Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflow

Abstract

Streamflow contemplates a fundamental criterion to evaluate the impact of human activities and climate changes on the hydrological cycle. In this study, a novel innovative deep neural network (DNN) structure by integrating a double Gated Recurrent Units (GRU) neural network model with a multiplication layer and meta-heuristic whale optimization algorithm (WOA) (i.e., hybrid 2GRU×–WOA model) is developed to improve the prediction accuracy and performance of mean monthly Chehel-Chai River’s streamflow (CCRSFm) in Iran. The Pearson’s correlation coefficient (PCC) and Cosine Amplitude Sensitivity (CAS) as feature (input) selection process determine the only precipitation (Pm) as the most effective input variable among a list of on-site potential climate time series parameters recorded in the study area. Thanks to a well-proportioned layer network structural framework in the suggested hybrid 2GRU×–WOA model, it leads to an appropriate total learnable parameter (TLP) compared to standard individual GRU and Bi-GRU as the benchmark models developed in the comparable meta-parameters. This hybrid model under the optimal meant meta-parameters tuned i.e., coupling a state activation functions (SAF) of tanh-softsign, dropout rate (P-rate) of 0.5, numbers of hidden neurons (NHN) of 70, outperforms with an R2 of 0.79, NSE of 0.76, MAE of 0.21 (m3/s), MBE of -0.11(m3/s), and RMSE of 0.36 (m3/s). Hybridizing the 2GRU× model with WOA algorithm causes to increase in the value of R2 by 6.8% and reduce in the value of RMSE by 20.4%. Comparatively, standard individual GRU and Bi-GRU models result in an R2 of 0.59 and 0.66, NSE of 0.55 and 0.6, MAE of 0.91 and 0.53 (m3/s), MBE of 0.047 and − 0.06 (m3/s), RMSE of 1.29 and 0.83 (m3/s), respectively. © The Author(s) 2025.