## 4 Restrictions on Selected Input Variables
Furthermore, four different neural network learning algorithms were used: multilayer perceptron, probabilistic neural network, and generalized feed-forward and linear regression. Among the forecasting methods, the multiple regression model attained the highest MAE (0.34 t\(\cdot\)ha\({}^{-1}\)). In turn, among the neural network learning techniques, the ANN linear regression model was characterized by the largest MAE, which was the same as for the multiple regression model, i.e., 0.34 t\(\cdot\)ha\({}^{-1}\). The probabilistic ANN model was characterized by the lowest error rate (MAE = 0.12 t\(\cdot\)ha\({}^{-1}\)). [PERSON] and [PERSON] [172] obtained similar results using a less popular approach of forecasting plant productivity, as they covered 2247 fields located in the United States and Canada. For the prediction of maize yield, four different models were applied: deep neural network (DNN), least absolute shrinkage and selection operator (LASSO), shallow neural network (having a single hidden layer with 300 neurons), and regression tree. The achieved cross-validation results indicated that the most accurate model was the DNN model, with an RMSE of 12.79 dt\(\cdot\)ha\({}^{-1}\). The LASSO model was the least accurate, with an average RMSE of 21.40 dt\(\cdot\)ha\({}^{-1}\). The further development of artificial neural networks in the forecasting of agricultural crops should be targeted toward determining to what extent this approach can be implemented and developed in precision agriculture [173]. The current trends in yield forecasting focus on remote sensing data that reflect the condition of the crop. Recent scientific works have demonstrated the possibility of estimating crop yield based on hyperspectral data combined with weather data. For example, Kuwata and [PERSON] [174] predicted the United States corn yield using independent weather data and satellite plant productivity indices as variables. The best yield prediction results were achieved using a deep neural network model. [PERSON] et al. [5] also used remote sensing data and weather information to assess the size of maize and soybean crops in the Midwestern United States. The following predictors were used in these studies: NDVI; EVI; LAI; FPAR; GPP; minimum, maximum, and average temperature; and sum of precipitation. The results highlighted that the ANN model had lower prediction accuracy compared with deep neural networks, whose prediction error was on average 7.6% and 7.8% (for maize and soybean, respectively). The correlation coefficient (r) for the created model was 0.95 for maize and 0.90 for soy. [PERSON] et al. [10] examined the relationship between the NDVI obtained from the UK-DMC-2 platform and soil parameters (pH, organic matter content, soil moisture, content of calcium, magnesium, phosphorus in the soil, CEC, and others) and the yield of winter wheat. The three models based on self-organizing maps forecasted yield with an accuracy of 91.30% to 92.15%. Hyperspectral and weather data are now widely used in predictive models because these data have become easily available to professional users of precision farming. In addition, the data can be downloaded and analyzed at any stage of the growing season, proving their utility in pre-harvest yield forecasts. Future research on the application of various types of environmental data in yield forecasting may focus not only on the hybrid use of remote sensing and weather data, but also on the search for new, more reliable indicators of plant productivity that will significantly improve the accuracy of prediction. [PERSON] et al. [74] proposed the use of solar-induced chlorophyll fluorescence (SIF) from a specific NIR band as one of the predictors in the prediction of wheat yield in Australia. The achieved results showed that the combination of climate and satellite data produces higher-quality prediction compared with using only weather data or only satellite data.