## 1 Introduction
The authors obtained higher accuracy using the ANN model prediction than with MLR. The ANN model used a network with the SigmoidAxon transfer function and the Levenberg-Marquart learning algorithm. The RMSE of the ANN model was 0.15 t-ha\({}^{-1}\), and the coefficient of determination (R\({}^{2}\)) was 0.93. For the MLR model, the RMSE was 0.21 t-ha\({}^{-1}\) and the R\({}^{2}\) was 0.79. Artificial neural networks were also compared with other crop yield estimation models. For example, [PERSON] et al. [15] compared the effectiveness of neural networks with projection pursuit regression and stepwise multiple linear regression. The analysis included fields located in the state of Missouri, USA. The study period covered 10 years and involved soybean and corn crops. The results showed that neural networks outperformed other techniques in terms of grain yield prediction quality, with R\({}^{2}\) values ranging from 0.31 to 0.74. [PERSON] et al. [60] analyzed the effectiveness of a hybrid model based on convolutional neural networks (CNNs) and recurrent neural networks. The developed model was compared with other popular methods such as random forest, deep fully connected neural networks, and LASSO. The models were used to forecast corn and soybean yields across the corn belt in the USA from 2016 to 2018. The model developed by the authors had a validation correlation coefficient ranging between 85.82% and 88.24%, and a training RMSE of 11.48 and 13.26. [PERSON] et al. [61] developed a long short-term memory model to forecast corn grain yields. The study area included nine states: Illinois, Indiana, Iowa, Kentucky, Michigan, Minnesota, Missouri, Wisconsin, and Ohio. The long short-term memory model accounted for 76% of yield variations and outperformed models like LASSO and random forest. [PERSON] and [PERSON] [62] used a Bayesian model to predict wheat grain yield. The crops located in the Canadian pra praities were included in the analysis and historical data ranged from 1976-2006. The model obtained by the authors had high prediction quality with an RMSE of 5.35 and R\({}^{2}\) of 0.70. Figure 1 shows the steps of working with predictive models. Over the years, ANNs have been successfully used to forecast the yields of agricultural plants [63; 64; 65; 66; 67; 68]. [PERSON] [69] experimented with ANN using a multilayer perceptron (MLP) topology to forecast the yield of winter rapeseed. The production fields were situated in Poland, in the southern part of the Opolskie voisvodeship. The author obtained a model that allowed forecasting the yield on June 30, having the lowest value of the mean absolute percentage error of 9.43%.The neural model research studies by [PERSON] and [PERSON] [70] explained the variability in biomass and the yield of barley grain at the level of 93% and 89%, respectively. According to [PERSON] et al. [71], in addition to the correct selection of a machine learning algorithm, an important element in creating forecasting models is choosing an appropriate number of predictors that actually shape the yield size. The choice of the independent variables constituting a predictive model is therefore a kind of compromise created by the model developer. First, data should be selected that are available throughout the entire forecast period. Secondly, variables that actually shape the quantity and quality of achieved crops should be considered. Therefore, the author of the predictive model must know the object of one's research perfectly. The factors influencing crop yield can be divided into primary and secondary. Primary factors include environmental indicators such as temperature, precipitation, insolation, soil pH, soil moisture, nutrients abundance in soil, and agronomic factors such as sowing period [4; 16; 66; 72]. The above-mentioned variables characterize the field research environment or result from local climatic conditions. Secondary factors are those that require additional measurements with the use of specialized devices and sensors in order to be known.