###### Abstract  
The application of superplastic forming for complex components manufacturing is attractive for automotive and aircraft industries and has been of great interest in recent years. The current analytical modeling theories are far from perfect in this area, and the results deduced from it characterize the forming conditions insufficiently well; therefore, successful numerical modeling is essential. In this study, the superplastic behavior of the novel Al-Mg-Fe-Ni-Zr-Sc alloy with high-strain-rate superplasticity was modeled. An Arrhenius-type constitutive hyperbolic-sine equation model (ACE) and an artificial neural network (ANN) were developed. A comparative study between the constructed models was performed based on statistical errors. A cross validation approach was utilized to evaluate the predictability of the developed models. The results revealed that the ACE and ANN models demonstrated strong workability in predicting the investigated alloy's flow stress, whereas the ACE approach exhibited better predictability than the ANN.  
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resistance of L1\({}_{2}\) precipitates, partial replacement of Sc by Zr is an effective way to provide a fine-grained structure at elevated temperatures [35; 36; 37; 38; 39; 40; 41]. As a result, bimodal particle-size distribution with coarse and fine particles helps to provide a fine-grained structure with a limited effect of the dynamic grain growth, leading to excellent superplasticity at the strain rates up to 1 \(\times\) 10\({}^{-1}\) s\({}^{-1}\)[16; 42; 43]. It should be noted that a high-strain-rate superplasticity is provided by a simple thermomechanical treatment including homogenization annealing, hot and cold rolling with low reduction.  
The material's deformation behavior has a significant effect on the quality of hot-worked products [44; 45]. In general, the superplastic flow stress depends on the temperature, strain rate, and strain. Depending on the alloy structure, strain hardening or strain softening accompanied the deformation. Thus, an appropriate constitutive model, which correlates with these factors, is required to designate the SPF parameters and predict the flow stress. Superplastic deformation modeling has been of great interest over the years, and many computational algorithms have been proposed for aluminum alloys [46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56]. Among these computational algorithms, constitutive equations and artificial neural networks (ANN) are widely used to model the superplastic flow behavior. [PERSON] et al. [56] examined the deformation behavior of the AA7050 Al-Zn-Mg-based alloy, which demonstrated strain hardening and developed a constitutive equation considering the strain compensation. The accuracy of the developed model for the AA7050 alloy was verified by comparing the experimental and predicted findings. [PERSON] et al. [44] modeled the hot deformation behavior of the AA7005 alloy. The comparisons between the experimental and the predicted data prove the quality of the constructed Arrhenius-type model. [PERSON] et al. [55] developed an artificial neural network (ANN) and Arrhenius-type constitutive models (ACE) to predict the flow behavior accompanied with strain softening for the Al-Zn-Mg-based alloy. The cross-validation technique demonstrated a good precision for both constructed models [55]. This study aims to develop a mathematical model for predicting the superplastic flow behavior of the novel Al-Mg-Fe-Ni-based alloy, demonstrating high-strain-rate superplasticity and strain softening during the deformation. For this purpose, the ACE and ANN approaches were involved, and their accuracies were compared.