###### Abstract
Moreover, prediction bands in place of deterministic predictions are effectively considered to account for all the source uncertainty typical of the AM fatigue response. In [17], a reinforcement ML algorithm is developed to assess the posterior distribution of the fatigue strength of an AM AlSi12 alloy. The Bayesian inferential statistics and the Metropolis Monte Carlo algorithms are used. The model has been validated on AlSi12 alloy results obtained through tests up to the Very High Cycle Fatigue (VHCF) life region. In [18], the fatigue life of AM AlSi10 Mg specimens is predicted by using Continuous-Damage-Mechanics (CDM)-informed ML algorithms. In [19], the fatigue life of AM components is predicted starting from the process parameters with an NN algorithm and a Physics-Informed NN algorithm based on the Murakami theory [4], to model the influence of defect size and microstructure. The developed ML algorithms have been validated on AlSi10 Mg literature experimental datasets. In [20], Artificial Neural Network (ANN), Support Vector Machine (SVR) and Random Forest (RF) models are employed to investigate the influence of defects on the High Cycle Fatigue (HCF)-VHCF response of AM AlSi10 Mg specimens. Moreover, these algorithms have been used to predict the VHCF life from the layer thickness process parameter, the stress ratio and the defect properties. In [21], the fatigue life of an industrial AM Ti6 Al4V demonstrator is predicted with a simulation-based approach and by employing a supervised Machine Learning algorithm. According to this literature review, ML algorithms can be reliably employed for the assessment of the fatigue response of AM components, with promising results. Approaches based on ML algorithms allow for simplifying the design against fatigue failures of AM components by exploiting already-available literature data and by embedding physical and phenomenological models, if the data for the training process are limited. In this paper, ML algorithms are employed to estimate the most critical defect in a part to be produced by SLM. The process parameters and the component volume are considered as the input of the developed Neural Network (NN) architecture. By also considering the component volume as an NN input, the dependence between the defect size and the part volume is also accounted for, i.e., the size effect is reliably modelled. The influence of surface roughness has not been accounted for, even if it is widely known that it significantly affects the fatigue response of AM parts and is among the most detrimental factors [5]. However, the surface roughness can be controlled through appropriate surface treatments. On the other hand, the focus of the present work is to estimate rare and large defects that randomly form in parts produced with optimized process parameters and contribute to lower the fatigue response of AM parts even if characterized by the same roughness of traditionally built parts. Two approaches are followed for designing the NN architectures: the first one provides the probability of a defect with a specific size for a set of process parameters and the part volume. The second one provides the location and the scale parameters of the statistical distribution of the defect size, assumed to follow a Largest Extreme Value Distribution (LEVD) for a set of process parameters and the part volume. Both approaches have been validated on literature data obtained by testing the AlSi10 Mg and the Ti6 Al4V alloy. It must be noted that several works proposing ML algorithms for the structural integrity of components have been proposed in the last years, but those focusing on the fatigue response of AM components are the ones previously analyzed, to the authors' best knowledge. However, none of these models aims at predicting the defect size starting from the process parameters. Indeed, the defect population is strongly dependent on the process parameters and the most effective damage-tolerant fatigue design should start from the process parameters.