###### Abstract
The solution to the above equations proposed by [PERSON] research team [8, 11] required them to be converted into a non-dimensional form, using vector potential and the simultaneous formulation of the initial and boundary conditions. Next, the resulting mathematical structures formed the basis for using numerical methods to obtain the solution. Thus the fields of discrete temperature obtained enabled the identification of the energy accumulated in the deposit. It is possible to use this procedure in a real situation, assuming we have an accumulator working in the vertical setting, an IT system to map the model, and the initial and boundary conditions. As mentioned before, the problem in evaluating the amount of thermal energy that was accumulated may be the unavailability and ignorance of the initial conditions based on the temperature distribution in the deposit at the beginning of the storage process. The available models are converted into algebraic equations, regarding layers of rock in a vertical system/layout. Having mathematical models to identify the temperature fields is necessary to determine the amount of energy stored within the deposits; however, first one must determine the initial input and boundary conditions [9; 10]. In practice, due to economic reasons, we lacked all the information on the conditions, and the data on the initial conditions were particularly sparse. This was a concern for almost all situations, especially the one in which a solar collector was used as a source of thermal energy. The stochastic character of this source, combined with the heterogenous flow of air during the loading phase preceded by the phase of battery stagnation, hindered the determination of the initial conditions, which are necessary in order to evaluate the volume of currently collected thermal energy within the battery using the available mathematical models. From a practical perspective, it is considered appropriate to find a limitation with regard to the economical points of temperature measurement within the rock deposit, the readings of which would allow one to determine the volume of thermal energy stored there. Knowing the initial conditions would then no longer be necessary. This mainly concerns situations that involve the battery being charged from a thermal source of stochastic character. The aim of the study is to answer the following question: To what extent can they be helpful in building up the methods of neural modeling? The answer to the above question must be preceded by a statement that confirms the possibility of designing neural models and describes the phase of storing thermal energy. This specific problem is the subject matter of this article. Having neural models depicting changeable temperatures in field, and in the function of time and space, allows us to identify thermal energy currently collected in a given deposit. This, in turn, will allow us to search for the smallest possible point or points of temperature measurement (considering economic reasons), which will allow us to identify thermal energy stored in rock deposits at any moment, independently of the initial conditions and with a broader knowledge of the boundary conditions [12; 13].