Metaheuristic-enhanced deep learning for monthly pan evaporation prediction under limited climatic data

Abstract This study introduces two recently developed bio-inspired metaheuristic algorithms, Artificial Protozoa Optimizer (APO, 2024) and Dung Beetle Optimizer (DBO, 2023), into long short-term memory (LSTM) networks for monthly pan evaporation prediction under limited climatic data. Representing the first application of these algorithms to hydrological modeling, these models integrate APO and DBO into the LSTM framework to optimize hyperparameters and enhance accuracy and generalization. Their performance is benchmarked against the standard LSTM and two established hybrids, LSTM-GWO and LSTM-HHO. A case study in southeast China using 40 years of data from two stations shows that both LSTM-APO and LSTM-DBO consistently outperform the alternatives across three data-splitting scenarios (M1, M2, M3). For the best test case (M3, Station 1), LSTM-APO reduced RMSE and MAE by 46.5% and 47.2%, respectively, compared to the best LSTM, while in Station 2 (M2) it achieved reductions of 43.9% and 40.7%, with gains of about 9% in R² and NSE. LSTM-DBO also yielded notable improvements, reducing errors by 20–30% and demonstrating robust predictive stability. Visual analyses confirm that LSTM-APO provides predictions closely aligned with observations, with LSTM-DBO performing comparably well. These findings highlight the role of metaheuristic optimization in boosting LSTM performance for nonlinear evaporation processes with sparse inputs. Overall, APO- and DBO-based hybrids show strong promise for reliable pan evaporation forecasting. Future research should assess their real-time applicability and transferability across diverse climates.