## 3 Results and Discussion
### Performance of the Development of the ANN Model  
Unlike traditional statistical methods, the ANN approach is a data-based strategy. Therefore, prior understanding of the connections between the input factors is not necessary in this instance [75]. Additionally, non-linear ANN models can be used to infer relationships between the input and output parameters that are more trustworthy and robust [76]. Although helpful, the published material does not cover all aspects of ANN theory and methodology [77; 78]. The selection of training algorithms and functions for ANN development depends on the nature of the problem and the dataset [79]. Additionally, the performance of the ANN model was evaluated based on various metrics, such as the root mean squared error, mean absolute error, and the coefficient of determination. By carefully monitoring the training process and evaluating the performance of the ANN model using appropriate metrics, we developed an ANN model with a high prediction \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Input Variables**} & **Working Field** & **Soil Texture Norm** & **Initial Soil Moisture** & **Horizontal Force** \\  & **Criterion (WFC)** & **(STN)** & **Content (MC)** & **Dependent Using** \\  & & & **Equation (1) Using** \\  & & & **New—Fi-Parameter** \\  & & & **(DD)** \\ \hline \hline \end{tabular}
\end{table} 
Table 7: [PERSON]’s correlation coefficients (r) between the explanatory variables (\(p\) \(<\) 0. 05). accuracy. However, the ANN model used in this study was a feed-forward-type ANN with a backpropagation algorithm for training purposes. It was established to estimate the modified values of the horizontal force based on four inputs: working field criterion, soil texture norm, initial soil moisture content, and horizontal force, as estimated by the ASABE standard when using the new--Fi-parameter. Table 8 depicts some numerical data for inputs, measured draft force (output), and predicted modified horizontal force using the developed ANN model (target). The established ANN model in this study used a dataset to train the ANN configurations with the various numbers of neurons in the hidden layer, the number of epochs, as well as the various initial connection weights that are made up of neurons with various transfer functions. Thus, several epochs and neurons were evaluated by trial and error in order to find the best configuration for the ANN in terms of predicting the modified values of the horizontal force of certain tillage implements. The best ANN configuration should have low values of MAE and RMSE, as well as a high R\({}^{2}\)[62]. The best ANN configuration from the network construction employed a single hidden layer with twenty nodes. Table 8 provides more information on the characteristics of the best ANN architectures. For the normalized data, the training error value was calculated to be 0.045099. For the training, testing, and validation datasets, as shown in Table 6, our ANN model demonstrated high values of R\({}^{2}\), as well as low values of RMSE and MAE. These outcomes demonstrated the high accuracy and great generalizability of our existing ANN for forecasting the modified horizontal force of tillage instruments. The RMSE, MAE, and R\({}^{2}\) values for the best ANN configuration for the testing dataset were 2.105 kN, 1.349 kN, and 0.8175, respectively (Table 9).