Correlating sunspot numbers with Alfve<acute accent>n and Magnetosonic Mach number across last four solar cycles and prediction of solar cycle 25 with LSTM+model

Solar activity dynamics are explored through an in-depth analysis of the interplay between sunspot numbers and critical magnetohydrodynamic parameters specifically Alfve<acute accent>n Mach number and Magnetosonic Mach number over the past four solar cycles (SC). Our investigation reveals a robust negative correlation between SSN and both Alfve<acute accent>n Mach number and Magnetosonic Mach number, shedding light on the intertwined nature of solar magnetic phenomena and magnetohydrodynamic processes. Significant temporal synchronicities are unveiled, elucidating compelling alignments between specific features of Alfve<acute accent>n Mach number and Magnetosonic Mach number and the peaks and troughs of SSN throughout the solar cycles. This temporal coherence underscores the complex interplay between solar magnetic activity and the broader dynamics of magnetohydrodynamic phenomena, providing deeper insights into solar cycle behavior. To enhance our understanding and predictive capabilities, we deploy an optimized LSTM+model for forecasting Alfve<acute accent>n Mach number and Magnetosonic Mach number in the ongoing solar cycle, SC-25. Rigorous validation of the model's accuracy is achieved through meticulous examination of prediction results for SC-24, affirming the reliability and robustness of our predictive framework. Furthermore, the anticipated timing of the first appearance to peak and the overall peak of SSN in SC-25 is calculated as 2 Jun. 2023 +/- 34 days and 16 Jan. 2025 +/- 27 days, respectively. Notably, these projections suggest the possibility of a double peak phenomenon in SC-25, characterized by comparable intensity levels around 160. (c) 2024 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/).