## 3 Experimental Validation
### AlSi10 Mg Validation
#### 3.1.2 Levd Ml Algorithm: Validation  
In this Section, the Levd ML algorithm (Section 2.3.2) is validated on AlSi10 Mg data. Figure 9 plots the loss function with respect to the k-fold considered for the validation. Figure 8: Validation of the investigated Probability ML algorithm: (**a**) Gumbel plot for the validation dataset for k = 4; (**b**) P-P plot for k = 4 by considering the training and the validation data. Figure 9: k-fold cross-validation for the Levd ML: loss function with respect to the k-fold considered for the validation. According to Figure 9, the loss function is almost flat and below 0.2 for all the considered folds, except for fourth fold. Accordingly, the LEVD ML has averagely good predicting capabilities on validation datasets. Figure 10 shows the Gumbel plot for the validation (Figure 10a) and a training (Figure 10b) fold for k = 4, i.e., the validation fold for which the loss function reaches its maximum. In Figure 10 and in the following Figures, \(R_{exp}^{2}\) and \(R_{ML}^{2}\) refer to the coefficient of determination computed by considering the experimental fit and the ML fit, respectively. According to Figure 10a, the ML LEVD is in good agreement with the experimental LEVD and provides an acceptable prediction, even if characterized by a higher slope. The \(R_{exp}^{2}\) and \(R_{ML}^{2}\) are very close, being equal to 0.94 and 0.93, respectively, thus confirming the effectiveness of the prediction. The predictive capability of this approach can be further improved by increasing the number of datasets available for the training. The experimental and the ML LEVD for the training dataset are close and tend to overlap, providing the same \(R_{exp}^{2}\) and \(R_{ML}^{2}\) values. An interesting further validation can be carried out by verifying the capability of the ML algorithm of predicting the LEVD variation with the risk-volume, and thus of modelling size effect. This can be done by considering the dataset in [30]. Indeed, experimental tests in [30] have been carried out on specimens produced with the same process parameters, but with horizontal and vertical building orientations and with different risk volumes (200 mm\({}^{3}\) and 2300 mm\({}^{3}\)). Figure 11 shows the Gumbel plot of experimental data in [30] for defects measured on the fracture surfaces of specimens built in a horizontal (Figure 11a) and vertical direction (Figure 11b) and with a risk volume of 2300 mm\({}^{3}\). These are the validation datasets for k = 2 (Figure 11a) and k = 3 (Figure 11b), and therefore have not been considered for the training. In Figure 11, the blue line is the LEVD estimated from the experimental data, whereas the green line is the ML LEVD. According to Figure 11, the predicted LEVDs are in good agreement with the experimental data and with experimental LEVD. In Figure 11a, \(R_{exp}^{2}\) and \(R_{ML}^{2}\) are close and are equal to 0.87 and 0.80, respectively. The percent differences between the location and the scale parameters, computed as the difference between the experimental and the ML values, normalized by the experimental values, are equal to 5.1% and 7.8%, respectively. The difference tends to be larger for vertical specimens (Figure 11b), for which \(R_{exp}^{2}\), equal to 0.84, is larger than the \(R_{ML}^{2}\) value, equal to 0.44. This decrement can be explained by analyzing the percentage difference between the location and the scale parameters, equal to 19.6% and 12.8%, respectively, with the ML fit being shifted rightward with respect to the experimental curve. However, in both cases, the predicted values are close to the experimental ones and the differences are in an acceptable range. This validation confirms the capability of the LEVD ML algorithm of modelling size effect, which has a fundamental importance when  
Figure 10: Gumbel plot for k = 4; (**a**) validation dataset; (**b**) training dataset.