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Despite the known general properties of the solar cycles, a reliable forecast of the 11-year sunspot number variations is still a problem. The difficulties are caused by the apparent chaotic behavior of the sunspot numbers from cycle to cycle and by the influence of various turbulent dynamo processes, which are far from understanding. For predicting the solar cycle properties we make an initial attempt to use the Ensemble Kalman Filter (EnKF), a data assimilation method, which takes into account uncertainties of a dynamo model and measurements, and allows to estimate future observational data. We present the results of forecasting of the solar cycles obtained by the EnKF method in application to a low-mode nonlinear dynamical system modeling the solar $alphaOmega$-dynamo process with variable magnetic helicity. Calculations of the predictions for the previous sunspot cycles show a reasonable agreement with the actual data. This forecast model predicts that the next sunspot cycle will be significantly weaker (by $sim 30%$) than the previous cycle, continuing the trend of low solar activity.
The prediction of solar flares, eruptions, and high energy particle storms is of great societal importance. The data mining approach to forecasting has been shown to be very promising. Benchmark datasets are a key element in the further development o
The use of data assimilation technique to identify optimal topography is discussed in frames of time-dependent motion governed by non-linear barotropic ocean model. Assimilation of artificially generated data allows to measure the influence of variou
We develop a physics-informed machine learning approach for large-scale data assimilation and parameter estimation and apply it for estimating transmissivity and hydraulic head in the two-dimensional steady-state subsurface flow model of the Hanford
The Sun exhibits a well-observed modulation in the number of spots on its disk over a period of about 11 years. From the dawn of modern observational astronomy sunspots have presented a challenge to understanding -- their quasi-periodic variation in
Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian posterior probabil