## 1 Introduction
This approach captures the uncertainty associated with the model weights and input data, resulting in more informative and robust predictions. Bayesian approaches enable the estimation of the posterior distribution of model parameters from observed data. This estimation can be used for model selection, prediction, and uncertainty quantification. Additionally, Bayesian approaches can improve the generalization performance of ANNs by reducing overfitting and providing a principled method for selecting the appropriate model complexity. Bayesian methods have the advantage of incorporating prior knowledge into the model, which is useful when training data are limited. They are also robust to outliers and less sensitive to overfitting than non-Bayesian methods due to constraints on model complexity [23; 24]. The transition from the traditional Bayesian approach to Bayesian regularization (BR) is a significant advancement in the field of neural networks and machine learning. This approach improves network performance, making it more robust and better able to generalize to new data, without the full complexity of traditional Bayesian methods [25; 26]. Bayesian analysis is a suitable approach for addressing uncertainties in civil engineering problems such as materials, excitation, modeling, and emission for damage prediction [24]. Moreover, the approach has been utilized to address various challenges in the medical field, including predicting disease progression, identifying diagnostic biomarkers, and customizing treatments to individual patient characteristics [27]. Nowadays, digital technologies and solutions for calibration, prediction, learning, and self-optimization have been implemented in manufacturing to eliminate inefficiencies [28]. The combination of AM and ML techniques offers the ability to identify relationships in large manufacturing datasets, providing the possibility of obtaining components with improved performance [29]. [PERSON] et al. [30] investigated tensile strength optimization by adopting an ML regression algorithm. The layer thickness, printing speed, and printing temperature were the process parameters considered. The results showed that a medium printing speed, temperature, and low layer thickness improved the tensile strength. The layer height, infill percentage, printing temperature, and printing speed were used as input to train an ML model for simultaneously predicting the minimum weight, minimum printing time, and maximum tensile strength. Although no unique optimal solution exists, the Pareto front provides an appropriate combination of input parameters to obtain the best trade-off between the outputs to meet the user's requirements [31]. The same printing processes were investigated by [PERSON] et al. using an ML nonlinear regression algorithm only for tensile strength prediction. The results were able to predict the tensile strength with a percentage error of less than 2.977 [32]. Models for predicting the ultimate tensile strength were developed using an ANN. The regression curve had a correlation coefficient of 0.999782. The input combinations between the print speed, infill density, build orientation, temperature, and layer thickness were evaluated based on the Taguchi orthogonal array. Having considered for each input three control levels, 33 experimentswere performed for the training and evaluation of a neural network. The error percentage value for the neural network is 1.10. The validation parameter indicates an error of 1.57 when comparing the actual and predicted outcomes using the ML method [33]. In the majority of the current study's results, the best combination of process parameters was discovered through independent experimental trials, with the experimental outcome that produced a better solution being classified as the optimum solution [34]. However, the optimal process parameter combination may differ from the experimental combinations, and it must fall within the permitted range of process parameters [35].