## 4 Results and Discussion
### Comparative Analysis of Color Prediction Based on the GWOAD-LSTM Model
Based on the above, the GWOAD-LSTM model outperformed the BPNN, LSTM, and GWO-LSTM models in terms of data capture and prediction accuracy for the hue (h) prediction of the six pigments. This superiority was particularly evident in the prediction for the rouge and cinnabar pigments. Table 4 shows the RMSE, MAE, and MAPE errors for the prediction of lightness (L) for the six pigments using the BPNN, LSTM, GWO-LSTM, and GWO-LSTM models; Figure 11 shows the comparison of the predicted lightness (L) for the six pigments. From the graphs, the GWOAD-LSTM model decreased the mean values of RMSE by 69.15%, 58.89%, and 18.78%; MAE by 64.09%, 58.38%, and 19.66%; and MAPE by 69.97%, 59.37%, and 21.01%, respectively, compared with those from the BPNN, LSTM, and GWO-LSTM models. The time series training accuracy of our proposed GWOAD-LSTM model was higher than those of the BPNN, LSTM, and GWO-LSTM models in terms of brightness L. \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{4}{*}{Lead Red (L)} & BPNN & 0.1787 & 0.1521 & 0.2513 & 0.3665 & 0.3473 & 0.5973 \\  & LSTM & 0.1897 & 0.1363 & 0.2247 & 0.7588 & 0.6653 & 1.1468 \\  & GWO-LSTM & 0.1479 & 0.1080 & 0.1791 & 0.1274 & 0.1084 & 0.1869 \\  & Proposed & 0.0797 & 0.0665 & 0.1099 & 0.0644 & 0.0546 & 0.0941 \\ \hline \multirow{4}{*}{Lithargite (L)} & BPNN & 0.5946 & 0.4281 & 0.6877 & 1.0103 & 0.9705 & 1.6723 \\  & LSTM & 0.2875 & 0.2230 & 0.3645 & 0.2567 & 0.2090 & 0.3597 \\  & GWO-LSTM & 0.1904 & 0.1546 & 0.2537 & 0.1403 & 0.1219 & 0.2111 \\  & Proposed & 0.1763 & 0.1467 & 0.2424 & 0.1292 & 0.1037 & 0.1796 \\ \hline \multirow{4}{*}{Rouge (L)} & BPNN & 1.2063 & 0.9603 & 1.5853 & 0.7502 & 0.5885 & 0.8440 \\  & LSTM & 1.1094 & 0.9044 & 1.5318 & 1.6937 & 1.4032 & 2.0342 \\  & GWO-LSTM & 0.4153 & 0.3547 & 0.5917 & 0.5738 & 0.4832 & 0.6936 \\  & Proposed & 0.4211 & 0.3299 & 0.5453 & 0.5305 & 0.4383 & 0.6195 \\ \hline \multirow{4}{*}{Cinnabar (L)} & BPNN & 0.1837 & 0.1577 & 0.3263 & 0.3330 & 0.3084 & 0.6324 \\  & LSTM & 0.2394 & 0.1766 & 0.3642 & 0.3828 & 0.3033 & 0.6190 \\  & GWO-LSTM & 0.0876 & 0.0667 & 0.1378 & 0.1716 & 0.1319 & 0.2691 \\  & Proposed & 0.0676 & 0.0550 & 0.1132 & 0.1631 & 0.1135 & 0.2302 \\ \hline \multirow{4}{*}{Azurite (L)} & BPNN & 0.2534 & 0.2032 & 0.5225 & 0.6198 & 0.5192 & 1.3131 \\  & LSTM & 0.1942 & 0.1521 & 0.3915 & 0.6516 & 0.5347 & 1.3677 \\ \cline{1-1}  & GWO-LSTM & 0.0976 & 0.0721 & 0.1870 & 0.2516 & 0.1973 & 0.5079 \\ \cline{1-1}  & Proposed & 0.0621 & 0.0491 & 0.1264 & 0.1244 & 0.1021 & 0.2549 \\ \hline \multirow{4}{*}{Malachite (L)} & BPNN & 0.5108 & 0.4555 & 0.8558 & 0.7436 & 0.7080 & 1.3025 \\ \cline{1-1}  & LSTM & 0.1763 & 0.1332 & 0.2499 & 0.2660 & 0.2160 & 0.3980 \\ \cline{1-1}  & GWO-LSTM & 0.1731 & 0.1380 & 0.2586 & 0.2175 & 0.1605 & 0.2968 \\ \cline{1-1}  & Proposed & 0.0960 & 0.0708 & 0.1329 & 0.1524 & 0.1222 & 0.2252 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: RMSE, MAE, and MAPE errors for the prediction of lightness (L) in six pigments. Figure 11: Comparison of the six pigments predicted lightness (L). Lead red (**a**), lightargite (**b**), rouge (**c**), cinnabar (**d**), azurite (**e**), and malalchite (**f**), respectively. (The subfigure shows the prediction results for the test set from 750 h to 1020 h). In terms of the prediction accuracy of L, from the test set in the table, it can be seen that our proposed optimized GWOAD-LSTM model had a higher prediction accuracy than the other models. The values decreased by 67.84%, 69.34%, and 17.04% on average for RMSE; by 72.86%, 71.96%, and 15.70% on average for MAE; and by 74.79%, 72.93%, and 29.25% on average for MAPE, when compared with those from the BPNN, LSTM, and GWO-LSTM models, respectively. As a result, the prediction accuracy in the lightness L was closer to the true value than the former three models.