## 4 Conclusions  
The microstructure and mechanical properties of the Inconel 625 superalloy AB samples and HT-1200 samples fabricated by WAAM were studied experimentally. To predict the mechanical behavior of Inconel 625, a new hybrid model combining a swarm intelligence optimization algorithm with a BPNN, named EDBO-BPNN, was proposed. On the basis of experiment data, the constitutive equation of the Inconel 625 superalloy was established using the proposed EDBO-BPNN model in this paper. The prediction results of the EDBO-BPNN are compared with the experimental results and some existing BPNN models in the literature. The main conclusions are drawn below. The microstructure of the AB sample was dominated by columnar grains, and the grains grew epitaxially along the direction of heat flow, while the microstructure of the HT-1200 sample was completely recrystallized. For the HT-1200 sample, the grains were refined, annealing twins were formed, and the texture was weakened. Compared with the AB sample, the yield strength of the HT-1200 sample is reduced, but the elongation is significantly improved. Compared with other hybrid BPNN models, the proposed EDBO-BPNN model agrees best with the experimental results and can well describe the flow stress of the Inconel 625 superalloy. The excellent predictive ability of the model may be attributed to the optimization to the weights and thresholds of the BPNN, which obtains the optimal global solution in the search space more efficiently. The EDBO-BPNN was used to simulate the tensile stress of  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & **MAPE** \\ \hline EDBO & 0.999964 & 1.118069 & 0.553425 & 0.001502 \\ DBO & 0.993321 & 15.26984 & 8.354193 & 0.018004 \\ JAYA & 0.991808 & 18.7458 & 9.563578 & 0.01978 \\ PSO & 0.989801 & 21.12981 & 11.90643 & 0.025724 \\ GWO & 0.985915 & 25.02655 & 15.33277 & 0.029815 \\ WOA & 0.990747 & 20.11049 & 12.08489 & 0.024129 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Means of evaluation metrics for the results of training data and testing data.  
Figure 7: Evaluation index comparison between experimental values and predicted values of HT-1200: (a) \(\mathrm{R^{2}}\); (b) RMSE; (c) MAE; (d) MAPE.  
the Inconel 625 superalloy under static load at room temperature. The establishment of a material constitutive model based on an EDBO-BPNN at high temperature and different strain rates and the verification of its predictive ability still need further study.  
Methodology, visualization, investigation, writing--original draft, data curation, formal analysis, D.X.; visualization, Z.L.; supervision, project administration, conceptualization, methodology, visualization, writing--review and editing, L.C.; supervision, conceptualization, methodology, writing--review and editing, funding acquisition, J.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant No. 11872190).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.