KAN groundwater level prediction model based on WPT secondary decomposition and CPO

To improve over-fitting of data processing, weak time series modeling, and difficult selection of hyperparameters in the Kolmogorov-Arnold network (Kan), a groundwater level prediction model based on wavelet packet transform (WPT) secondary decomposition and Chinese Pangolin optimizer (CPO) algorithm was proposed to optimize KAN hyperparameters, and WPT-CPO-Transformer, WPT-CPO-LSTM, WPT-CPO-gated circulation unit (GRU), WPT-CPO-least squares support vector machine (LSSVM), WPT-CPO-extreme gradient ascent machine (XGBoost), WPT-CPO-MLP, and WPT-KAN were constructed. These seven kinds of comparative analysis models were verified by the daily average groundwater level time series prediction examples of Xicheng, Wenlan, Lin'an, and Caoba stations in Yunnan Province. Firstly, the WPT secondary decomposition technology was used to decompose the groundwater level time series data and divide the training set and the verification set. Then, the CPO was used to optimize the hyperparameters of KAN to overcome the tedious and inefficient manual debugging and avoid local optimization. Finally, the WPT-CPO-KAN model was established by using the optimal hyperparameters to train, predict, and reconstruct the decomposed components of the groundwater level time series. The results show that: (1) compared with that of the WPT-CPO-Transformer, WPT-CPO-LSTM, WPT-CPO-GRU, WPT-CPO-XGBoost, WPT-CPO-LSSVM, WPT-CPO-MLP, and WPT-KAN models, the prediction accuracy of the WPT-CPO-KAN model is improved by 15.6%, 37.4%, 26.5%, 36.4%, 18.6%, 7.2%, and 26.7%, respectively (MAPE index), which has a smaller prediction error and better universality. (2) Under the same WPT secondary decomposition and CPO, KAN can better capture the complex nonlinear space and time dependence in groundwater level time series data and is more suitable for the distribution of groundwater level time series data. Its performance is better than that of the transformer, LSTM, GRU, XGBoost models, traditional LSSVM, and MLP network. (3) The prediction error of the WPT-CPO-KAN model increases with the increase in the prediction step. Within three days, the prediction accuracy of the WPT-CPO-KAN model is higher. (4) The reasonable selection of hyperparameters is of great significance to improve the performance of the KAN model. By using CPO to optimize KAN hyperparameters, the performance of KAN and the level of prediction automation are significantly improved. The optimization method can provide a reference for improving the performance of KAN. (5) KAN can reveal the variation characteristics of groundwater level time series data with fewer parameters, thus enhancing the interpretability of the WPT-CPO-KAN model.