## 5 Conclusions  
In this paper, we presented a framework to analyze and optimize the SLM process other than the more widely-used experimental and numerical techniques. We used machine learning (ML) methods with the SLM numerical model to study the sensitivity and uncertainty during the additive process. Neural networks and polynomial chaos expansions were the primary machine learning methods that we considered. The dataset of full-order numerical solutions was performed using ANSYS additive software and the results were validated using publicly available experimental results. The 3D thermo-mechanical finite element model was used to solve a set of 360 samples created using the Sobol sampling technique. The outputs from the 360 samples were then used to train and test the surrogate models. We found that the deep neural network model was faster than the PCE model, so we adopted the DNN model for the rest of the analyses. Once the DNN model was trained, it was combined with the Monte Carlo technique to find the number of simulations needed to perform the sensitivity and uncertainty analyses in the SLM process. The standard deviation convergence plots for each sample set helped us to conclude that 6000 samples are sufficient to perform the study. The sensitivity analysis revealed that the Young's modulus and Poisson coefficient are the most critical parameters during the process, while the layer thickness, laser speed, and hatch spacing are less important. However, the machine parameters still hold significant importance (5% to 10%). As all the parameters hold significant importance in the SLM process, we considered all five parameters for the optimization analysis. The surrogate DNN model was utilized to optimize with three different algorithms: GA, PSO, and DE. The results were compared, and all three algorithms were found to be equally good at calculating the optimal solution; however, PSO took the least time. The combination of DNN and PSO for optimization provided good results and incurred significantly less computation cost. In the future, as an extension of this study, we will work with the physically informed machine learning models to improve results.  
Conceptualization, S.C. and A.S.; methodology, S.C. and A.S.; software, S.C.; validation, S.C.; formal analysis, S.C. and A.S.; investigation, S.C.; resources, A.S.; data curation, S.C.; writing--original draft preparation, S.C.; writing--review and editing, A.S. and S.C.; visualization, S.C.; supervision, A.S.; project administration, A.S.; funding acquisition, A.S. All authors have read and agreed to the published version of the manuscript.  
Figure 21: Confidence intervals of simulation results from DNN model and for the optimized parameters obtained from PSO. (**a,b**) represent the x and y strains, respectively.  
**Funding:** This research was enabled by funding from the Natural Sciences and Engineering Research Council of Canada, and by computational support from Calcul Quebec and Compute Canada.  
**Data Availability Statement:** The experimental data can be found on the NIST website: [[https://www.nist.gov/ambench/amb2018-01-description](https://www.nist.gov/ambench/amb2018-01-description)]([https://www.nist.gov/ambench/amb2018-01-description](https://www.nist.gov/ambench/amb2018-01-description)) (accessed on 22 December 2021). Whereas the workbench additive simulation and the data generated using the simulation are available on the GitHub account: [[https://github.com/shubhamets/SLM_simulation.git](https://github.com/shubhamets/SLM_simulation.git)]([https://github.com/shubhamets/SLM_simulation.git](https://github.com/shubhamets/SLM_simulation.git)) (accessed on 22 December 2021).  
**Conflicts of Interest:** The authors declare no conflict of interest.