Hybrid GWO–GA optimized LSTM–MLP framework for highly accurate palmer drought severity index prediction

Accurate prediction of the Palmer Drought Severity Index (PDSI) is essential for drought monitoring, climate-risk assessment, and the effective management of water resources. This study proposes a hybrid Long Short-Term Memory–Multilayer Perceptron (LSTM–MLP) model for PDSI prediction, integrated with a Grey Wolf Optimizer–Genetic Algorithm (GWO–GA) optimization framework. The model is evaluated using a climate dataset comprising 864 observations characterized by scenario information and multiple climatic variables, including pr, tas, tasmin, tasmax, and srad. The predictive performance of the proposed approach is assessed using the mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), median absolute error (MedAE), mean absolute percentage error (MAPE), and coefficient of determination ( $$R^2$$ ). Furthermore, its performance is compared with several deep-learning architectures, including convolutional neural network (CNN), LSTM, gated recurrent unit (GRU), bidirectional LSTM (BiLSTM), and bidirectional GRU (BiGRU) models. The proposed LSTM–MLP model achieved an MSE of 0.0004, RMSE of 0.0201, MAE of 0.0169, MedAE of 0.0160, MAPE of 0.0018, and an $$R^2$$ of 99.97%. In comparison, the CNN, LSTM, GRU, BiLSTM, and BiGRU models achieved $$R^2$$ values of 94.58%, 90.84%, 88.70%, 87.39%, and 86.48%, respectively. These results demonstrate that the proposed LSTM–MLP framework provides highly accurate PDSI predictions and consistently improves predictive performance relative to the investigated benchmark deep-learning models. The findings give a focus to the potential of the proposed hybrid modeling framework as an effective data-driven approach for PDSI prediction and drought-related climate analysis.