## 5 Results of Viscosity Estimation Using ANN Models  
The proposed ANN models were applied to the viscosity estimation of polymer solutions as shown in Table 2. The measured viscosity, viscosity estimated by the ANN model and viscosity estimated by the Carreau model using [PERSON]'s correlation [44] were compared, as shown in Figures 8-10. The viscosity estimate from the Carreau model using [PERSON]'s correlation did not match well with the measured viscosity in the case of low salinity conditions (0.1 wt % NaCl), as shown in Case #1 of FlopaamTM 3330S and FlopaamTM 3360S. The viscosity estimate from the ANN model was in good  
Figure 5: Comparison of the measured and estimated data for FlopaamTM 3330S, cp is centi-poise. (a) Training. (b) Validation. (c) Test.  
Figure 6: Comparison of the measured and estimated data for FlopaamTM 3630S. (a) Training. (b) Validation. (c) Test.  
Figure 7: Comparison of the measured and estimated data for AN-125. (a) Training. (b) Validation. (c) Test.  
agreement with the measured viscosity overall. The accuracy of the estimated viscosity was evaluated using the average absolute relative deviation (AARD), as shown in Equation (9).  
\[AARD\ (\%)=\frac{100}{n_{A}}\sum_{i=1}^{N}\left|\frac{y_{i}-x_{i}}{x_{i}}\right| \tag{9}\]  
Figure 8: Comparison between the measured and estimated viscosities of FlopaamTM 3330S. Line, viscosity estimated by the ANN model; dot, measured viscosity; dotted line, viscosity estimated by the Carreau model using [PERSON]’s correlation.  
Figure 9: Comparison between the measured and estimated viscosities of FlopaamTM 3630S. Line, viscosity estimated by the ANN model; dot, measured viscosity; dotted line, viscosity estimated by the Carreau model using [PERSON]’s correlation.  
AARD, which is also known as the maximum average error percentage, average absolute percentage error or average absolute relative error (fraction form), has been widely used for evaluating the accuracy of the results by ANN models [22; 23; 24; 25; 26; 27]. The calculated AARD is shown in Figure 11.  
Figure 10: Comparison between the measured and estimated viscosities of AN-125. Line, viscosity estimated by the ANN model; dot, measured viscosity; dotted line, viscosity estimated by the Carreau model using [PERSON]’s correlation.  
In all cases, the AARD of the viscosity estimate from the ANN model was lower than that of the Carreau model using [PERSON]'s correlation, which means that the ANN model tends to estimate the viscosity of the polymer solution more closely to the measured viscosity than does the [PERSON] correlation. If the ANN model cannot recognize the relationship between influential parameters and viscosity, it cannot estimate viscosity accurately for some conditions of polymer solutions. For high accuracy of the [PERSON] correlation, a strong linear relationship between polymer concentration and \(\ln\left(\left(\eta_{0}-\eta_{\infty}\right)/\eta_{\infty}C_{\mathrm{P}}\right)\) needs to exist. According to [PERSON] [46], this relationship in low salinity conditions is not linear, unlike that in higher salinity conditions, which is one of the possible reasons for the low accuracy of the [PERSON] correlation. Another possible reason is that the measured \(\lambda\) of FlopaamTM 3630S did not match well with the \(\lambda\) estimated by the [PERSON] correlation, unlike FlopaamTM 3330S and AN-125 [46]. In certain conditions, the relationships between the influential parameters and viscosity can change.