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 surface layers. Helioseismology makes it possible to probe solar dynamics in the convective zone, but variations in differential rotation and meridional circulation are currently available for only two solar activity cycles. It has been demonstrated that sunspot observations, which cover over 400 years, can be used to calibrate the Parker-Kleeorin-Ruzmaikin dynamo model, and that the Ensemble Kalman Filter (EnKF) method can be used to link the modeled magnetic fields to sunspot observations and make reliable predictions of a following activity cycle. However, for more accurate predictions, it is necessary to use actual observations of the solar magnetic fields, which are available only for the last four solar cycles. In this paper I briefly discuss the influence of the limited number of available observations on the accuracy of EnKF estimates of solar cycle parameters, the criteria to evaluate the predictions, and application of synoptic magnetograms to the prediction of solar activity.