1. Introduction

[2]  Forecasting of ionosphere parameters for intervals from 30 min up to a few hours is used to increase the reliability of the shortwave (SW) radio communication. Solving this problem one founds that sophistication of the used physical models often does not lead to the desirable result. It happens because the entire physical picture of ionosphere processes is fairly various and involves many factors and parameters. In these conditions a complication of the analytical model does not lead to an improvement of the forecasts. Moreover, the ionosphere-magnetosphere interaction caused by the solar-terrestrial relations is significant. However, there exists an alternate approach for solution of similar problems: the method based on using a mathematical simulation of the artificial intellect [Kruglov and Borisov, 2000]. It is a method of artificial neural networks (ANN). It combines a correlative processing with nonlinear transformation of the studied multiple-factor sequence.

[3]  Neural networks are trained on the basis of experimental data and during the learning process fit automatically the weight coefficients between its elements (neurons). After that they can successfully forecast the studied process. The advantage of the ANN method is a possibility of obtaining implicit model of the system without building of its particular physical model using only rather large experimental databases. At the same time, using the experimental data in the ANN technology one has to have physical concepts on the studied cause-effect relations.

[4]  The analysis of the works related to a usage of neural networks for solution of physical and mathematical problems shows that the neural network approach have advantages (as compared to the traditional methods) in three cases. First, when the considered problem because of particular features cannot be adequately formalized by traditional mathematical methods because it contains elements of uncertainly. Second, when the considered problem is formalized but currently there is no algorithm for its solution. Third, when for the considered, well-formalized problem there exists a corresponding mathematical algorithm, but a realization of calculations with the help of it on the basis of the available computer systems does not satisfy the requirements of obtaining the solution in time, power consumption, etc. In such situation one has either to simplify the algorithms and so to decrease the solution quality or to apply the corresponding neural network approach if it provides the needed quality of the problem solution [Dyakonov and Kruglov, 2001].

[5]  Very high interest to neural networks shown by specialists from various spheres of activity is due first of all, to a very wide range of the problems solved by it and also by some advantages in comparison to other methods. Neural networks are intensively used in processing of images and nonlinear control, clarification of images and adaptive filtration, identification, and financial forecasting.

[6]  Currently, the ANN method is actively applied in forecasting problems for various geophysical applications. An incomplete list of problems successfully solved with attraction of this method is the following: long-term forecasting of the solar activity indices [Barkhatov et al., 2001], forecasting of the Dst geomagnetic index [Barkhatov et al., 2000], recovering of gaps in the records of some magnetic observatories using the data of other stations [Barkhatov et al., 2002a, 2002b], determination of the influence of a substorm on geomagnetic storms [Munsami, 2000], simulation of the solar wind influence on the magnetosphere [Gleisner and Lundstedt, 2001], forecasting of magnetic storms [Gleisner et al., 1996; Lundstedt and Wintoft, 1994], identification of substorms using the P2 pulsations [Sutcliffe, 1997], simulation of the development of the geomagnetic diurnal variation [Sutcliffe, 2000], and forecasting of solar activity [Conway et al., 1998; Fessant et al., 1996] and processes in the solar wind [Wintoft and Lundstedt, 1999].

[7]  The ANN method has been used also for a forecasting of ionospheric parameters, including forecasting of ionospheric electron density profile [McKinnell, 2003], forecasting of the ionosphere critical frequency in moderately quiet conditions [Barkhatov et al., 2003] and during geomagnetic disturbances [Wintoft and Cander, 2000].

[8]  However, Barkhatov et al. [2003] did not take into account solar-terrestrial relations. Therefore is seems important to specify the physical model taking into account the impact of varying parameters of the solar wind and interplanetary magnetic field on the ionospheric processes. Moreover, the used Elman network (due to the simple algorithm of the gradient descent) has limited intellectual possibilities and this leads to a simple remembering of the analyzing process.

[9]  This paper is dedicated to the study of possibilities of forecasting of the critical frequency taking into account not only the process prehistory, but introducing into the consideration also solar wind parameters (PSW), interplanetary magnetic field (IMF), their physically reasonable combinations, and also indices of global and local geomagnetic activity. In other words the systematized approach which is taking into account input into the neural network of predictors determining a level of the solar-terrestrial interactions is proposed. The physical aims of the study determine a choice of more branched ANN based on a more sophisticated algorithm than the Elman network.