# Truncated Newton Kernel Ridge Regression for Prediction of Porosity in Additive Manufactured SS316L
###### Abstract
These techniques effectively simulate the input-output interactions of complex systems. Support vector regression (_SVR_) and kernel ridge regression (_KRR_) have been shown to perform well in various applications related to materials design. _SVR_ has been used in predicting the cutting forces and surface roughness of turning 4140 steel [11], estimating the flow stress of austenitic stainless steel 304 at high temperatures and low strain rates [12], and predicting the transition temperature of different superconductors of doped MgB2 system [13]. Furthermore, _KRR_ has been employed in estimating the local magnetic moments and formation energies of metal alloys [14], predicting the specific discharge capacity and properties of battery materials [15], and fabricating high entropy alloys with a high degree of hardness [16]. ML has also been used to predict the porosity or relative density based on different combinations of process parameters in L-PBF processes [9; 10; 17]. Metal AM aims to achieve full density parts, as porosity substantially impacts the mechanical performance of the parts, particularly the fatigue properties. [PERSON] et al. [18] have developed a random forest network ML model to predict the porosity of Inconel 718 parts fabricated using the L-PBF process based on process parameters, including part orientation, part location, and the fraction of recycled powder. [PERSON] et al. [19] have used a multi-layer perceptron to predict the porosity and microhardness of bronze parts based on the laser power, scan speed, and hatch distance. Another study [20] has estimated the porosity of stainless steel 17-4 PH parts at any combination of laser power and scan speed using genetic programming. Using artificial neural networks and _SVM_, the porosity content of titanium alloy parts fabricated by an L-PBF process has been quantified as a function of the hatch spacing, laser velocity, and laser power [21]. Few studies have compared different ML algorithms for either material extrusion processes, such as fused deposition modeling, or the use of non-metal materials in powder bed fusion processes. A hybrid M5\({}^{\prime}\)-genetic programming approach has been used to predict the compressive strength of parts fabricated with fused deposition modeling [4]. This study compared the goodness of fit of the model to those of the \(SVR\) and the adaptive neuro-fuzzy inference system. Another study [2] has compared the results of multi-layer perceptron, decision tree regression, gradient boosting regression, \(SVR\), and linear regression of the laser-sintered polyamide parts to predict their dimensional features. Stainless steel 316L (SS316L) is commonly used in powder bed fusion processes due to its excellent mechanical properties, including high structural strength and corrosion resistance. A recent study by [PERSON] et al. [22] has developed seven supervised ML regression models (i.e., \(SVM\), decision tree, random forest, gradient boosting, Gaussian process, K-nearest neighbors, and multi-layer perceptron) to predict the relative density of SS316 samples fabricated by the SLM process. They collected 112 data points from the literature and applied 5-fold cross-validation to assess the developed models. However, considering the importance of SS316L in L-PBF processes, the size of their collected dataset might have limited their conclusions about the performance of regression. Furthermore, there may be other promising regression algorithms to consider. Hence, this study aims to construct a more comprehensive dataset from multiple data sources extracted from the literature and lab experiments and use the selected ML algorithms to develop predictive models for the relative density of SS316L parts fabricated by SLM. The selected ML techniques are \(SVR\) and \(KRR\); ridge regression (\(RR\)) is used as a benchmark. \(KRR\) has become a very important data mining method, and little work has been done using this powerful algorithm to predict the performance of AM parts [23].