# Advancing Additive Manufacturing Through Machine Learning Techniques: A State-of-the-Art Review
## 3 Applications of Supervised Learning in Additive Manufacturing
### Fatigue Life Prediction
[PERSON] and colleagues presented pioneering work where they developed a physics-informed neural network (PINN) or physics-informed machine learning (PIML) framework to predict the finite fatigue life of defective materials [109]. Notably, the PINN is trained using a combination of data loss and physics loss, as illustrated in Figure 4. The dataset was provided by [PERSON] et al., who fabricated aluminum alloy samples using AM techniques like selective laser melting (SLM) [110]. These samples underwent CT scans to reconstruct the morphology and location of defects. The morphological features include the defects' volume, external surface, and the projection of the external surface onto the plane normal to the direction of the applied load. The defects' sphericity and diameter can be calculated from these features. Additionally, the distance between the defects and the free surface of the specimen can be evaluated through CT scans. Fatigue testing was conducted by applying a cyclic load of constant stress amplitudes, and the fatigue lives were measured. The samples were then investigated using fractography to detect pores, called killer defects, where fatigue cracks were triggered. In their proposed PINN framework, the neural network is enforced with phenomenological constraints from physics, specifically the linear elastic fracture mechanics (LEFM) model. In addition to the data loss from the direct prediction of the neural network, the physics loss was determined from [PERSON]'s law for stress-fatigue life diagrams. The sum of these two loss functions was employed in the backpropagation process to optimize the network weights and bias. This research highlighted that incorporating physics laws into the neural network could be highly effective for accurately predicting the finite fatigue life of materials. In another recent study, [PERSON] et al. introduced physics-guided ML frameworks aimed at enhancing fatigue life prediction in AM materials [111]. Traditionally, evaluating fatigue life, particularly fatigue crack growth life, relies on Paris' law, incorporating empirical model parameters [112]. However, this physics-based model often overlooks the influence of defect characteristics such as size and location. To address this limitation, data-driven approaches like ML prove beneficial [113]. The authors employed two ML models, SVR and ANN, with inputs comprising the range of applied stress and defect features. They devised adaptive ML models using Bayesian optimization to fine-tune model hyperparameters and k-fold cross-validation for robustness. These models were trained and assessed using three different AM materials, aluminum alloy, titanium alloy, and alloy steel, across datasets varying in size from 8 to 30 [114; 115; 115]. Their findings sugg  
Figure 4: The training process of a PINN. model for scenarios with limited data and the SVR model for relatively large datasets. They also extended this physics-guided ML framework to a probabilistic model using maximum likelihood estimation. The study demonstrated that while the physics-based Paris law ensures predicted results consistent with physical observations, data-driven approaches account for the variability in fatigue lives attributed to defect features. Ultimately, the integrated physics-guided ML model maintained high prediction accuracy while mitigating overfitting issues associated with limited fatigue data. [PERSON] et al. explored the predictability of various ML models in forecasting the fatigue lives of titanium structures produced via AM methods, such as electron beam melting (EBM) [116]. The authors utilized experimental data [117]. The ML regression models examined in this study comprised multiple linear regression (MLR), ANNs, SVR, and random forests (RF). Initially, the study assessed the influence of density, porosity, yield stress, and fatigue stress on the predicted fatigue lives of samples. The resulting correlation matrices and heatmaps emphasized the significant impacts of yield stress and fatigue stress on the target prediction.