## 4 ANN-Based Prediction Model Development and Validation
### Prediction Model Development
#### 4.1.2 Division of the Datasets  
As the number of data points in the datasets for each space of the hot stamping was small, we divided the datasets into an input dataset and test dataset. Initially, 80% of the data points in the overall dataset were allocated to the input dataset for training the model, while 20% were allocated to the test dataset. We exploited statistical techniques to optimally utilize limited data. We utilized the _k-fold_ cross-validation (_k-fold_ CV) technique, which has proven to be very useful for small datasets [56]. _k-fold_ CV provides the opportunity for each data point in the input dataset to be used for cross-validation at least one time and for training \(k\) one time [56], as shown in Figure 3.  
In this work, the input dataset consisted of 40 data points, while the test dataset contained 10 data points. Fourfold cross-validation was employed on the input dataset to generate distinct combinations of the training and CV datasets. This helps to prevent overfitting and ensure optimal utilization of the input data. The input dataset contained 30 points for training and 10 data points for cross-validation.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**PSPP** & & **Input Parameters** & **Output Parameters** \\ \hline \multirow{8}{*}{**Process–Structure**} & \multirow{4}{*}{**Heating**} & a. & Initial Microstructure & a. & Austenite phase fraction values (\%) \\  & & b. & Heating Rate & b. & Ferrite phase fraction values (\%) \\  & & c. & Soaking Temperature & c. & Pearlite phase fraction values (\%) \\  & & d. & Suaking Time & c. & Pearlite phase fraction values (\%) \\ \cline{2-4}  & \multirow{4}{*}{**Forming and Quenching**} & a. & Austenite Phase Fraction Value (\%) & \\  & & b. & Various temperature ranges to & a. & Martensite phase fraction values (\%) \\  & & which the blank is heated & b. & Bainite phase fraction values (\%), \\  & & c. & Various starting temperatures for & and \\  & & d. & Cooling Rate & c. & Ferrite phase fraction values (\%) \\  & & e. & Various deformation amounts (\%) & \\ \hline \multirow{4}{*}{**Structure–Property**} & a. & Martensite phase fraction values (\%) & & a. & Hardness \\  & b. & Bainite phase fraction values (\%) & & b. & Tensile Strength \\ \cline{1-1}  & c. & Ferrite phase fraction values (\%) & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters involved in the PSPP chain of the Hot Stamping Process.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Initialization Methods**} & **Description** \\ \hline (1) & Conventional Random Initialization & \(W^{l}=np.random.randn(l-1,\ l)\) \\ \hline (2) & [PERSON] Random Initialization [59] & \(W^{l}=np.random.randn(l-1,\ l)*np.sqrt(2/l-1)\) \\ \hline (3) & A variance of the Random Initialization Proposed by [PERSON] et al. [59] & \(W^{l}=np.random.randn(l-1,\ l)*np.sqrt(2/(l-1+l))\) \\ \hline (4) & [PERSON] Random Initialization [60] & \(W^{l}=np.random.randn(l-1,\ l)*np.sqrt(1/l-1)\) \\ \hline (5) & Normal (Gaussian) Distribution & \(W^{l}=np.random.normal(mean,sigma,(l-1,\ l))\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Random Initialization Methods.