## 3 Experimental Studies
### Model Development  
Many models, from classical ML methods to complex ANN algorithms, were tested within the scope of the study. Regarding the ML approaches, there were certain parameters determining the performance and flexibility of the algorithms that were used in the model development phase. These parameters are often called \"hyperparameters\" and control aspects of the model, such as how it learns, generalizes, and manages complexity. The study results indicated that regression-based models and hyperparameters were used for each model and are illustrated in detail in Table S1. Immediately after the regression models' development, DT-based ML models were developed. The hyperparameters and detailed  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**SN** & **Cycle\_Index** & **Temperature** & **Voltage (V)** & **Current (A)** & **Discharge\_Capacity (Ah)** \\ \hline
1 & 1 & 10 & 3 & \(-\)2.2821 & 2.6448 \\
2 & 1 & 10 & 2.9999 & \(-\)2.2819 & 2.6517 \\
3 & 1 & 10 & 3 & \(-\)2.2820 & 2.3965 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Example LIB data.  
information about the developed models are presented in Table S2. The other type of ML model analyzed in this study was the SVM-based approach. Information about the SVM types and the hyperparameters used in these types are demonstrated in Table S3.  
Following classical ML models, ANN-based models were included in the study. Hyperparameters of the ANN models, which were analyzed within the scope of the study, are demonstrated in Table S4.  
While many models were used, a new model was created using curve fitting based on an ANN. Here, it was inclined to reach the discharge capacity results expected to be obtained as a result of 4 input data in the input layer. After the input data X1, X2, X3, and X4, there was a hidden layer of the network, as well as the output layer that was expected to be reached. The image of this neural network is shown in Figure 3.  
As seen in Figure 3, an estimation of the discharge capacity value in the output layer was attempted with 4 input data in the input layer. The Levenberg-Marquardt method was employed for the optimization of this neural network. This optimization method ensures that the network runs faster and produces results. The results obtained were found to be promising. By using 20% cross-validation of the dataset, the data were randomly selected, and the training and testing processes were carried out in 5 separate clusters. This is an important factor that increases the reliability of training and testing. The training was carried out over 1000 epochs, and the results are shown in Figure 4.  
Figure 3: The architectural structure of the proposed model (blue circles are input and output layer neurons; orange circles are hidden layer neurons.).  
The graph showing the performance of the model during training is pointed out in Figure 5. It was obvious that the error rate of the model was gradually decreasing. In Figure 5, the error rate of the model was highlighted depending on the mean square error and the number of iterations.  
Table 4 provides information about the operations performed for the model. The dataset, the ratio allocated for training and testing, the number of iterations, the optimization method that was used, and the information required for the input and output are included in Table 4.  
Figure 4: Results obtained from the proposed model.  
Figure 5: Training performance graph of the model.  
The hyperparameters were implemented to give the best results in the developed neural network, given in Table 4. Although different numbers of hidden layers were applied in the performance of the model, it was observed that the best result consisted of 33 layers. It consisted of 4 input layers, 33 intermediate layers, and 1 output layer. The output layer served as the prediction layer. The obtained information, such as MSE 0.0281 and Result = 0.9147, have been explained in detail in the Section 4.