  We apply a nonlinear mean-field dynamo model which includes a budget equation
for the dynamics of Wolf numbers to predict solar activity. This dynamo model
takes into account the algebraic and dynamic nonlinearities of the alpha
effect, where the equation for the dynamic nonlinearity is derived from the
conservation law for the magnetic helicity. The budget equation for the
evolution of the Wolf number is based on a formation mechanism of sunspots
related to the negative effective magnetic pressure instability. This
instability redistributes the magnetic flux produced by the mean-field dynamo.
To predict solar activity on the time scale of one month we use a method based
on a combination of the numerical solution of the nonlinear mean-field dynamo
equations and the artificial neural network. A comparison of the results of the
prediction of the solar activity with the observed Wolf numbers demonstrates a
good agreement between the forecast and observations.
