# Prediction of Harvest Time of Apple Trees: An RNN-Based Approach
## 5 Discussion  
In the results obtained with the MR method (Table 6), the RMSE metric obtained an average value of 2.58 in the selected samples, and the metric of the MLP method (Table 7) obtained an average value of the RMSE metric of 3.09. Comparing these results, the MR method had a better result with a difference of 0.51. However, it was observed that the standard deviation measure, which is a measure of dispersion around the mean, shows that the results obtained with MLP are more uniform. The values obtained with PredHarv (Table 3) in the RMSE metric are 0.90 with a standard deviation of 0.17 for the selected samples. These values are lower than those obtained with the MR and MLP method. The difference between the results obtained with PredHarv is 2.19 lower compared to MLP, and it is 1.68 lower than with MR. The standard deviation measurement of the PredHarv method also shows uniformity in the results obtained.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **RMSE** & **MAE** \\ \hline
1 & 3.68 & 3.47 \\
2 & 1.54 & 1.16 \\
3 & 1.23 & 0.95 \\
4 & 3.92 & 3.41 \\
5 & 2.56 & 2.16 \\ \hline Average & 2.58 & 2.23 \\ Standard deviation & 1.21 & 1.19 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Best results using AutoSklearn with MR.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **RMSE** & **MAE** \\ \hline
1 & 4.13 & 3.78 \\
2 & 2.94 & 3.31 \\
3 & 1.97 & 1.69 \\
4 & 4.46 & 3.67 \\
5 & 1.96 & 1.55 \\ \hline Average & 3.09 & 2.80 \\ Standard deviation & 1.17 & 1.09 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Best results using AutoKeras with MLP.  
Auto-sklearn and Autokeras are fully automatic AutoML methods. They are black box models, and their internal structure is unknown, being limited to measures of input and output relationships. However, these methods search a vast space of models and build complex sets of high precision, building models based on the data, which collaborates with the purpose for which they were submitted in this work. Investigations of other methods that can be applied to the problem demonstrate that the choice of the LSTM method is adequate to the nature of the problem. The ML method used exploits the potential of LSTM networks, which are a special type of RNN to deal with problems involving time series. PredHarv model predictions are made from the phenological stage of full bloom. These time series are a set of observations ordered in time, and they have a temporal dependence between the observations. Recurrent networks applied to this type of problem have the ability to capture part of the information implicit in the series, reflecting the impact of a sequence of environmental stimuli on plant development.  
Linear models that use the sum of degree-days have been used to estimate the duration of phenological periods of apple trees and other crops ([PERSON] and [PERSON], 2017). These models, when adjusted to estimate phenological sub-periods of apple trees, present results with a lower variability in the accumulation of degree-days for most phenological stages between seasons, compared to the number of days, responding better to the thermal sum than to the chronological time (calendar days). According to ([PERSON] and [PERSON], 2017), linear models have the obvious defect that the capability of the model is limited to a linear function, and therefore, the model may not explain the interaction between any two input variables. The PredHarv model uses thermal sum models as a baseline, but it uses a multivariate approach. We use the thermal sum relating the accumulation of degree-days to the duration of the period and other temperature-related variables in order to estimate the chronological time. The inclusion of other variables, with the multivariate strategy associated with the use of an ML method as proposed in this work, significantly improves the response, as can be seen in