## 4 Results and Discussion  
The performance of various machine learning algorithms for predicting the Remaining Useful Life (RUL) was evaluated using key metrics as shown in Table 1 and discussed subsequently. Excluding Cycle Count as a feature resulted in a noticeable drop in overall model accuracy as shown in Table 1. Among the tested algorithms, the Random Forest with Extra Trees Regressor maintained the best performance (R\({}^{2}\) = 0.98, MAE = 8.86) while offering low computational cost with a training time of 15.87 s and a prediction time of 0.51 s. In contrast, the LSTM model took a much longer training time of 954.72 s, although capable of modeling temporal patterns, showed an R\({}^{2}\) of 0.89, making it less optimal for fast deployment in edge or low-resource environments. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ML** & **MSE** & **RMSE** & **MAE** & **R\({}^{2}\)** & **Training** & **Prediction** \\
**Model** & & & & & **Time (s)** & **Time (s)** \\ \hline LSTM & 12,291.69 & 110.87 & 65.39 & 0.89 & 954.72 & 5.62 \\ \hline
**LR** & 3363.206 & 57.995 & 44.55 & 0.90 & 5.97 & 0.16 \\ \hline
**ANN** & 2456.65 & 49.56 & 37.21 & 0.94 & 593.54 & 3.03 \\ \hline
**RF with** & & & & & \\
**ETR** & 384.27 & 19.85 & 8.86 & 0.98 & 15.87 & 0.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance Metrics of models without cycle count as a feature. Figure 14: Training and validation loss curves for the LSTM model after hyperparameter tuning. Figure 13: Training and validation loss curves for the LSTM model. Analyzing the Role of Cycle Count and Key Features in Reducing MSE for Lithium-Ion Battery RUL Prediction  
We see that as the cycle count of the lithium-ion battery increases, its RUL diminishes. As observed in Table 1, it is vital to notice the high MSE and MAE when compared to Table 2, which shows a relatively high gap between the actual and predicted values. This issue has been addressed and confirms that the cycle count plays a key role alongside other features in forecasting the RUL of lithium-ion batteries. Including Cycle Count as a feature led to a significant improvement in overall model performance as shown in Table 2. Among all tested algorithms, the Random Forest with Extra Trees Regressor achieved the best results, with an R\({}^{2}\) score of 0.99, MAE of 1.99, and low computational cost, requiring just 7.34 s to train and 0.05 s to predict. While Linear Regression also performed well (R\({}^{2}\) = 0.98, MAE = 4.54), it could not capture nonlinear relationships in the data. The LSTM model, although effective in modeling sequential patterns, required substantially more training time (532.72 s) and still yielded an R\({}^{2}\) of 0.97 which is better than that of the ANN and MAE of 12.04. Similarly, the ANN model performed reasonably well (R\({}^{2}\) = 0.96), but with a higher MAE of 36.06 and less training time (276.80 s) than it takes the LSTM. Overall, Random Forest with Extra Trees provided the best accuracy, efficiency, and practical balance. As seen, the Extra Tree Regressor model outperforms other models as observed from the values of the MSE and coefficient of determination, which also shows the model's accuracy. The ability of the extra trees regressor to use multiple parameters for prediction makes it a very powerful model. It is important to emphasize that the original HNEI database was generated under controlled room temperature conditions, which means the proposed models were trained and tested on datasets under controlled temperature conditions (25 \({}^{\circ}\)C) for consistency, but temperature wasn't included as an input feature. This implies that the model's predictive accuracy is optimized for standard environments. However, external temperatures such as excessive heat or extreme cold can significantly accelerate battery degradation and negatively impact RUL.