Multi-Objective Hyperparameter Optimization Improves the Interpretability of LSTM Rainfall–Runoff Models

Rainfall–runoff modeling is a key challenge in hydrological research. Despite the extensive application of long short-term memory (LSTM) networks in rainfall–runoff modeling, our understanding of the influence of different hyperparameter configurations on various hydrograph components, as well as the linkages between hydrological concepts and LSTM architectures, remains elusive. Here, we integrated Multi-Objective Particle Swarm Optimization (MOPSO) with LSTM hyperparameter optimization by targeting the root mean square error of the overall hydrograph (RMSEall), high-flow (RMSEhigh) and low-flow (RMSElow) dynamics, and water volume deviation (Dv). The MOPSO-LSTM framework was applied to the upstream catchments of the Miyun Reservoir in Beijing, China. At a lead time of 1d, the optimal solution achieved an NSE of 0.920 in the Chaohe River Basin, with a minimum RMSEall of 0.848 m3/s, RMSEhigh of 2.081 m3/s, RMSElow of 0.382 m3/s, and Dv of 0.002%. However, as the lead time increased to 3 and 7 days, the maximum NSE declined to 0.747 and 0.560, respectively, with process-related metrics deteriorating more substantially than water balance-related metrics. The Baihe River Basin performed better, with maximum NSE and KGE values of 0.949 and 0.970 at a lead time of 1d. Clear trade-offs among different evaluation objectives were further identified, particularly the competitive relationship between RMSEhigh and RMSElow, as well as the coupling between RMSElow and Dv. SHAP (Shapley additive explanation) and partial dependence plots (PDPs) were used to quantify and interpret the effects of hyperparameters on model performance, and the results showed that learning rate, number of units, and lookback window served as the most influential hyperparameters. Moreover, optimization preferences resulted in distinct hyperparameter configurations, where Dv-oriented solutions favored smaller learning rates, longer lookback windows, and larger batch sizes than RMSE-oriented solutions. Compared with the Chaohe River Basin, the larger Baihe River Basin favored LSTM configurations with longer lookback windows, more hidden units, higher learning rates, and lower dropout rates, which was associated with the hydrological memory of the catchment. Overall, this study provides a novel multi-objective LSTM optimization framework, improving the understanding of LSTM hyperparameters and offering practical guidance for hydrological prediction and water resource management.