## 3 Results and Discussion
### Comparisons of Different ML Models for Estimating Leaf Area of \(D\). mobile Leaves  
A sum of 63 different ML models was developed for estimating the LA of \(D\). _nobile_ leaves. Input combinations are described in Table 1, which forms the various ML models: MLR (1-9), SVR (1-9), and GBR (1-9), each has nine models using the various input combinations. ANN also used these input combinations along with different network architectures which are described in Table 2. Among the 36 ANN models (Table 6) developed for each input combination, the best nine ANN models were taken based on higher R\({}^{2}\) and lower MAE and RMSE values. Therefore, for LW, LW\({}^{2}\), LW\({}^{3}\), L\({}^{2}\)W, L\({}^{2}\)W\({}^{3}\), L\({}^{3}\)W, L\({}^{3}\)W\({}^{2}\), and L\({}^{3}\)W\({}^{3}\) input combinations ANN2 (2-5-1), ANN6 (2-5-1), ANN10 (2-5-1), ANN15(2-10-1), ANN18 (2-5-1), ANN22 (2-5-1), ANN26 (2-5-1), ANN31 (2-10-1), and ANN35 (2-10-1) models, respectively, were compared with other models, i.e., MLR, SVR, and GBR. Table 7 depicts the LA models developed using different input combinations of L and W of \(D\). _nobile_ leaves using MLR (MLR1-MLR9) machine learning techniques. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Inputs**} & \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Training**} & \multicolumn{4}{c}{**Testing**} \\ \cline{3-8}  & & **R\({}^{2}\)** & **MAE** & **RMSE (cm\({}^{2}\))** & **R\({}^{2}\)** & **MAE** & **RMSE (cm\({}^{2}\))** \\ \hline LW & ANN1 & 0.96 & 0.93 & 1.29 & 0.96 & 0.89 & 1.21 \\
**LW** & **ANN2** & **0.96** & **0.87** & **1.27** & **0.96  
A comparison of the performance statistics of MLR, SVR, GBR, and ANN models used for LA estimation was performed based on testing and training results using R\({}^{2}\), MAE, and RMSE values which are enumerated in Table 8. The R\({}^{2}\) value in the training phase varied from (0.95-0.97), 0.94, 0.96, and (0.73-0.96) in case of MLR, SVR, GBR, and ANN, respectively. Similarly, the MAE values in the training phase varied from (0.84-1.11), (0.87-0.93), 0.86 and (0.87-2.77), for MLR, SVR, GBR, and ANN, respectively. RMSE values in the training phase ranged from (1.15-1.42) cm\({}^{2}\), (1.47-1.58) cm\({}^{2}\), 1.18 cm\({}^{2}\) and (1.25-3.78) cm\({}^{2}\), for MLR, SVR, GBR, and ANN, respectively. In the testing phase, the R\({}^{2}\) values ranged from (0.94-0.96), 0.96, 0.96, and (0.88-0.97) for MLR, SVR, GBR, and ANN, respectively. Similarly, the MAE values in the testing phase varied from (0.85-1.12), (0.83-0.86), 0.82 and (0.77-1.35), for MLR, SVR, GBR, and ANN, respectively. RMSE values ranged from (1.13-1.46) cm\({}^{2}\), (1.21-1.28) cm\({}^{2}\), 1.11 cm\({}^{2}\) and (1.03-2.06) cm\({}^{2}\), for MLR, SVR, GBR, and ANN, respectively. It was observed in our study that R\({}^{2}\), MAE, and RMSE values among the different input combinations in the training as well as in the testing dataset in GBR models showed nearly indifferent performance values. GBR showed a stable high R\({}^{2}\) values and low MAE and RMSE values in the dataset studied (Table 8) and outperformed other ML methods studied as also evident from the AR ranking methodology (Table 9). This can be attributed due to GBR models ensembling individual models which can have characteristics of being both weak and overfitting nature but the final ensembled model leads to overcome these problems, also it requires lower data preprocessing leading to low error of prediction and high stability [93,94]. No reports of GBR for LA prediction modeling in plants is known to date. However, the outperformance of GBR over other ML methods are noticed in other fields. A recent study reported that gradient boosting regression algorithm (GBR) and random forest (RF) was employed for predicting and analyzing the net ecosystem carbon exchange (NEE) at UK-Gri, based on the flux data and meteorological data.