The auroral activity indices AU, AL, AE, introduced into geophysics at the beginning of the space era, although they have certain drawbacks, are still widely used to monitor geomagnetic activity at high latitudes. The AU index reflects the intensity of the eastern electric jet, while the AL index is determined by the intensity of the western electric jet. There are many regression relationships linking the indices of magnetic activity with a wide range of phenomena observed in the Earth's magnetosphere and atmosphere. These relationships determine the importance of monitoring and predicting geomagnetic activity for research in various areas of solar-terrestrial physics. The most dramatic phenomena in the magnetosphere and high-latitude ionosphere occur during periods of magnetospheric substorms, a sensitive indicator of which is the time variation and value of the AL index. Currently, AL index forecasting is carried out by various methods using both dynamic systems and artificial intelligence. Forecasting is based on the close relationship between the state of the magnetosphere and the parameters of the solar wind and the interplanetary magnetic field (IMF). This application proposes an algorithm for describing the process of substorm formation using an instrument in the form of an Elman-type ANN by reconstructing the AL index using the dynamics of the new integral parameter we introduced. The use of an integral parameter at the input of the ANN makes it possible to simulate the structure and intellectual properties of the biological nervous system, since in this way an additional realization of the memory of the prehistory of the modeled process is provided.