## 6 Implementation of the Proposed Method and Solution Space Exploration
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Error\(\backslash\)Data Type**} & \multicolumn{1}{c}{**Input Dataset**} & \multicolumn{1}{c}{**Test Dataset**} \\ \cline{2-4}  & \multicolumn{1}{c}{Martensite \%} & \multicolumn{1}{c}{5.58} & \multicolumn{1}{c}{6.31} \\ \cline{2-4} Root Mean Squared & \multicolumn{1}{c}{Bainite \%} & \multicolumn{1}{c}{4.17} & \multicolumn{1}{c}{1.73} \\ \cline{2-4} Error \% (RMSE) & \multicolumn{1}{c}{Ferrite \%} & \multicolumn{1}{c}{4.90} & \multicolumn{1}{c}{5.42} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Loss Functions for Step 2 (RMSE). \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Limits**} & \multicolumn{2}{c}{**Final Requirements**} \\ \cline{2-3}  & \multicolumn{1}{c}{**Hardness (HV)**} & \multicolumn{1}{c}{**Tensile Strength (Mpa)**} \\ \hline Lower Limit & 350 & 1250 \\ \hline Upper Limit & 430 & 1500 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Requirements on Mechanical Properties (Step 2). Figure 9: Feasible Region for Microstructure Parameters. followed as in step 2 with ANN parameters given in Table 4 for step 3.1. Figures 10 and 11 present visualizations of the predicted output and actual output for both the input dataset and test dataset, respectively. The requirements on the microstructure combinations were received from step 2 as shown in Table 10. The microstructure requirements are provided in the ranges that satisfy mechanical property requirements. Upon mapping these requirements with the results for the ANN model, a feasible region was identified as shown by the green rectangular area in Figure 12. The same procedure was followed to draw Figure 12. The red line represents the martensite phase fractions for each processing parameter combination. The martensite phase fraction was selected because the target for the forming and quenching phase is always to achieve as much martensite as possible. From the feasible region, a set of feasible values of austenite %, temperature at \(t=0\), cooling rate CR, deformation amount, and deformation temperature were identified as shown in Table 11. These identified combinations of the processing parameters for forming and quenching satisfy the microstructure requirements received from the previous step. After identifying the combinations of the processing parameters for the forming and quenching phase, i.e., austenite %, temperature at \(t=0\), cooling rate CR, deformation amount, and deformation temperature, the design information on austenite % is communicated to step 3.2. The austenite % phase fraction is the target for step 3.2. Figure 10: Predicted Output and Actual Output Comparison for Step 3.1 (for Input Dataset). **Step 3.2 Microstructure-Process Space (Heating Phase)**: The phase fraction % of martensite after forming and quenching is greatly affected by the phase fraction % of austenite. The formation of austenite during the heating phase is very influential upon the final properties of the product produced by hot stamping. The dataset for this step was obtained from [47], which involves the austenite phase fraction % as an input parameter, while the output parameters are _heating rate HR_, _soaking temperature_, and _soaking time_. The same process was followed as for previous steps with ANN parameters given in Table 4 for step 3.2. Figures 13 and 14 present plots of the predicted output and actual output for both