## 4 Results and Discussion
### Comparative Analysis of Color Prediction Based on the GWOAD-LSTM Model
In summary, our proposed GWOAD-LSTM model showed greater advantages in the training and prediction of two pigments, rouge (L) and azurite (L). Overall, in terms of the training and prediction accuracy for the lightness (L) of all six pigments, our GWOAD-LSTM model outperformed the BPNN, LSTM, and GWO-LSTM models. Table 5 shows the RMSE, MAE, and MAPE results of the six pigments for predicting chroma C. Figure 12 shows the comparison results of the six pigments for predicting C. As a result, the average RMSE of our proposed GWOAD-LSTM model was 52.34%, 40.22%, and 8.80% lower in the training set compared with those from the BPNN, LSTM, and GWO-LSTM models, respectively; the average MAE was 52.75%, 39.17%, and 9.28% lower, respectively; and the average MAPE was 46.45%, 34.99%, and 8.82% lower, respectively. In summary, the GWOAD-LSTM model had higher accuracy in training data capture. Figure 12: Comparison of the six pigments predicted chroma (C). Lead red (**a**), lighargite (**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). Furthermore, in terms of data prediction, as a result, the GWOAD-LSTM model reduced the average RMSE by 69.96%, 39.02%, and 28.23%; the average MAE by 76.49%, 48.55%, and 28.23%; and the average MAPE by 68.84%, 47.60%, and 28.23% compared with those from the BPNN, LSTM, and GWO-LSTM models, respectively. Thus, the GWOAD-LSTM model was closer to the original data in terms of time series prediction. Overall, when predicting the time series variation in chroma (C), our GWOAD-LSTM model outperformed the three previous models in terms of both training and prediction accuracy in the time series. This was particularly evident in accurately capturing data trends for the lead red, lithargite, and rouge pigments. In summary, as shown in Figures 13 and 14, taking lead red as an example, the results predicted by the BPNN model and LSTM model for the six pigments' hLC optical change deviated from the actual results, and the prediction effect was gradually worsened as the time series increased; the GWO-LSTM model was slightly worse in the prediction accuracy and had the above phenomenon of gradually increasing prediction error; however, our proposed GWOAD-LSTM model had a larger overlap with the actual values in both training data and prediction data, the prediction effect was more ideal, and no phenomenon of the prediction effect becoming worse as the time series increased was observed. These were apparent advantages. Figure 14: Comparison of color difference of the lead red test set. Figure 13: Scatter plot of prediction errors for the four models in predicting lead red. (Scatterplot of prediction error for lead red hue (**a**), lead red lightness (**b**), lead red chroma (**c**)). According to the color blocks in Table 6, routee had the largest variation. The different models had deviations in predicting the color of the color blocks. The predicted color of the BPNN model and the LSTM model had larger differences from the actual color. The GWO-LSTM model performed slightly better in prediction, but noticeable color differences were observed. In contrast, our proposed GWOAD-LSTM model demonstrated less color difference and better color reconstruction accuracy for routee. Table 7 shows the average prediction results of the color gamut data for the six pigment test sets. The BPNN model and the LSTM model had lower color prediction accuracy, especially in the rouge color reconstruction with higher color differences. The GWO-LSTM model and GWOAD-LSTM model had good prediction results, among which our proposed GWOAD-LSTM model performed better in terms of color difference and has higher color reconstruction accuracy. From the scatter plot analysis, the BPNN model had poor data capturing accuracy, the LSTM model exhibited weak data fitting amplitude, and the GWO-LSTM model showed low prediction accuracy in the peak.