# A Multiple-Input Neural Network Model for Predicting Cotton Production Quantity: A Case Study
## 6 Numerical Experiments
Additionally, MNN\({}_{2}\) exhibited 10.5-22.6% and 13.6-23.4% lower MAPE and sMAPE scores, respectively compared to the performance of the neural network-based models. LSTM, GP, kNN, and LR presented competitive performance to MNN\({}_{1}\); however, they were considerably outperformed by the versions of the proposed model which utilized recurrent hidden layers, i.e., MNN\({}_{2}\) and MNN\({}_{3}\). This implies that the utilization of hidden layers with recurrent units favored the performance of the proposed MNN model. Additionally, LASSO and SVR reported the worst performance, regarding all metrics. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Model** & **Type** & **MAE** & **RMSE** & **MAPE** & **sMAPE** \\ \hline \begin{tabular}{c} FFNN \\ LSTM \\ GRU \\ \end{tabular} & Neural network-based & 46.784 & 57.776 & 16.464 & 16.030 \\ \begin{tabular}{c} Neural \\ regressors \\ \end{tabular} & 43.303 & 55.378 & 14.203 & 14.598 \\ \begin{tabular}{c} Stochastic \\ \end{tabular} & 44.826 & 56.103 & 15.124 & 15.243 \\ \hline \begin{tabular}{c} DTR \\ GP \\ \end{tabular} & State-of-the-art & 45.942 & 57.920 & 17.081 & 15.407 \\ \begin{tabular}{c} Stochastic \\ \end{tabular} & 41.475 & 54.634 & 15.697 & 13.964 \\ \begin{tabular}{c} kNN \\ LASSO \\ \end{tabular} & 45.441 & 54.963 & 16.030 & 15.236 \\ \begin{tabular}{c} LASSO \\ LR \\ \end{tabular} & 57.647 & 72.792 & 18.199 & 19.480 \\ \begin{tabular}{c} LR \\ SVR \\ \end{tabular} & 41.480 & 54.641 & 15.699 & 13.965 \\ \begin{tabular}{c} Stochastic \\ \end{tabular} & 65.517 & 79.045 & 20.024 & 22.881 \\ \hline \begin{tabular}{c} MNN\({}_{1}\) \\ MNN\({}_{2}\) \\ MNN\({}_{3}\) \\ \end{tabular} & Proposed model & 40.479 & 52.741 & 14.272 & 13.632 \\ \
\begin{tabular}{c} Proposed model \\ MNN\({}_{3}\) \\ \end{tabular} & 39.612 & 49.439 & 13.164 & 12.840 \\
\begin{tabular}{c} MNN\({}_{3}\) \\ \end{tabular} & **38.707** & **48.213** & **12.713** & **12.608** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance of the proposed MNN model and the state-of-the-art prediction models. In summary, the interpretation of Table 5 reveals that the three different architectures of the proposed MNN model exhibited the best overall performance, regarding all metrics. Furthermore, the utilization of the recurrent layers (LSTM and GRU), instead of the traditional dense layers, benefited its performance considerably. It is also worth mentioning that the proposed model exhibited slightly better performance utilizing GRU layers, instead of LSTM layers. This may be due to the fact that each LSTM unit has more gates for the gradients to flow through, causing steady progress to be more difficult to maintain [22; 31]. Nevertheless, this is surprising since GRU frequently suffers from the vanishing gradient problem [32]. By taking these into consideration, we are able to conclude that the vanishing gradient problem rarely or did not occur in our experiments. A possible explanation for this could be the utilization of ReLU activation function, the less complex architecture of the proposed model compared to that of a fully connected network, as well as the complexity and size of the used dataset. This is certainly worth being investigated in the near future.