## 1 Introduction
[9] found that lead red pigments that were not mixed with organic binder faded more readily under UV fluorescence irradiation at 90% humidity than lead red pigments that were mixed with organic binder. The protective and inhibitory effects of organic binder on pigment  
Figure 1: Comparison of the copy restoration of Cave 249 (Western Wei dynasty) of the Mogao Caves (yellow box “a” is fading color; red box “b” is peeling skin; blue box “c” is de-powdering). discoloration were discussed. [PERSON] et al. (2019) investigated the effect of humidity and organic binders on the fading of lead red pigments. They observed that the fading rate of binder-free lead red was faster than that of lead red pigments mixed with binders when the time of exposure to UV was extended. Furthermore, a higher humidity level resulted in faster initial fading rates, but fading in the later stages was not noticeable. [PERSON] et al. (2019) simulated the irradiation of painted cultural relics by ten narrow-band spectra. The adverse impact data of different spectra on color for various types of pigments were collected, analyzed, and fitted to develop damage functions. These damage functions could serve as a basis for light source selection and access standard determination in the lighting of painted relics. The research mentioned above has achieved some results on the virtual restoration of painted relics and the determination of fading factors of pigments. However, there is a gap in the research of the chronological fading mechanism. Investigating the chronological mechanisms of pigment fading can provide valuable insights for the restoration of painted cultural artifacts. In the field of artificial intelligence, the long short-term memory (LSTM) network architecture was proposed by [PERSON] and [PERSON] (2012) in 1997. This architecture effectively addressed issues such as exploding gradients and vanishing gradients, which were commonly encountered in recurrent neural networks. Superior performance in short-term prediction tasks was demonstrated by the LSTM model compared to conventional prediction models. However, the LSTM model involved intricate hyperparameters that were not explicitly defined. Hyperparameters are predetermined values that are set before the start of machine learning. Different choices of hyperparameters result in different expected outcomes. Therefore, the rational selection of hyperparameters became a vital and challenging aspect of simulating time series prediction in machine learning. To tackle the aforementioned challenges, [PERSON] (2013) proposed the gray wolf optimizer (GWO) in 2014, an optimization algorithm inspired by the social behavior of gray wolves. Rapid convergence and global search optimization were demonstrated by this algorithm. The hyperparameter selection problem was effectively addressed by iteratively optimizing the hyperparameter values. Furthermore, [PERSON] et al. (2014) introduced the GWO-LSTM composite model, which outperformed the standalone LSTM model in terms of chronological regression, prediction accuracy, and generalization capability. In recent years, scholars have made further advancements to enhance the model's performance. For example, [PERSON] et al. (2015) proposed an enhanced GWO algorithm based on complex-valued encoding, representing the genes of gray wolves as diploids, significantly expanding the information content of individual genes. The exploration and exploitation abilities of the GWO were balanced by [PERSON] et al. (2016) through the adjustment of parameter \"a\" to prevent the model from becoming trapped in local optima. Improved algorithms, such as those mentioned above, followed the \"No Free Lunch Theorems for Optimization\", where any enhanced performance over one class of problems was offset by the performance over another class of problems (2017). Thus, these algorithms are not ideal for application in the fading of painted pigments of cultural relics.