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Various methods (or recipes) have been proposed to predict future solar activity levels - with mixed success. Among these, some precursor methods based upon quantities determined around or a few years before solar minimum have provided…

Total solar irradiance variations, about 0.1% between solar activity maximum and minimum, are available from accurate satellite measurements since 1978 and thus do not provide useful information on longer-term secular trends. Recently,…

We discuss the difficulties of predicting the solar cycle using mean-field models. Here we argue that these difficulties arise owing to the significant modulation of the solar activity cycle, and that this modulation arises owing to either…

This note deals with a multivariate stochastic approach to forecast the behaviour of a cyclic time series. Particular attention is devoted to the problem of the prediction of time behaviour of sunspot numbers for the current 23th cycle. The…

Solar activity forecasting is an important topic for numerous scientific and technological areas, such as space mission operations, electric power transmission lines, power transformation stations and earth geophysical and climatic impact.…

Reliable prediction of the solar cycle is a formidable challenge, yet it is increasingly vital in our technology-dependent society as solar activity drives space weather. Various methods, including precursors, nonlinear curve fitting and…

A review of solar cycle prediction methods and their performance is given, including forecasts for cycle 24 and focusing on aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of the review is…

Having advanced knowledge of solar activity is important because the Sun's magnetic output governs space weather and impacts technologies reliant on space. However, the irregular nature of the solar cycle makes solar activity predictions a…

A review of solar cycle prediction methods and their performance is given, including early forecasts for cycle 25. The review focuses on those aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of…

We discuss a prediction of the solar activity on a short time-scale applying the method based on a combination of a nonlinear mean-field dynamo model and the artificial neural network. The artificial neural network which serves as a…

When building linear or nonlinear models one is faced with the problem of selecting the best set of variable with which to predict the future dynamics. In nonlinear time series analysis the problem is to select the correct time delays in…

This article reviews some of the leading results obtained in solar dynamo physics by using temporal oscillator models as a tool to interpret observational data and dynamo model predictions. We discuss how solar observational data such as…

The dynamic activity of stars such as the Sun influences (exo)planetary space environments through modulation of stellar radiation, plasma wind, particle and magnetic fluxes. Energetic stellar phenomena such as flares and coronal mass…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

The solar cycle and its associated magnetic activity are the main drivers behind changes in the interplanetary environment and the Earth's upper atmosphere (commonly referred to as space weather). These changes have a direct impact on the…

Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…

Building a reliable forecast of solar activity is a long-standing problem that requires to accurately describe past and current global dynamics. However, synoptic observations of magnetic fields and subsurface flows became available…

Prediction of solar activity cycles is challenging because physical processes inside the Sun involve a broad range of multiscale dynamics that no model can reproduce and because the available observations are highly limited and cover mostly…

Solar power harbors immense potential in mitigating climate change by substantially reducing CO$_{2}$ emissions. Nonetheless, the inherent variability of solar irradiance poses a significant challenge for seamlessly integrating solar power…

Solar activity is an important driver of long-term climate trends and must be accounted for in climate models. Unfortunately, direct measurements of this quantity over long periods do not exist. The only observation related to solar…