## 3 Results and Discussion
### Comparisons of Different ML Models for Estimating Leaf Area of \(D\). mobile Leaves
GBR outperformed three state-of-the-art ML regression prediction models viz., stochastic gradient descent, support vector machine, and Bayesian ridge as GBR allows to tune a sufficient number of hyperparameters [31]. Another study depicted a model built on the gradient boosting regression tree (GBRT) with a limited sample size of data for predicting complex battery dynamics and its lifespan; having many extracted features was shown to outperform other ML algorithms. They suggested the hyperparameters viz., learning rate, maximum number of splits, and number of trees as the key to such performance. A 5-fold cross-validation technique was also applied to GBRT to prevent overfit [32]. Similar tuning of the hyperparameters (n_estimator, maximum_depth, min_sample split and learning rate) and a 10-fold cross-validation technique were applied in our leaf area modeling study and may have resulted in the best performance of GBR in our study. Again, an experiment was performed for predicting the return temperature over other ML models of district heating systems in Tianjin, China on a decision tree-based ensemble algorithm gradient boosting (GB) and it can be seen that GB outperforms other ML models without the requirement of complex feature transformation and they highlighted the importance of n_estimator in lowering the RMSE values of the tree-based \begin{table}
\begin{tabular}{c c} \hline \hline
**Model Input Combinations** & **Models** \\ \hline MLR1 & LA = \(-\)18.72 + L \(\times\) 1.74 + W \(\times\) 8.41 \\ MLR2 & LA = \(-\)9.01 + L \(\times\) 1.79 + W\({}^{2}\) \(\times\) 1.65 \\ MLR3 & LA = \(-\)6.76 + L \(\times\) 1.92 + W\({}^{3}\) \(\times\) 0.40 \\ MLR4 & LA = \(-\)9.56 + L\({}^{2}\) \(\times\) 0.08 + W\({}^{2}\) \(\times\) 8.34 \\ MLR5 & LA = 0.28 + L\({}^{2}\) \(\times\) 0.75 + W\({}^{2}\) \(\times\) 0.98 \\ MLR6 & LA = 3.37 + L\({}^{2}\) \(\times\) 0.089 + W\({}^{3}\) \(\times\) 0.40 \\ MLR7 & LA = \(-\)6.6 + L\({}^{3}\) \(\times\) 0.00049 + W\({}^{3}\) \(\times\) 0.45 \\ MLR8 & LA = 3.5 + L \(\times\) 1.79 + W\({}^{2}\) \(\times\) 1.65 \\ MLR9 & LA = 6.8 + L\({}^{3}\) \(\times\) 0.0054 + W\({}^{3}\) \(\times\) 0.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Developed LA models for three orders of L and W input combinations of \(D\). _nobile_ leaves using MLR techniques. model GB and RF [95]. A plot of RMSE of GBR with n_estimator tuned for our study is drawn in Figure 5. In our study RMSE equals to 2.78 when n_estimator is 100 and there is a decreasing trend upon increment of the n_estimator. RMSE is reduced to around 1.21 and 1.12 when n_estimator is 300 and 400, respectively. Eventually, the RMSE stabilizes to 1.1 at n_estimator 500 and achieves asymptote until it reaches 1000. This revealed the general principle that an improvement in the performance of the serial framework-based model, i.e., GBR model may be achieved (through decreased RMSE) upon increasing the n_estimator number [95]. Similarly, another report supporting GBR performance over other ML methods revealed that gradient boosting models achieved the best performance outperforming random forest and SVM for identifying the relation extraction of medications to the adverse effects of drugs, [96]. A recent report on the outperformance of GBR over ANN can be seen in the prediction of risk analysis of offshore platform integrity for its subsequent use or reuse for alternative energy applications. They studied the effect of stressors on the Remaining Useful Life (RUL). The performance metrics in the study viz., R\({}^{2}\), MAE, MSE, and RMSE depicted a slightly higher value of R\({}^{2}\) for GBR and a lower value for MAE, MSE, and RMSE than ANN model [30]. The results of these studies on the recent literatures were in general agreement of our observation highlighting our result of the best performance of GBR models in LA prediction in _D. nohile_ orchid over the three ML models MLR, SVR, and ANN.