## 2 Materials and Methods  
The Al-4.9 Mg-0.9 Fe-0.9 Ni-0.2 Zr-0.1 Sc (wt.%) alloy was investigated. The alloy was processed in a laboratory. The 99.85% Al, 99.5% Mg, and the master alloys of Al-10% Fe, Al-10% Ni, Al-2% Sc, and Al-5% Zr were used for the alloy preparation. A Nabertherm K4/13 electric furnace (Nabertherm GmbH, Lilienthal, Germany) with air atmosphere was used for melting. The casting was processed at a temperature of 780 \(\pm\) 10 \({}^{\circ}\)C. The ingot with a size of 30 \(\times\) 120 \(\times\) 250 mm was cast using a semicontinuous method in a water-cooled system providing a casting-cooling rate of about 5 K/s. The sheet was processed using the following stages: (1) homogenization annealing at 350 \({}^{\circ}\)C for 8 h and 450 \({}^{\circ}\)C for 2 h, (2) hot rolling at a temperature of 400 \(\pm\) 10 \({}^{\circ}\)C for the reduction of 70%, and (3) cold rolling at room temperature for the reduction of 50%. The heat treatment was performed in a Nabertherm N60/85 HA furnace (Nabertherm GmbH, Lilienthal, Germany) with air-force convection.  
The microstructure was examined with scanning electron microscopy (SEM) using a Tescan-VEGA3 (Tescan Brno s.r.o., Kohoutovice, Czech Republic) equipped with an X-MAX80 (Oxford Instruments plc, Abingdon, UK) energy dispersive spectrometry (EDS) system. The samples were prepared by mechanical grinding using SiC papers and polishing in a 20% water solution of colloidal silica-based suspension. An Axiovert 200 MMAT (Carl Zeiss, Oberkochen, Germany) light microscopy (LM) with polarized light was used to analyze the grain structure. The samples were subjected to anodizing at a voltage of 20 V for 20 s in a 10% water solution of the H\({}_{3}\)BO\({}_{4}\) saturated in the HF.  
A JEOL JEM 2100 (JEOL, Japan) transmission electron microscope (TEM) was used to study the dislocation structure and fine precipitates' parameters. The operating voltage was 200 kV. The TEM samples of 3 mm in diameter were cut from a plate of 0.25 mm thickness.  
The electrochemical thinning of the samples was performed in a Struers TenuPol-5 (Struers APS, Ballerup, Denmark) at a voltage of 22 \(\pm\) 1 V using an A2 electrolyte (Struers APS, Ballerup, Denmark) at a temperature of 0 \(\pm\) 2 \({}^{\circ}\)C.  
Isothermal uniaxial tensile tests via a Walter + Bay LFM100 test machine (Walter + Bai AG, Lohningen, Switzerland) were used to characterize the investigated alloy's superplastic flow behavior. The tests were performed at a temperature of 420, 460, 500, and 540 \({}^{\circ}\)C and a strain rate range of 0.002-0.1 s\({}^{-1}\). The flow behavior data were used to construct ACE and ANN models. In the ACE model, the model parameters were correlated with strain for accurate prediction. Three layers of the backpropagation network were involved, i.e., the input layer (strain, strain rate, and temperature), the output layer (flow stress), and the hidden layer. The predictability of the constructed models is quantified by the correlation coefficient (R) (Equation (1)), the average absolute relative error (\(AARE\)) (Equation (2)), and the root mean square error (\(RMSE\)) (Equation (3)):  
\[R=\ \frac{\sum_{i=1}^{N}(E_{i}-\ \overline{E})\big{(}P_{i}-\ \overline{P})}{\sqrt{ \sum_{i=1}^{N}\big{(}E_{i}-\ \overline{E}\big{)}^{2}\sum_{i=1}^{N}\big{(}P_{i}-\ \overline{P}\big{)}^{2}}} \tag{1}\]  
\[AARE\ (\%)=\frac{1}{N}\sum_{i=1}^{N}\left|\frac{E_{i}-P_{i}}{E_{i}}\right| \tag{2}\]  
\[RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(E_{i}-P_{i})^{2}} \tag{3}\]  
where;  
* \(E_{i}\), and \(P_{i}\) are the experimental and modeled flow stress,
* \(\overline{E}\) and \(\overline{P}\) are the mean values of the experimental and modeled flow stress, and
* \(N\) is the sample size.