T. Super-strong magnetic field in sunspots[J]. The Astrophysical Journal Letters, 2018, 852(1):L16. DOI:10.3847/2041-8213/aaa3d8.
[2] Schwabe H. Sonnenbeobachtungen im Jahre 1838[J]. Astronomische Nachrichten, 1839, 16(12/13):185-186. DOI:10.1002/asna.18390161205.
[3] 唐洁, 刘晓琴. 太阳黑子相对数的多时间尺度及混沌特性分析[J]. 中国科学:物理学力学天文学, 2018, 48(2):103-110. DOI:10.1360/SSPMA2017-00260.
[4] 田中大, 李树江, 王艳红, 等. 太阳黑子数平滑月均值的混合预测模型[J]. 中国科学:物理学力学天文学, 2016, 46(11):105-114. DOI:10.1360/SSPMA2016-00191.
[5] Dani T, Sulistiani S. Prediction of maximum amplitude of solar cycle 25 using machine learning[J]. Journal of Physics:Conference Series, 2019, 1231(1):012022. DOI:10.1088/1742-6596/1231/1/012022.
[6] Zhao H J, Wang J L, Zong W G, et al. Prediction of the smoothed monthly mean sunspot numbers by means of RBF (radial basic function) neural networks[J]. Chinese Journal of Geophysics, 2008, 51(1):20-24. DOI:10.1002/cjg2.1190.
[7] Ding L G, Jiang Y, Lan R S. Prediction of the smoothed monthly mean sunspot area using artificial neural metwork[C]//2012 Fifth International Conference on Information and Computing Science. July 24-25, 2012, Liverpool, UK. IEEE, 2012:33-36. DOI:10.1109/ICIC.2012.42.
[8] Pala Z, Atici R. Forecasting sunspot time series using deep learning methods[J]. Solar Physics, 2019, 294(5):1-14. DOI:10.1007/s11207-019-1434-6.
[9] Benson B, Pan W D, Prasad A, et al. Forecasting solar cycle 25 using deep neural networks[J]. Solar Physics, 2020, 295(5):1-15. DOI:10.1007/s11207-020-01634-y.
[10] Hochreiter S, Schmidhuber J. Long short-term memory[J]. Neural Computation, 1997, 9(8):1735-1780. DOI:10.1162/neco.1997.9.8.1735.
[11] Achkar R, Elias-Sleiman F, Ezzidine H, et al. Comparison of BPA-MLP and LSTM-RNN for stocks prediction[C]//20186th International Symposium on Computational and Business Intelligence (ISCBI). August 27-29, 2018, Basel, Switzerland. IEEE, 2018:48-51. DOI:10.1109/ISCBI.2018.00019.
[12] Tong W T, Li L X, Zhou X L, et al. Deep learning PM2.5 concentrations with bidirectional LSTM RNN[J]. Air Quality, Atmosphere & Health, 2019, 12(4):411-423. DOI:10.1007/s11869-018-0647-4.
[13] Sun L, Du J, Dai L R, et al. Multiple-target deep learning for LSTM-RNN based speech enhancement[C]//2017 Hands-free Speech Communications and Microphone Arrays (HSCMA). March 1-3, 2017, San Francisco, CA, USA. IEEE, 2017:136-140. DOI:10.1109/HSCMA.2017.7895577.
[14] Siami-Namini S, Tavakoli N, Siami Namin A. A comparison of ARIMA and LSTM in forecasting time series[C]//201817th IEEE International Conference on Machine Learning and Applications (ICMLA). December 17-20, 2018, Orlando, FL, USA. IEEE, 2018:1394-1401. DOI:10.1109/ICMLA.2018.00227.
[15] Cheng S, Qiao X J, Shi Y L, et al. Machine learning for predicting discharge fluctuation of a karst spring in North China[J]. Acta Geophysica, 2021, 69(1):257-270. DOI:10.1007/s11600-020-00522-0.
[16] Fukuoka R, Suzuki H, Kitajima T, et al. Wind speed prediction model using LSTM and 1D-CNN[J]. Journal of Signal Processing, 2018, 22(4):207-210. DOI:10.2299/jsp.22.207.
[17] Panigrahi S, Pattanayak R M, Sethy P K, et al. Forecasting of sunspot time series using a hybridization of ARIMA, ETS and SVM methods[J]. Solar Physics, 2021, 296(1):1-19. DOI:10.1007/s11207-020-01757-2.
[18] He K M, Zhang X Y, Ren S Q, et al. Delving deep into rectifiers:surpassing human-level performance on ImageNet classification[C]//2015 IEEE International Conference on Computer Vision (ICCV). December 7-13, 2015, Santiago, Chile. IEEE, 2015:1026-1034. DOI:10.1109/ICCV.2015.123.
[19] Kingma D P, Ba J. Adam:a method for stochastic optimization[EB/OL]. arXiv:1412.6980. (2014-12-22)[2021-7-24]. https://arxiv.org/abs/1412.6980.
[20] Covas E, Peixinho N, Fernandes J. Neural network forecast of the sunspot butterfly diagram[J]. Solar Physics, 2019, 294(3):1-15. DOI:10.1007/s11207-019-1412-z.
[21] Li K J, Feng W, Li F Y. Predicting the maximum amplitude of solar cycle 25 and its timing[J]. Journal of Atmospheric and Solar-Terrestrial Physics, 2015, 135:72-76. DOI:10.1016/j.jastp.2015.09.010.
[22] Okoh D I, Seemala G K, Rabiu A B, et al. A hybrid regression-neural network (HR-NN) method for forecasting the solar activity[J]. Space Weather, 2018, 16(9):1424-1436. DOI:10.1029/2018SW001907.
[23] McIntosh S W, Chapman S, Leamon R J, et al. Overlapping magnetic activity cycles and the sunspot number:forecasting sunspot cycle 25 amplitude[J]. Solar Physics, 2020, 295(12):1-14. DOI:10.1007/s11207-020-01723-y.
[24] Li Q, Wan M, Zeng S G, et al. Predicting the 25th solar cycle using deep learning methods based on sunspot area data[J]. Research in Astronomy and Astrophysics, 2021, 21(7):184. DOI:10.1088/1674-4527/21/7/184.
[25] Gleissberg W. A long-periodic fluctuation of the sun-spot numbers[J]. The Observatory, 1939, 62:158-159.
[26] Charbonneau P. Dynamo models of the solar cycle[J]. Living Reviews in Solar Physics, 2010, 7:1-91. DOI:10.1007/s41116-020-00025-6.
[27] Solanki S K, Krivova N A. Analyzing solar cycles[J]. Science, 2011, 334(6058):916-917. DOI:10.1126/science.1212555.
[28] Mendoza B, Velasco-Herrera V M. On mid-term periodicities in sunspot groups and flare index[J]. Solar Physics, 2011, 271(1):169-182. DOI:10.1007/s11207-011-9802-x.
[29] Petrovay K. Solar cycle prediction[J]. Living Reviews in Solar Physics, 2020, 17:1-93. DOI:10.1007/s41116-020-0022-z.
[30] Velasco Herrera V M, Mendoza B, Velasco Herrera G V. Reconstruction and prediction of the total solar irradiance:from the Medieval Warm Period to the 21st century[J]. New Astronomy, 2015, 34:221-233. DOI:10.1016/j.newast.2014.07.009.
[31] Basu S, Meckesheimer M. Automatic outlier detection for time series:an application to sensor data[J]. Knowledge and Information Systems, 2007, 11(2):137-154. DOI:10.1007/s10115-006-0026-6.
[32] Papadimitriou S, Kitagawa H, Gibbons P B, et al. LOCI:fast outlier detection using the local correlation integral[C]//Proceedings 19th International Conference on Data Engineering (Cat. No.03CH37405). March 5-8, 2003, Bangalore, India. IEEE, 2003:315-326. DOI:10.1109/ICDE.2003.1260802.