# Truncated Newton Kernel Ridge Regression for Prediction of Porosity in Additive Manufactured SS316L
## 5 Conclusions  
The relative density of SS316L fabricated by SLM has been studied using data from the literature merged with experimental data collected for this study. Different plots visualize the trends between the input process parameters (i.e., laser power, scan speed, hatch distance, and layer thickness) and the corresponding relative density. ML techniques, such as \(RR\), \(SVR\), and \(KRR\), are used to predict the relative density of the parts, and their performances are compared.  
Based on observational analysis of the dataset, the laser power and scan speed have a strong effect on the relative density: high power and high speed would generate better densification of the parts. In comparisons between the \(RR\), \(SVR\), and \(KRR\) models, \(KRR\) outperformed \(RR\) and showed a slightly better performance than \(SVR\) based on its lower \(MSE\) and higher \(R^{2}\) values. The \(KRR\) may have sufficient predictability for the relative density of the SS316L parts as a function of the laser power, scan speed, hatch distance, and layer thickness.  
The methods and findings in this study would be beneficial for AM designers who seek high-precision models to predict AM part properties using input process parameters. It could also reduce the expense of more experimental trials by prescribing the optimal process parameters, consuming less energy, and generating environmental benefits [50]. The presented machine learning methods predict the porosity of 3D printed materials by identifying the relationship between the process parameters and pores. Thus, the formation of pores can be inhibited by finding the appropriate process parameters. Future work can use the developed predictive models combined with an optimization method to prescribe the optimal process parameters for minimizing pores.  
Conceptualization, I.B. and H.A. ([PERSON]); Data curation, H.A. ([PERSON]), I.B. and H.A. ([PERSON]); Formal analysis, H.A. ([PERSON]), M.M. and I.B.; Funding acquisition, I.B. and H.A. ([PERSON]); Methodology, I.B. and M.M.; Project administration, I.B. and H.A. ([PERSON]); Software, H.A. ([PERSON]) and M.M.; Writing--original draft, H.A. ([PERSON]); Writing--review & editing, M.M., I.B. and H.A. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Optimal Parameters**} & \multicolumn{2}{c}{**Accuracy**} \\ \cline{3-4}  & & \(\mathbf{R^{2}}\) & \(\mathbf{MSE}\) \\ \hline \(RR\) & \(\lambda=0.006\) & 0.701 & 0.299 \\ \hline \(SVR\) & \(\gamma=0.4\), \(\varepsilon=0.05\) & 0.830 & 0.170 \\ \hline \(KRR\) & \(\lambda=0.01\), \(\sigma=2.9\) & 0.853 & 0.161 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Optimal tuning parameters and accuracy of the models.  
**Funding:** This research was funded by Khalifa University of Science and Technology grant number RCII-2019-003.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.