## 1 Introduction  
Forest fires represent a natural phenomenon that causes economic and societal losses around the world [1, 2]. The size of a forest fire in 3-5% of cases reaches 100 hectares [3]. At the same time, only 1% of the largest fires account for 80-96% of the burnt area [4]. The spread of WUI zones provides greater contact between wild vegetation and anthropogenic activity, which can cause an increase in the zones of possible sources of ignition and, as a consequence, an increased destructive effect [5, 6]. In the event of a forest fire, not only vegetation, but also soil, suffers. Heat is transferred down to colder areas deeper in the soil, which can lead to an increase in soil temperature in shallow subsurface layers up to 600 \({}^{\circ}\)C [7]. Such extremely high temperatures can irreversibly change the biological and chemical properties of the soil, significantly reduce the water content in the soil and damage all organisms contained within [8, 9, 10, 11]Currently, the fight against this phenomenon is taking place not only directly in the places of origin, but in scientific laboratories around the world. To reduce the destructive effect, it is important to develop not only methods of extinguishing a fire, but also methods for predicting the occurrence of a forest fire, the development of detection systems [12] and predicting its further behavior. The simulation results will improve the quality of forest fire fighting. In [13], methods of combating the movement of a forest fire front were described. In [14], a simulation of the effectiveness of blocking the spread of fire in the field was carried out. There are many areas of development, from predicting the likely environmental impact to predicting the spread of smoke within confined spaces. According to [15], about 40% of PM emissions are associated with forests. The development of forecasting methods consists in the development of algorithms, the development of probabilistic and deterministic models, the development of monitoring technologies. So, in [16] a carbon sensor was presented, which allows us to capture carbon particles from the forest fire front, while not taking into account particles from other sources. In [17], the simulation of the effect of forest fires on soil erosion was carried out. In [18], a model was presented that predicts the rate of fuel mass loss in a confined space, taking into account ventilation. In [19], a numerical simulation of the environmental impact of fires on the territory of Siberia, Russian Federation, on air quality over Central Asia, Mongolia and North China was carried out. Active research is underway to develop flame propagation models. Many studies have examined the effect of landscape on fire propagation with a wide sample of forest fires and different weather conditions [20]. Usually, the bulk of research has been based on research using software modeling to test the ultimate effect of landscape composition on ease or inhibition of fire propagation [21; 22; 23; 24; 25]. Zone or field models are used to simulate fire propagation. Zonal models give better performance results than analytical models [26; 27]. However, they require the availability of experimental data, which can give a large error. Nowadays, field models are being actively developed, which divide the volume by the computational grid, and within this grid, the differential equations of the fire flow with varying complexity are numerically solved [28; 29; 30]  
Neural networks are great for probabilistic models since they are able to learn by calculating the model without initial data sets. Machine learning is widely used for classification, regression and clustering in various fields such as predictive analysis, computer vision and risk analysis [31; 32; 33; 34]. So, machine learning is used to analyze climate change for the risk of forest fires [35; 36]  
Deterministic models can be used to predict the spread of forest fires.