This article proposes a mathematical model for protecting helicopter turboshaft engines from surges, starting with fuel metering supply and maintaining stable compressor operation. The model includes several stages: first, fuel is supplied according to a specified program; second, an unstable compressor operation signal is determined based on the gas temperature in front of the compressor turbine and the gas generator rotor speed derivatives ratio; at the third stage, when the ratios’ threshold value is exceeded, fuel supply is stopped, and the ignition system is turned on. Then, the fuel supply is restored with reduced consumption, and the rotor speed is corrected, followed by a return to regular operation. The neural network model implementing this method consists of several layers, including derivatives calculation, comparison with the threshold, and correction of fuel consumption and rotor speed. The input data for the neural network are the gas temperature in front of the compressor turbine and the rotor speed. A compressor instability signal is generated if the temperature and rotor speed derivatives ratio exceed the threshold value, which leads to fuel consumption adjustment and rotor speed regulation by 28…32%. The backpropagation algorithm with hyperparameter optimization via Bayesian optimization was used to train the network. The computational experiments result with the TV3-117 turboshaft engine on a semi-naturalistic simulation stand showed that the proposed model effectively prevents compressor surge by stabilizing pressure, vibration, and gas temperature and reduces rotor speed by 29.7% under start-up conditions. Neural network quality metrics such as accuracy (0.995), precision (0.989), recall (1.0), and F1-score (0.995) indicate high efficiency of the proposed method.