## 4 Results and Discussion
### Comparative Analysis of Color Prediction Based on the GWOAD-LSTM Model
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Pigment** & **Evaluation** & \multicolumn{3}{c}{**Train Set**} & \multicolumn{3}{c}{**Test Set**} \\ \cline{3-8}
**Type** & **Standards** & **RMSE** & **MAE** & **MAPE (\%)** & **RMSE** & **MAE** & **MAPE (\%)** \\ \hline \multirow{3}{*}{Lead Red (h)} & BPNN & 0.1991 & 0.1193 & 0.2472 & 0.7156 & 0.6872 & 1.4880 \\  & LSTM & 0.2000 & 0.1616 & 0.3395 & 0.2680 & 0.2189 & 0.4761 \\  & GWO-LSTM & 0.2040 & 0.1643 & 0.3453 & 0.4119 & 0.3216 & 0.6988 \\  & Proposed & 0.1509 & 0.1207 & 0.2539 & 0.1841 & 0.1490 & 0.3228 \\ \hline \multirow{3}{*}{Lithargite (h)} & BPNN & 0.3095 & 0.2258 & 0.3115 & 0.4443 & 0.3908 & 0.5401 \\  & LSTM & 0.2613 & 0.2025 & 0.2789 & 0.5261 & 0.4543 & 0.6282 \\  & GWO-LSTM & 0.2437 & 0.1881 & 0.2593 & 0.4134 & 0.3412 & 0.4733 \\  & Proposed & 0.2114 & 0.1606 & 0.2214 & 0.4073 & 0.3381 & 0.4688 \\ \hline \multirow{3}{*}{Rouge (h)} & BPNN & 4.2246 & 1.8991 & 26.3730 & 5.8673 & 4.9861 & 38.7220 \\  & LSTM & 4.0463 & 1.8421 & 21.8229 & 3.7508 & 2.5750 & 20.9684 \\  & GWO-LSTM & 2.3363 & 0.9389 & 12.0732 & 2.0961 & 1.5238 & 11.2220 \\  & Proposed & 1.6224 & 0.6875 & 8.4318 & 1.6826 & 1.2668 & 9.0555 \\ \hline \multirow{3}{*}{Cinnabar (h)} & BPNN & 0.4821 & 0.3703 & 1.1389 & 1.0630 & 0.7566 & 2.2167 \\  & LSTM & 0.1968 & 0.1519 & 0.4708 & 0.6109 & 0.4746 & 1.3998 \\  & GWO-LSTM & 0.1941 & 0.1552 & 0.4798 & 0.3749 & 0.3041 & 0.8908 \\  & Proposed & 0.1921 & 0.1484 & 0.4568 & 0.3428 & 0.2691 & 0.7929 \\ \hline \multirow{3}{*}{Azurite (h)} & BPNN & 0.1836 & 0.1472 & 0.0519 & 0.2758 & 0.2180 & 0.0768 \\  & LSTM & 0.1764 & 0.1462 & 0.0515 & 0.4151 & 0.3690 & 0.1300 \\  & GWO-LSTM & 0.1617 & 0.1338 & 0.0471 & 0.3462 & 0.3082 & 0.1086 \\  & Proposed & 0.1083 & 0.0881 & 0.0310 & 0.1702 & 0.1363 & 0.0481 \\ \hline \multirow{3}{*}{Malachite (h)} & BPNN & 0.8806 & 0.5897 & 0.3506 & 0.9628 & 0.9229 & 0.5360 \\  & LSTM & 0.3097 & 0.2534 & 0.1537 & 0.5835 & 0.5011 & 0.2911 \\ \cline{1-1}  & GWO-LSTM & 0.3169 & 0.2601 & 0.1574 & 0.8252 & 0.7427 & 0.4317 \\ \cline{1-1}  & Proposed & 0.2287 & 0.1893 & 0.1146 & 0.2022 & 0.1660 & 0.0963 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMSE, MAE, and MAPE errors for the prediction of hue (h) in six pigments. Figure 10: _Cont._From the graphs, for the hue (h) of six pigments, the BPNN model achieved an average RMSE of 1.0466, MAE of 0.5586, and MAPE of 4.7455%. The LSTM model achieved an average RMSE of 0.8651, MAE of 0.4596, and MAPE of 3.8529%. The GWO-LSTM model achieved an average RMSE of 0.5761, MAE of 0.3067, and MAPE of 2.2265%. The GWOAD-LSTM model demonstrated the best performance, with an average RMSE of 0.4190, MAE of 0.2324, and MAPE of 1.5849%. Our proposed optimized GWOAD-LSTM model had a higher accuracy of the training set than the other models. The RMSE decreased by 59.97%, 51.57%, and 27.27% on average; the MAE decreased by 58.40%, 49.43%, and 20.25% on average; and the MAPE decreased by 66.60%, 58.86%, and 28.82% on average compared with those from the BPNN, LSTM, and GWO-LSTM models, respectively. Thus, the GWOAD-LSTM model was better than the BPNN, LSTM, and GWO-LSTM models in terms of the accuracy for capturing the training samples with respect to the hue (h) when multiple data were processed. Based on the test set in the prediction of hue (h), the BPNN model achieved an average RMSE of 1.5548, MAE of 1.3269, and MAPE of 7.2633%. The LSTM model achieved an average RMSE of 0.9749, MAE of 0.7655,  
2.3042%. Our proposed optimized GWO-LSTM model achieved an average RMSE of 0.4982, MAE of 0.3876, and MAPE of 1.7974%. Our proposed optimized GWOAD-LSTM model had a higher prediction accuracy than the other models. The values decreased by 67.96%, 48.90%, and 33.09% on average for RMSE; by 70.79% 49.37%, and 34.34% on average for MAE; and by 75.25%, 54.87%, and 21.99% on average for MAPE compared with those from the BPNN, LSTM, and GWO-LSTM models, respectively. As a result, GWOAD-LSTM's prediction accuracy of the hue h was closer to the real value than the BPNN model, LSTM model, and GWO-LSTM model.