###### Abstract  
This study exhibits the possibility of using an artificial neural network (ANN) to model the mechanical behavior of wire arc additive manufacturing (WAAM) for Inconel 625. For this reason, tensile tests of Inconel 625 superalloy as-built (AB) samples and samples after heat treatment at 1200 \({}^{\circ}\)C (HT-1200) by WAAM were performed. For the HT-1200 samples, the yield stress decreased, and the elongation increased significantly due to grain refinement and the formation of annealed twins. A new hybrid model combining a swarm intelligence optimization algorithm with a back propagation neural network (BPNN) was developed to simulate the flow behavior of the superalloy. Compared with other hybrid BPNN models that have been reported, the proposed BPNN model is in better agreement with the experimental data and provides a better description of the flow stress of the Inconel 625 superalloy. The excellent predictive ability of the model may be attributed to the optimization of the weights and thresholds of the BPNN, which obtains the optimal global solution in the search space more efficiently. additive manufacturing; Inconel 625 superalloy; artificial neural network; optimization algorithm; mechanical properties +
Footnote †: journal: Applied Sciences  
Footnote †  
basis of metal forming problems, but also the key factor for numerical analysis. In the past, for the mechanical problems of engineering structures, traditional theoretical research methods were usually used. For example, [PERSON] et al. [12] employed the strain energy density (SED) approach to predict the tensile strength of polyetheretherketone in corrosive environments. Subsequently, they studied the fracture of notched Ti-6 Al-4V via the SED approach and the theory of critical distance (TCD) method [13]. Other similar studies can be found in the literature [14; 15; 16; 17; 18]. In particular, the empirical constitutive relationship has been considered an effective method for predicting plastic deformation in metals [19; 20], but the high complexity of mathematical modeling has limited its wide application. With the application of artificial intelligence in the field of materials, machine learning has been utilized to construct constitutive models and has gained wide application in recent years [21; 22]. For example, artificial neural networks (ANNs) have been widely used to accurately predict the hot deformation behaviors of nickel-based superalloys [23; 24; 25; 26; 27; 28; 29]. A BPNN is a kind of artificial neural network which uses a backpropagation algorithm to automatically update internal random parameters in the process of training and can realize the random nonlinear mapping of input and output, which has great advantages in solving nonlinear problems. At present, this method has been applied to the fields of material performance prediction, complex structural performance prediction, and structural optimization. However, the initial weights and thresholds of the original BPNN model are randomly set, which makes it easy to obtain local optimal solutions, leading to the problem of slow convergence speed. More importantly, when the amount of data is large and the training time is long, the training mode of the BPNN may have a problem overfitting. Therefore, it is of great significance to use optimization algorithms to optimize the initial parameters of the BPNN to avoid getting local optimal solutions. For example, [PERSON] et al. [30] proposed a hybrid algorithm combining a BPNN and simulated annealing. The experimental results showed that the proposed mixed model had good prediction accuracy in predicting the mechanical properties of rocks. [PERSON] et al. [31] constructed a hybrid model combining an adaptive evolutionary artificial bee colony algorithm and a BPNN. The experimental results showed that under the guidance of historical error data, the prediction accuracy of the proposed hybrid model was still better than other algorithms. [PERSON] et al.