## 5 Conclusions  
In this study, a new technique to improve the accuracy of the thermal analysis model for LPBF process simulation by nonlinear regression and an optimization algorithm was proposed, and validation was performed by evaluating the errors using a finite element thermal analysis model. A regression model was constructed using the thermal analysis results for analysis parameter cases generated by Box-Behnken design, and sensitivity analysis and parameter optimization were performed on analysis parameters. According to the sensitivity analysis, it turned out that the porosity, OPD, and absorptivity had a dominant influence on the melt pool size. By applying arbitrary analysis parameter cases for these dominant parameters to the thermal analysis model and using the regression model for validation, it was confirmed that the regression model behaves similarly to the thermal analysis model for the given parameter ranges. By using this regression model, the dominant thermal analysis parameters were optimized so that the thermal analysis model could produce the thermal analysis results closest to the given reference data, which were the melt pool sizes in this study. The optimization results show that the proposed technique can accurately and efficiently find the values of the dominant thermal analysis parameters of the originally assumed thermal analysis model, which has generated the reference data. The thermal analysis parameters obtained by the optimization had a maximum error of 1.72% from the originally assumed \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Parameter**} & \multicolumn{1}{c}{**Gradient**} & \multicolumn{1}{c}{**Error (\%)**} & \multicolumn{1}{c}{**PSO**} & \multicolumn{1}{c}{**Error (\%)**} & \multicolumn{1}{c}{**Genetic**} & \multicolumn{1}{c}{**Error (\%)**} \\ \hline Analysis & Porosity & 0.39 & 0.393 & 0.8 & 0.39 & 0.11 & 0.39 & 0.03 \\ parameter & OPD (\(\upmu\)m) & 150 & 152.52 & 1.68 & 152.27 & 1.51 & 152.36 & 1.57 \\ case 1 & Absorptivity & 0.57 & 0.569 & 0.18 & 0.57 & 0.25 & 0.57 & 0.22 \\ \hline Analysis & Porosity & 0.41 & 0.406 & 0.97 & 0.41 & 0.96 & 0.41 & 0.96 \\ parameter & OPD (\(\upmu\)m) & 160 & 162.2 & 1.37 & 162.14 & 1.34 & 162.15 & 1.34 \\ case 2 & Absorptivity & 0.47 & 0.468 & 0.41 & 0.39 & 0.43 & 0.47 & 0.42 \\ \hline Analysis & Porosity & 0.39 & 0.393 & 0.8 & 0.39 & 0.73 & 0.39 & 0.78 \\ parameter & OPD (\(\upmu\)m) & 130 & 132.23 & 1.72 & 132.21 & 1.7 & 132.24 & 1.72 \\ case 3 & Absorptivity & 0.53 & 0.531 & 0.16 & 0.53 & 0.2 & 0.53 & 0.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Relative error in melt pool size between analysis model and regression model. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Gradient** & **PSO** & **Genetic** \\ \hline Number of iterations & 254 & 296,847 & 495,000 \\ Time (sec) & 0.133 & 136.61 & 157.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The number of iterations and elapsed time according to optimization algorithm. analysis parameter values. Therefore, if the proposed technique is applied to the actual LPBF process, it is expected that a high-fidelity thermal analysis model that can accurately predict the characteristics of actual products from the reference data obtained from minimal experimental builds can be constructed efficiently, and this thermal analysis model can significantly reduce the experimental builds required to determine proper process parameters to fulfill quality requirements of additively manufactured products. E.G.P., J.W.K., J.Y.C. and J.H.K. all contributed to the collection of data and preparation of the paper. All authors have read and agreed to the published version of the manuscript. This research was funded by the Ministry of Land, Infrastructure and Transport of the Korean government and Korea Agency for Infrastructure Technology Advancement, grant number (21 CHTR-C128889-05) from Establishment of Design and Manufacturing Certification Infrastructure on Rotocrraft Certification. The APC was funded by 21 CHTR-C128889-05.