The buildup of thermodynamic cycle parameters is the main way to increase gas turbine engine efficiency. However, the growth of engine pressure and temperature ratio leads to the increase in the turbine heat load, which reduces the engine lifetime dramatically. In terms of gas turbine engines, to avoid the engine life loss is a crucial problem especially for small engines, because the limited size of a small gas turbine engine does not allow implementing various measures for nozzle vane cooling. In light of this, the contribution of the turbine heat control is essentially increasing. It places great demands on the accuracy of control over the main engine variables (such as the rotor speed and turbine outlet temperature). The state-of-the-industry gas turbine engines use an on-board engine mathematical model to improve the quality of the control. These models deal with engine processes of short duration and considerable overshooting. For that reason, the model accuracy is the main aspect in the control process. However, the issues of accurate and at the same time resource-saving calculation of rapidly varying processes of changing the rotor speed and the turbine gas temperature remain under-investigated. In the work, neural network methods were used to model the unsteady modes of a small gas turbine engine. Using the data obtained as a result of firing tests of the JetCat P-60 engine, the engine regression neural network model was created. The main issue that arose during the creation of the model was to describe the dynamics of rapidly varying processes with pronounced overshoot. For this purpose, modification of the architecture of the classical LSTM network was carried out, the essence of which was to add a functional dependence of the exit node on the memory tensor. This allowed us to make the memory size independent of the number of model outputs, thereby increasing the modeling accuracy. The developed architecture was proposed a new name - VMLSTM network. As a result of comparison with the traditional Elman network and the classic LSTM network, the developed VMLSTM network showed the least value of the average error with a comparable number of modifiable model parameters. In addition, unlike the existing neural networks, the developed network demonstrated the ability to simulate turbine outlet gas over-temperature at the moments when the engine operating mode changes. The developed neural network architecture increases the reliability of modeling the dynamics of a small gas turbine engine as an object of control, which in the conditions of economical use of computing resources opens up possibilities of its application in on-board microcomputers.